JEFFERSON MATH PROJECT REGENTS AT RANDOM€¦ · JEFFERSON MATH PROJECT REGENTS AT RANDOM All 884...

JEFFERSON MATH PROJECTREGENTS AT RANDOM

All 884 NY Math A Regents Exam Questionsfrom June 1999 to June 2007 at Random

(Answer Key)

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Dear Sir

I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished the6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a furtherpursuit of that branch of science would be useful to you. there are some propositions in the latter books ofEuclid, & some of Archimedes, which are useful, & I have no doubt you have been made acquainted withthem. trigonometry, so far as this, is most valuable to every man, there is scarcely a day in which he will notresort to it for some of the purposes of common life. the science of calculation also is indispensible as far asthe extraction of the square & cube roots; Algebra as far as the quadratic equation & the use of logarithmsare often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; butnot to be indulged in by one who is to have a profession to follow for his subsistence. in this light I view theconic sections, curves of the higher orders, perhaps even spherical trigonometry, Algebraical operationsbeyond the 2d dimension, and fluxions. Letter from Thomas Jefferson to William G. Munford, Monticello, June 18, 1799.

Math A Regents Exam Questions at Random Page 1www.jmap.org

[1]

a [2] 3072

or an equivalent value is found and

an appropriate explanation is given.[1] An acceptable method is used correctly,such as a tree diagram, sample space, orcombinations, but the correct answer is notgiven.or [1] Replacement is used, and an answer of3681

or an equivalent is found.

or [1] 3072

and no work is shown.

b [2] 3672

or an equivalent value is found and

an appropriate explanation is given.or [2] An appropriate probability for anincorrect denominator for part a is found.[1] An appropriate method is shown, but onecomputational mistake is made.or [1] Replacement is shown, and the answer3681

or an equivalent is found.

or [1] The student does not take into account

both orders and answers 1872

or an equivalent.

or [1] 3672

and no work is shown.

or a and b[1] An error in method is made but theerroneous answer is interpreted correctly ineither part a or b or both.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[2]

[4] x(x + 10) = 144 or an equivalent equationand 8 = width and 18 = length, andappropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made.or [3] A correct equation is used and a correctsolution is found, but only one dimension isidentified.[2] An appropriate solution is found to anincorrect equation of equal difficulty.or [2] A correct equation set equal to zero isshown, with no further work or incorrectwork.[1] A conceptual error is made, such aswriting the equation 2x + 2(x + 10) = 144, butthe dimensions are found appropriately.or [1] x(x + 10) = 144 and 8 = width and 18 =length, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[3] B

[4]

[4] 12 and an appropriate method is shown,such as ( ) .AB 2 2 29 8= +[3] An incorrect length is found for AE, butthen it is used to correctly complete theproblem.or [3] An appropriate method is shown, butone computational mistake is made.or [3] An appropriate method is shown, butthe answer is not given to the nearest foot,such as 145 .[2] AE = 8 and one computational mistake ismade using the Pythagorean theorem.or [2] An incorrect length is found for AE, butthen it is used to complete the problemcorrectly, but the answer is not rounded.[1] AE = 8 is found, but the Pythagoreantheorem is not used.or [1] 12 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[5]

[2] 8,100 and appropriate work is shown,such as 9 10 10 9× × × .[1] 10,000 but appropriate work is shown.or [1] Appropriate work is shown, but thestudent multiplies incorrectly.or [1] An appropriate pattern is shown, suchas 9 10 10 9× × × .or [1] 8,100 but no work is shown.[0] 38 is shown.or [0] The student attempts to use thecounting principle, but adds.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[6]

[2] x − 33

and multiplication by the reciprocal,

correct factoring, and canceling are shown.[1] The difference of two squares,x x x2 9 3 3− = + −( )( ), is factored correctly.or [1] Appropriate work is shown, but thefinal answer is incorrect.

or [1] x − 33

but no work is shown.

[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[7]

[4] Milk Chocolate bar = $0.75 and CreamyNougat bar = $0.50, and appropriate work isshown, such as equations, a trial-and-errormethod with at least two trials andappropriate checks, or an algebraic or graphicsolution.[3] Appropriate work is shown, but onecomputational error is made.[2] The cost of one candy bar is determinedcorrectly with appropriate work shown, butno attempt is made to find the cost of theother candy bar.or [2] Appropriate work is shown, but morethan one computational error is made.[1] Appropriate work is shown, but no answeris found.or [1] Milk Chocolate bar = $0.75 andCreamy Nougat bar = $0.50, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[8]

[2] 33 5

xx y+

[1] One correct factoring is shown, either3x(3x – 5y) or (3x – 5y)(3x + 5y).[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[9] D

[10] B

[11] D


[12]

[3] The frequency table is completedcorrectly, showing frequencies of 6, 2, 4, 5,and 3, and a frequency histogram is drawnand labeled correctly.[2] The frequency table is completedcorrectly, but one graphing error is made,such as not labeling the axes, having nonequalintervals, or starting the x-axis at 50.or [2] The frequency table is completedincorrectly, but an appropriate frequencyhistogram is drawn.or [2] The frequency histogram is drawn andlabeled correctly, but the frequency table isnot completed.[1] The frequency table is completedcorrectly, but two or more graphing errors aremade.or [1] The frequency table is completedcorrectly, but no frequency histogram isdrawn or a bar graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[13] B

[14] A

[15]

[3] 33, and appropriate work is shown, suchas a Venn diagram.[2] Appropriate work is shown, but thenumber of households that purchased onlyBrand A and only Brand B is found, 22 + 35= 57.or [2] Appropriate work is shown, but onecomputational error is made.[1] A conceptual error is made, such assubtracting 87 from 100.or [1] 33, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[16] A

[17] D

[18]

[2] 38 and an appropriate method is shown,

such as 36.64 - (21 + 6.14) = 9.50 and 9 5025.

. =

38 or an equation such as 21 + .25c + 6.14 =36.64.[1] 38 and no work is shown.or [1] An appropriate method or equation isshown, but one computational mistake ismade.or [1] The answer of $9.50 for local calls isfound but is not divided by .25.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[19]

[2] 57°, and appropriate work is shown, suchas determining that m FYD m BXY∠ ≅ ∠ and∠AXY is supplementary to ∠BXY .or [2] 57°, and a correctly labeled diagramwith appropriate angles is shown.[1] ∠CYX or ∠BXY is determined, but onecomputational error is made in subtracting tofind m AXY∠ .or [1] An angle is determined incorrectly, butan appropriate solution is found.or [1] 57°, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[20] D


[21]

[3] At least one example is shown that makesthe statement true, such as 2, 3, 5, 7, 9, or adefined variable; and one example is shownthat makes the statement false, such as anyeven number other than 2, with a correctexplanation that shows that the student canrecognize odd numbers and prime numbers.The explanation can be in words or as a Venndiagram.[2] Two correct examples are shown, one thatshows the statement is true and one thatshows the statement is false, but noexplanation or an inappropriate explanation isgiven.or [2] Only one correct example is shown, butan appropriate explanation is given.[1] Only one correct example is shown, andno explanation or an incorrect explanation isgiven.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[22]

[3] -5, -3, -1, and appropriate work is shown,such as solving the inequality or trialand error with at least three trials andappropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, and the

inequality x ≥ −5 13

is written, but no further

correct work is shown.or [2] The trial-and-error method is used tofind the correct solutions, but only twotrials and appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but thesolutions are not found.or [1] -5, -3, -1, but no work or only one trialwith an appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[23] D


[24]

[4] $2,950.33 and a correct method is shown,such as area 1204π square feet multiplied by$0.78.or [4] Various correct values of π are usedthat lead to slightly different totals such as$2,948.84 (if 3.14 is used).[3] The shaded area is found, such as 1204π(or similar values based on πapproximation).or [3] The correct shaded area is found, butone computational mistake is made in theprice, or the final cost is not roundedcorrectly.[2] The two separate areas are found but notcorrectly used.or [2] An inappropriate formula for areas isshown, but work is carried to an appropriatevalue.or [2] Only one appropriate area is found andan appropriate cost is computed.or [2] The area found is incorrect butcalculated to an appropriate cost.[1] Only one appropriate area is found, either2500 1296π πor .or [1] An inappropriate area is found, and onecomputational mistake is made in calculatingthe cost.or [1] $2,948.84 through $2,950.33 and nowork is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[25]

[2] An isosceles triangle that is not acute isdrawn, and its three angles are labeled, suchas 20, 20, 140 or 45, 45, 90.[1] An isosceles triangle is drawn that showsan angle that is not acute, but the base anglesare not labeled.or [1] The three angles are stated correctly,but no triangle is drawn.[0] The triangle that is drawn and labeled isnot isosceles or is acute.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[26] B

[27] A

[28] A

[29]

[4] 210, and appropriate work is shown, suchas a system of equations or the linear equation5x + 2(295 – x) = 1,220.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but thenumber of children’s tickets is found as theanswer.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect equation of equaldifficulty is solved appropriately.or [2] 210, but a method other than analgebraic solution is used.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The correct system of equations orlinear equation is written, but no furthercorrect work is shown.or [1] 210, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[30] A

[31] C

[32] B

[33] A

[34] C

[35] C


[36]

[3] y x x= + −2 3 18 , and appropriate workleading from the roots to the equation isshown.[2] Appropriate work is shown, but onecomputational error is made.or [2] x x2 3 18 0+ − = , but appropriate workis shown.or [2] Only the correct factors (x + 6) and (x –3) are shown.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Only the roots –6 and 3 are shown,such as x = –6, x = 3.or [1] y x x= + −2 3 18 , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[37] A

[38]

[2] 42 nickels and 21 dimes, and appropriatework is shown, such as 0.1x + (0.05)2x = 4.20or a guess and a check with a minimum oftwo trials and appropriate checks or anotherappropriate method.[1] 42 nickels or 21 dimes, but appropriatework is shown.or [1] Appropriate work is shown, but noanswer or an incorrect answer is found.or [1] 42 nickels and 21 dimes, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[39] C

[40] B

[41] A

[42]

[3] -6 and 4, and appropriate work is shown,such as factoring or trial and error with atleast three trials and appropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but onlyone correct value for x is found.or [2] The trial-and-error method is used tofind the correct solutions, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The equation is factored correctly, butno values are found.or [1] The equation is factored incorrectly, buttwo appropriate values are found.or [1] -6 and 4, but no work or only one trialwith an appropriate check is shown.[0] -6 or 4, but no work or only one trial withan appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[43] B

[44] C


[45]

[3] The figure is drawn accurately and thenew coordinates are labeled and stated asJ'(7,-2), B'(2,-1), C'(3,-2), and D'(2,-4).[2] One error is made in drawing the figure,such as misplotting one point, but the newcoordinates are labeled and statedappropriately, based on that figure.or [2] The figure is drawn and labeledaccurately, but the new coordinates are notstated or are stated incorrectly.or [2] The new coordinates are labeled andstated correctly, but the figure is not drawn.[1] Two errors are made in drawing thereflected figure, but the new coordinates arelabeled and stated appropriately, based on thatfigure.or [1] Appropriate work is shown, but oneconceptual error is made, such as reflectingthe figure in the x-axis or the origin.or [1] Correct points are plotted and labeled,but the figure is not drawn, and thecoordinates are not stated.or [1] The figure is drawn correctly, but thenew coordinates are not labeled or stated.[0] An appropriate reflection in the x-axis isdrawn, and the coordinates are not labeled orstated.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[46] A

[47]

[3] 820

or an equivalent answer, and

appropriate work is shown, such as using atree diagram or writing the equation6

20220

820

+ = .

[2] One computational error is made in

finding 620

or 220

, but an appropriate sum is

found.

or [2] 220

and 620

are found, but no sum is

shown.

[1] 620

or 220

, and appropriate work is

shown.or [1] An appropriate answer is found, usingreplacement with a tree diagram or an

equation such as 35

35

25

25

1325

• + • = .

or [1] 820

, but no work is shown.


[48] C


[49]

[3] The student says the point does not lie onthe line and an appropriate method is shown,such as slope of -2 does not work with thenew point (-25,81) and either other point (0,4)or (2,0), or accurately shows a graph where (-25,81) is not on line .[2] The student says the point does not lie onthe line but gives an inappropriateexplanation of slope.or [2] The student tries to use slope conceptbut makes one computational mistake andgives an appropriate answer based on thismistake.[1] Only the slope of -2 is found.or [1] The correct diagram is drawn with nointerpretation.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[50] C

[51] A

[52] B

[53] B

[54] A

[55] B

[56] A

[57] C

[58] C

[59] B

[60] B

[61] A

[62] A

[63]

[3] 80, and appropriate work is shown.[2] x = 30 is shown, but the student fails tosubstitute to find m AEC∠ .or [2] x = 30 is shown, but the student statesthat the answer is 100° , by finding thesupplement of ∠AEC .or [2] The student makes one computationalerror in the solution of the correct equation4x - 40 = x + 50 but appropriately substitutesthe incorrect value to solve for m AEC∠ .[1] The student makes one computationalerror in the solution of the correct equation 4x- 40 = x + 50 and fails to substitute to findm AEC∠ .or [1] The student makes more than onecomputational error in the solution of thecorrect equation 4x - 40 = x + 50, butappropriately substitutes the incorrect value tosolve for m AEC∠ .or [1] 80, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[64] B

[65] A

[66] B

[67] A

[68] C

[69]

[3] 15 and an appropriate method orexplanation is shown, such as trial and erroror the inequality 6x + 15 ≥ 100.[2] An appropriate method is shown, but itstops at 14.[1] An appropriate method is shown, but noanswer is found.or [1] 15 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[70] A


[71] D

[72]

a [2] A correct sketch is drawn that showstwo possible locations, such as parallel linesand a perpendicular bisector. Students candraw their own sketch or use the diagramgiven.[1] A correct sketch is drawn, but with noindication of where the treasure is buried.or [1] A partial sketch is drawn, showingeither the distances from the fence or thedistance from the trees.b [1] 5 feetor [1] An appropriate answer is found for anincorrect part a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[73]

[3] 10 and 30, and appropriate work is shown,such as 2x + 2(2x + 10) = 80 or trial and errorwith at least three trials and appropriatechecks.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but onlyone of the dimensions is found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] Appropriate solutions are found basedon the incorrect use of the perimeter formula,such as 3x + 10 = 80.or [1] 10 and 30, but no work or only one trialwith an appropriate check is shmvn.[0] 10 or 30, but no work or only one trialwith an appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[74] B

[75] A


[76]

[3] 3, 12, and 30 and an appropriatearithmetic method or equation is shown, suchas 40 10803x = .[2] An appropriate equation or method isshown, but not all three dimensions are found.or[2] An appropriate method is shown, andalthough one computational mistake is made,the student does find three dimensions basedon this mistake, such as dividing 1080 by 40incorrectly.[1] The student shows that multiplication isrequired to find volume but sets up anincorrect method and does not find threedimensions.or[1] 3, 12, and 30 and no work is shown.[0] The sum is used instead of the product,or[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[77] B

[78]

[2] 12, and a correct tree diagram or a correctsample space is shown.[1] An incomplete tree diagram or samplespace is shown with at least 8 possiblecombinations shown, and an appropriatenumber of outfits is found.or [1] A correct tree diagram or sample spaceis shown, but the number of possible outfits ismissing or is incorrect.or [1] 12, but 3 4× is used to find the numberof outfits.[0] 12, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[79] B

[80] D

[81] C

[82] C

[83] C

[84] B

[85] A

[86]

[3] 84% and appropriate work is shown, suchas mathematics or technology = 42, the total =50, and the percentage = 84%.[2] The correct numbers of students areshown, but the percentage is incorrect.or [2] One error in computing the numbers ofstudents is made, but the percentage isappropriate for those numbers.[1] Only one number is correct, such as 28taking mathematics.or [1] An appropriate percentage is shown fortwo incorrect values.or [1] 84% but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[87] C

[88]

[2] 7x - 2 or x + 3x + 3x - 2, and appropriatework is shown, such as x + 3x + 3x - 2 whenchips = x, pretzels = 3x, and nachos = 3x - 2.[1] The expressions for snacks are representedcorrectly, but one computational error is madein adding the expressions.or [1] The expressions for snacks arerepresented incorrectly, but the expressionsare added appropriately.or [1] 7x- 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[89] D


[90]

a [3] A parabola is correctly graphed through(0,0), (1,10), (2,16), (3,18), (4,16), (5,10), and(6,0).[2] A correct table of values is shown, but notall the points are graphed correctly.or [2] The correct points are graphed but as abroken-line graph, not a curve.or [2] At least four values are calculatedcorrectly and graphed.[1] The student has at least two of the valuescalculated correctly and has tried to graph allthe points.[0] Fewer than two values are calculatedcorrectly.b [1] A maximum height of 18 is found.or [1] Correct y is found for an incorrectgraph in part a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[91] D

[92] D

[93]

[2] 5, and appropriate work is shown, such assolving the linear equation 80x + 100x = 900,using a diagram or proportion or trial anderror.[1] Appropriate work is shown, but onecomputational error is made.or [1] 5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[94] D

[95] C

[96] C

[97]

[2] 75, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] An incorrect equation of equaldifficulty, such as x + 5x = 180, is solvedappropriately, and an appropriate anglemeasure is found.or [1] A correct equation is written and solvedfor x, but no further correct work is shown.or [1] 75, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[98]

a [1] c = 10m + 100 for Ron's Rental and c =20m + 20 for Josie's Rental.b [2] Two lines, rays, or segments are graphedand labeled correctly, using values arrived atby using a table or by using the slope and y-intercept.[1] Two lines, rays, or segments are graphedcorrectly, but they are not labeled.or [1] One line, ray, or segment is graphedand labeled correctly, using values arrived atby using a table or by using the slope and y-intercept.c [1] 8or [1] An appropriate number of months isfound, based on an incorrect graph in part b.a, b, and c [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[99] A

[100] D

[101] C

[102] A


[103]

[3] 4, 6, and 8, and appropriate work isshown, such as the correct quadratic equationor trial and error with at least three trials andappropriate checks.[2] The correct quadratic equation is solved,but one computational error is made, but threeappropriate ages are listed.or [2] The correct quadratic equation issolved, but the negative root is not rejected,but three appropriate ages are listed.or [2] The correct quadratic equation issolved, but only one age is found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] An incorrect equation of lesser difficultyis solved appropriately, and the three ages arelisted.or [1] An incorrect quadratic equation ofequal difficulty is solved appropriately, andthe three ages are listed.or [1] The correct quadratic equation isshown, but more than one computational erroris made.or [1] The correct quadratic equation isshown, but no further correct work is shown.or [1] 4, 6, and 8, but no work or only onetrial with an appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[104] A

[105]

[2] 5 22rs , and appropriate work is shown.[1] A partially correct answer is found, suchas 5 2 4r s or 5 22 2s r , and appropriate workis shown.or [1] 7 07 2. rs , but appropriate work is shown.or [1] 5 22rs , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[106] B

[107] A

[108] A

[109] A

[110]

[4] $148.54, and appropriate work is shown.[3] The correct pre-tax amount of $137.54 isfound, but no tax or an incorrect tax is shown.or [3] Appropriate work is shown, but onecomputational error is made.[2] The correct area of 46 2ft is found, but nocost is shown.or [2] Appropriate work is shown, but morethan one computational error is made.or [2] An incorrect area is determined, such asby adding or multiplying all sides, but then afinal cost including tax is determinedappropriately.[1] An incorrect area is shown, and onecomputational error is made.or [1] $148.54, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[111]

[3] Three correct equations are shown, suchas y x= + 7, y x= − − 6, and 2 2 12y x= − .[2] Only two correct equations are shown.[1] Only one correct equation is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[112] C


[113]

[2] 6, and appropriate work is shown, such asa Venn diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 1, the number of friends with only aVCR player, is found, and appropriate work isshown.or [1] 6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[114] A

[115]

[3] 490, and appropriate work is shown, suchas 7•7•10.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but anincorrect answer is found, based on anincorrectnumber of possible dessert combinations oran incorrect number of soup or appetizerchoices.or [2] Appropriate work is shown, but anincorrect answer is found, based on one errorinthe tree diagram.

or [2] 1490

, but appropriate work is shown.

[1] 7, 7, and 10 are added instead ofmultiplied.or [1] The counting principle is usedcorrectly, but incorrect substitutions aremade, butan appropriate answer is shown.or [1] 490, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[116] D

[117]

[4] w(w + 3) = 40, width = 5, and length = 8,and appropriate work is shown.[3] w(w + 3) = 40 and appropriate work isshown, but one computational error is madein finding the length and width.or [3] w(w + 3) = 40 and appropriate work isshown, but only the width is found.[2] w(w + 3) = 40 and appropriate work isshown, but the length and width are notidentified.or [2] w(w + 3) = 40 and appropriate work isshown, but more than one computational erroris made in finding the length and width.or [2] An incorrect equation of equaldifficulty is solved appropriately for thelength and width.[1] w(w + 3) = 40, but no further correct workis shown.or [1] Appropriate work is shown, but oneconceptual error is made, such as solving theequation 2w + 2w + 6 = 40.or [1] w(w + 3) = 40, width = 5, and length =8, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[118] B

[119] A

[120] D

[121] C

[122] C

[123] B


[124]

[4] Quadrilaterals ABCD and A’B’C’D’ aredrawn and labeled correctly and 24 is foundas the area, and appropriate work is shown.[3] One graphing error is made in thetransformation, but an appropriate area ofA’B’C’D’ is found.or [3] Correct quadrilaterals are drawn andlabeled, but one computational error is madein determining the area.or [3] Quadrilaterals ABCD and A’B’C’D’ aredrawn correctly and 24 is found as the area,but the vertices are not labeled.[2] Correct quadrilaterals are drawn andlabeled, but no further correct work is shown.or [2] One conceptual error is made, such asreflecting in the x-axis, but the correct area isfound.[1] 24, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[125] C

[126]

[4] 2,058, and appropriate work is shown,such as the accompanying diagram andequation.

[3] Appropriate work is shown, including acorrect diagram and the use of the tangentfunction, but one computational error is made.or [3] Appropriate work is shown, including acorrect diagram and the use of the tangentfunction, but the answer is not rounded or isrounded incorrectly.[2] A correct diagram is drawn, but anincorrect trigonometric function is selected,but it is solved and rounded appropriately.or [2] A correct diagram is drawn and thetangent function is selected, but no furtherwork is shown.or [2] An incorrect diagram is drawn, but theappropriate trigonometric function, based onthe drawing, is selected, solved, and roundedappropriately.[1] An incorrect diagram is drawn and anincorrect trigonometric function is selected,but it is solved and rounded appropriately.or [1] Only a correct diagram is drawn.or [1] 2,058, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[127]

[2] 32, and appropriate work is shown, suchas a diagram or “let” statements and anappropriate equation, such as 5x + 20 = 180.or [2] 32, and an appropriate trial-and-errormethod with at least two trials andappropriate checks are shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] An incorrect equation set equal to 180°is shown, but it is solved appropriately, suchas 4x + 20 = 180; or an incorrect equation setequal to 360° is shown, such as 5x + 20 =360.or [1] 32, and an appropriate trial-and-errormethod with less than two trials andappropriate checks are shown.or [1] 32, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[128] C

[129] B

[130] D

[131]

a [1] B, and an appropriate explanation isgiven.b [1] 5 minutesa and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[132] D

[133] C

[134]

[2] 2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown to find thenumber of students for any flavor other thancoffee.or [1] 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[135]

[2] A correct construction is drawn, showingthe arcs intersecting above and below AB ,and line c is drawn.[1] A correct construction is drawn, but line cis not labeled.[0] A drawing that is not a construction isshown with arc marks sketched.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[136] A

[137] A

[138]

[4] $167.50, and appropriate work is shown,such as 350x + (150)(130) = 1.25(62,500) ortrial and error with at least three trials withappropriate checks.[3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.or [2] $167.50, but only one trial with anappropriate check is shown.[1] $167.50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[139] C


[140]

[2] 15, and any equivalent proportion,equation, or fraction conversion is shown,

such as 1216 20

=x .

[1] An appropriate proportion, equation, orfraction conversion is shown, but onecomputational or conceptual error is made.or [1] An incorrect proportion, equation, orfraction conversion is shown, but anappropriate answer is found for the incorrectproportion.or [1] 15, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[141]

[3] 32, and appropriate work is shown, suchas finding the circumference to be 10π anddividing 1,000 by 10π .[2] Appropriate work is shown, but onecomputational or rounding error is made orthe answer is expressed in terms of π .[1] An incorrect circumference formula isused, but an appropriate number ofrevolutions is found.or [1] The circumference of the wheel isfound to be 10π or an equivalent decimal, butno further correct work is shown.or [1] 32, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[142]

[3] 45, and appropriate work is shown, such

as tan .6620

°=x

[2] A correct trigonometric ratio is used, andvalues are substituted correctly, but onecomputational or rounding error is made, orthe calculator is left in radian mode.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric ratio.or [1] An incorrect diagram is drawn, but anappropriate solution is found.or [1] A correctly labeled diagram is drawn,but no further correct work is shown.or [1] A correct trigonometric ratio is written,but no further correct work is shown.or [1] 45, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[143]

[3] 4, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[144]

[4] 146, and appropriate work is shown, suchas solving the equation 2x = 5x - 51.[3] Appropriate work is shown, but onecomputational error is made.or [3] The measure of ∠FHB or ∠DGH isfound to be 34, and appropriate work isshown, but no further correct work is shown.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, such as solving theequation 2x + 5x - 51 = 180.or [2] The correct equation is solved for x =17, but no further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The correct equation is written, but nofurther correct work is shown.or [1] 146, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[145] D

[146]

[2] False, and an appropriate explanation isgiven.[1] Appropriate work is shown, but the truthvalue is missing or is incorrect.[0] False, but no explanation is given.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[147] B

[148]

[2] A correct graph is drawn on the numberline, with a closed circle at the left end and anopen circle at the right end.[1] Appropriate work is shown, but onegraphing error is made, such as writing anincorrect scale on the number line.or [1] Appropriate work is shown, but oneconceptual error is made, such as using aclosed circle instead of an open circle.or [1] A correct inequality is written, but thegraph is not drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[149] B

[150] C

[151] B

[152]


as 240360

900 600⋅ = .

[1] Appropriate work is shown, but onecomputational error is made or the answer isexpressed as a fraction.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The central angle of 240° is found, butthe number of students is not calculated.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 600, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[153] A

[154] D

[155] C

[156] B


[157] A

[158] D

[159] B

[160]

[2] 2.4 and appropriate work is shown.[1] The student shows correct use of thedistributive property to obtain 2x – 6 or otherappropriate algebraic technique.or [1] 2.4 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[161] A

[162] D

[163] B

[164] B

[165] A

[166]

[2] 15, and appropriate work is shown, suchas using the Pythagorean theorem,Pythagorean triples, or trigonometricfunctions.[1] The data are substituted incorrectly, but anappropriate answer is found and is roundedcorrectly.or [1] Appropriate work is shown, but one ormore computational errors are made.or [1] 15, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[167] D

[168] C

[169]

a [2] 59, and the equation tan x = 280170

is

shown, or the Pythagorean theorem is usedfirst to find the hypotenuse, and either sine orcosine is used correctly to find x.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 59, but no work is shown.b [2] 122, if the Pythagorean theorem is usedor if a trigonometric function of the angle isused before it was rounded to 59°.

or [2] 120, if cos59 170=

hyp is used.

or [2] 123, if sin59 170=

hyp is used.

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 122 or 120 or 123, but no work isshown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[170]

[4] 100 and a correct parabolic arch is drawn,and appropriate work is shown, such as atable of values for the parabola or correctlylabeled points.[3] 100 and a correct parabolic arch is drawn,but no table of values or labeled points areshown.or [3] 100 and a correct parabolic arch isdrawn, and appropriate work is shown, but noscale or an incorrect scale is shown.or [3] A correct parabolic arch is drawn, butthe maximum height is missing or isincorrect.[2] An incorrect parabolic arch is drawn, butan appropriate maximum height is found.or [2] A correct height is determinedalgebraically, but a parabolic arch is notdrawn.or [2] 100 and an appropriate parabolic arch isdrawn, but it is not drawn between0 20≤ ≤x .[1] A correct parabolic arch is drawn, but nowork is shown, such as a table of values orcorrectly labeled points, and the maximumheight is missing or is incorrect.or [1] 100, but no work is shown and noparabolic arch is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[171]

[2] 6 and appropriate work is shown, such asusing the combination 4 2C , listing all sixpossible outcomes, or drawing a correct treediagram.[1] A correct setup of combinations is shown,but an incorrect solution, such as leaving 4 2C ,or no integral solution is found.or [1] An appropriate list or tree diagram isshown, but an incorrect solution is found,such as 5, by omitting one of the possiblecombinations.or [1] 12 but a complete list or tree diagram isshown.or [1] 6 but no work is shown.[0] The answer is completely incorrect, suchas 4 2P or 4 3× .or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[172] D

[173]

[3] 102, and appropriate work is shown, suchas using the equation 2x + 10 + 3x = 180 or anequivalent equation.[2] The equation 2x + 10 + 3x = 180 is solvedcorrectly for x, but m B∠ is not determined oris determined incorrectly.[1] Appropriate work is shown, but onecomputational error is made or x is notdetermined.or [1] The equation 2x + 10 + 3x = 360 issolved correctly, and an answer of 210 isfound.or [1] 102, but no work is shown.[0] The equation 2x + 10 = 3x where x = 10 isgiven.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[174] A

[175] C

[176] B


[177] A

[178] C

[179]

[4] A correct table and histogram withappropriate labels and scales are shown, suchasthe table below.SCORE TALLY FREQUENCY40-49 / 150-59 / 160-69 /// 370-79 /// 380-89 /// 3[3] An incorrect table is shown, but thehistogram is appropriate, based on this table.or [3] A correct table is shown, but one erroris made on the histogram, such as usingincorrect labels or no labels.or [3] An incomplete table is shown, but thehistogram is correct.[2] An incomplete table is shown, and thehistogram is partially correct.or [2] A correct table is shown, and a correctbar graph is made.[1] A correct table is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[180] A

[181] C

[182] B

[183] A

[184] D

[185]

[4] 28.2, and an appropriate equation is

shown, such as tan 6215

=x .

[3] Appropriate work is shown, but theanswer is rounded incorrectly.or [3] The student uses the correct tangentfunction and rounds the answer, but makesone computational error.[2] The student uses the correct tangentfunction, but makes several errors.or [2] An incorrect trigonometric function isused, but appropriate work is shown.[1] The tangent function is indicated, but theratio is set up incorrectly.or [1] 28.2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[186] D

[187] D

[188] C

[189] D

[190] B

[191] B

[192] A

[193] D

[194] C


[195]

[4] 65 adult tickets and 85 student tickets andan appropriate equation is shown, such as7.50x + 4.75(150 - x) = 891.25, or any otheracceptable method is used.[3] Either 65 or 85 and appropriate work isshown.or [3] Appropriate work is shown, but onecomputational error is made that leads to twoappropriate answers.[2] An incorrect equation is shown, but it issolved appropriately for two answers.or [2] The correct equation is shown, but twocomputational errors are made.[1] Appropriate work is shown, but no answeris found.or [1] 65 and 85 but no work is shown.[0] Either 65 or 85 and no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[196] A

[197] D

[198] C

[199] B

[200] C

[201]

a [3] A parabola with points graphed at (0,0),(1,32), (2,48), (3,48), (4,32), and (5,0) isshown. [Points do not have to be labeled onthe graph for full credit.][2] Appropriate work is shown, such as atable of values, but one graphing error ismade.or [2] The correct points are graphed, but theparabola is drawn incorrectly, such asconnecting (2,48) and (3,48) as a line segmentor not connecting the points at all.or [2] At least four correct values are found,and the parabola is graphed appropriately.or [2] A correct table of values is shown forall values from 0 to 5, but no graph is drawn.[1] Two or three correct values are found, andthe parabola is graphed appropriately.or [1] A correct table of values is shown foran incorrectly transcribed equation, such ash t t= +8 402 , but no graph is drawn.b [1] 2.5 is found algebraically or identifiedfrom a table or from the graph of theparabola.or [1] An appropriate value of t is found,based on an incorrect graph.or [1] 2 < t < 3 is given as the range of valuesbased on the line segment drawn in part a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[202] A

[203] A

[204] B


[205]

[2] 6x – 2 or an equivalent expression, andappropriate work is shown, such as 2(2x + 3)+ 2(x – 4) = 6x – 2.[1] The length is represented correctly as 2x +3 and the width as x – 4, but therepresentation of the perimeter is determinedincorrectly.or [1] The length, the width, and the perimeterare represented appropriately, but by avariable other than x.or [1] One or both dimensions are representedincorrectly, but the perimeter is representedappropriately.[0] One or both dimensions are representedincorrectly, and the perimeter is notdetermined.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[206] C

[207]

[4] 270 and an appropriate method is shown,such as using the Pythagorean theorem ortrigonometry to find base AC = 36.[3] An appropriate method is shown, but onecomputational mistake is made.[2] An inappropriate formula for the area ofthe triangle is used, but work is carried to asolution.or [2] The Pythagorean theorem is usedcorrectly, but only the area of triangle ADB isfound, as 150.or [2] The Pythagorean theorem is usedincorrectly arriving at incorrect AB, but workis carried to its appropriate solution fortriangle ADC.[1] Only the area of triangle DBC is found, as120.or [1] The Pythagorean theorem is usedincorrectly, and the area is not found.or [1] 270 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[208] C

[209] B

[210] A

[211]

[2] 2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error or one conceptual error ismade.or [1] 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[212] D

[213] C

[214] B

[215]


as sin50200

°=x .

[3] An appropriate analysis is shown, but onecomputational or rounding error is made.[2] An incorrect trigonometric function is

used, such as cos50200

°=x , but it is carried

to an appropriate final answer and is roundedcorrectly.[1] An incorrect trigonometric function isused and solved appropriately, but it isrounded incorrectly.or [1] Only an appropriate diagram is shown.or [1] 153, but no work is shown.[0] Use of the Pythagorean theorem, such as200 502 2 2= + x , is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[216]

[3] 20, and appropriate work is shown, suchas an equation, trial and error, or a graph.[2] Appropriate work is shown, such as 12.95+ 0.25x = 14.95 + 0.15x, but onecomputational error is made.or [2] Appropriate work is shown, but ananswer of $17.95 is found.or [2] 20, and only a check is shown.[1] The student starts appropriate work to findwhen the prices are equal but does notcomplete it, such as starting to solve thecorrect equation, showing one incorrect trial,or drawing an incomplete graph.or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[217] C

[218]

[3] 120, and appropriate work is shown, suchas solving the equation 5 2 12 180x x+ + = .[2] Appropriate work is shown, but onecomputational error is made.or [2] The correct equation is solved for x, butno further correct work is shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately, and anappropriate measure is found for ∠D.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[219] D

[220]

a [2] 125.6 or 125.7 (correct for the value ofπ used) and appropriate work is shown.[1] The area is left as 40π or the answer isnot rounded correctly.or [1] An appropriate method is shown, butone computational mistake is made.or [1] The correct areas of both circles arefound, but the two areas are not subtracted.or [1] The circumference formula is usedcorrectly for both circles and thecircumferences are subtracted for an answerof 25.1.or [1] 125.6 or 125.7 and no work is shown.b [2] 49 and an appropriate explanation isgiven.or [2] An appropriate percent for an incorrectpart a is found and supported by areaformulas.

[1] The answer is left as 4081ππ

.

or [1] An appropriate fraction for an incorrectpart a is found but not given as a percent.or [1] An appropriate percent for an incorrectpart a is found and is supported bycircumference formulas.or [1] 49 and no work is shown.

[0] 49

or 44% and no work is shown.

or [0] 4 is found by subtracting the radii.or a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[221] D

[222] D

[223] D


[224]

[3] The student draws an obtuse triangle andall sides and all angles are correctlycalculated, such as by using 120°, 30°, and30° and sides 4, 4, and 10.[2] The student has the angles correctlyindicated and the two congruent sidesmarked, but the length of the longest side isincorrect or is missing.or [2] All sides are correctly marked, but theangles do not add to 180°, but an obtuse angleand two congruent angles are shown.[1] Only the angles are correctly shown.or [1] Only the sides are correctly shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[225]

[2] $350, and appropriate work is shown,

such as 14505

360+=

x or trial and error with

at least three trials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] The total of the five salaries is shown tobe 5 x 360 = 1800, but no further correctwork is shown.or [1] $350, but no work is shown or fewerthan three trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[226]

[2] 8 and the use of trigonometry, thePythagorean theorem, or Pythagorean triple isshown.[1] The Pythagorean theorem or trigonometryis used, but a computational mistake is madeor substitution is incorrect, such as6 102 2 2= + x .[1] 8 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[227] B

[228]


as the proportion 2516

250=

x.

[1] Appropriate work is shown, but onecomputational error or one conceptual error is

made, such as 54

250=

x.

or [1] 160, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[229]

[4] x = 19.62990915 and y = 9.814954576 orequivalent answers, and appropriate work is

shown, such as sin 60 17°=

x and

tan60 17°=

yor the Pythagorean theorem.

[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown, and thecorrect answers are found, but not identified.[2] Appropriate work is shown, but oneconceptual error is made, such as

sin 6017

°=x .

or [2] Appropriate work is shown, but morethan one computational or rounding error ismade.[1] Appropriate work is shown, but twoconceptual errors are made, such as

sin 6017

°=x and tan60

17°=

y .

or [1] x = 19.62990915 and y = 9.814954576or equivalent answers, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[230]

[4] 11, and appropriate work is shown, suchas solving the quadratic equation 3x(x + 5) =150 or trial and error with at least three trialsand appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown todetermine that 5 is the shorter side of the box,but the shorter side of the original sheet is notfound or is found incorrectly.or [3] An incorrect quadratic equation ofequal difficulty is solved appropriately, andan appropriate shorter side of the originalsheet is found.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately, butthe shorter side of the original sheet is notfound.or [2] A correct quadratic equation is setequal to zero, but no further correct work isshown.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] One conceptual error is made in findingthe shorter side of the box, and thecorresponding shorter side of the originalsheet is not found or is found incorrectly.or [1] A correct quadratic equation is written,but it is not set equal to zero, and no furthercorrect work is shown.or [1] 11, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[231] C

[232] B

[233] D

[234]

[2] 6, and appropriate work is shown, such assolving the equation 2x + 3 = 15 or trial anderror with at least three trials and appropriatechecks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 6, but no work or fewer than three trialsand appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[235]

[2] 5(n + 4)(n - 4), and appropriate work isshown.[1] Appropriate work is shown, but onefactoring error is made or the expression isnot simplified completely.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[236] B

[237] B

[238] D

[239] A


[240]

[2] 196, and an appropriate explanation isgiven.[1] An incorrect answer is chosen, but anappropriate explanation is given.or [1] 196, but no explanation or anincorrect explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[241]

[4] Both inequalities are graphed correctlyand at least one is labeled, and the solution setis labeled S.[3] Appropriate work is shown, but onegraphing error is made, such as drawing asolid line for y x> − 4 or shading incorrectly,but the solution set is labeled S.or [3] Both inequalities are graphed correctlyand at least one is labeled, but the solution setis not labeled or is labeled incorrectly.or [3] Both inequalities are graphed correctly,the solution set is labeled, but neitherinequality is labeled.[2] Appropriate work is shown, but two ormore graphing errors are made, but anappropriate solution set is labeled.or [2] Appropriate work is shown, but oneconceptual error is made, such as graphing thelines y x= − + 2 and y x= − 4 and labelingthe point of intersection S.[1] One inequality is graphed and shadedcorrectly, but no further correct work isshown.or [1] The lines y x= − + 2 and y x= − 4 aregraphed correctly, but no solution isindicated.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[242] C

[243] B

[244]

[2] 31, and appropriate work is shown, suchas 5x + 25 = 180.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as setting thegiven angles equal to each other.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 31, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[245] B

[246]

[3] 6.7, and appropriate work is shown, suchas using the distance formula.[2] Appropriate work is shown, but onecomputational or rounding or graphing erroris made or the answer is left in radical form.[1] Appropriate work is shown, but more thanone computational or rounding or graphingerror is made.or [1] Only an appropriate diagram or graph isshown.or [1] The horizontal distance is determinedto be 3, and the vertical distance isdetermined to be 6, but the shortest distance isnot found.or [1] 6.7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[247] B


[248]

[3] 34 and an appropriate explanation is

given, such as 38 46 23

=+ x .

[2] An appropriate method or equation isshown, but one computational mistake ismade.or [2] The student does not take intoconsideration two dogs of equal weight andgives an answer of 68.[1] The student understands weighted averagein that three dogs averaging 38 pounds musthave a total weight of 114 pounds but doesnot subtract the known weight.or [1] 34 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[249] B

[250] A

[251] A

[252] D

[253]

[3] 499 days and appropriate work is shown,

such as 17 000 000

1420 24

, , milesmileshour

hoursday

×.

[2] Appropriate work is shown, but onecomputational error is made or the studentincorrectly calculates 17 107. × by onedecimal place.or [2] Appropriate work is shown, but theanswer is rounded incorrectly or is notrounded.[1] 17 107. × = 17,000,000 is shown.

or [1] 17 101420

11 9718317. , .×= hours is shown.

or [1] 34,080 miles in 1 day is shown.or [1] 499 but no work is shown.[0] The student does not understand scientificnotation.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[254] B

[255]

[3] 2, 6, 10, 14, and 18 and an appropriatemethod is shown.[2] One mistake is made with selection, suchas including 0.[1] One of the appropriate sets is found: either2, 4, 6, 8, 10, 12, 14, 16, 18, 20 or not 4, 8,12, 16, 20.or [1] The correct numbers are found, and nowork is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[256]

[4] Median = 91.5, mode = 92, and seventhtest score = 96, and appropriate work isshown.[3] Appropriate work is shown, but onecomputational error is made.or [3] Seventh test score = 96, but only themedian or the mode is found correctly, butappropriate work is shown.or [3] 91.5, 92, and 96, and appropriate workis shown, but the median and mode are notlabeled or are labeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] Both the median and the mode arefound and labeled correctly, and appropriatework is shown, but the seventh test score isnot found or is found incorrectly.or [2] Seventh test score = 96, and appropriatework is shown, but the median and the modeare not found or are found incorrectly.[1] Either the median or the mode is foundand labeled correctly, and appropriate work isshown, but no further correct work is shown.or [1] Median = 91.5, mode = 92, and seventhtest score = 96, but no work is shown.[0] Median = 91.5 or mode = 92 or seventhtest score = 96, but no work is shown.or [0] 91.5, 92, and 96, but no work is shownand the answers are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[257] D

[258]

a [2] 3 and an appropriate method is shown,such as trial and error or the equation32 8 26 10+ = +x x .[1] 3 and no work is shown.or [1] An appropriate method is shown, but anincorrect answer is found.b (1) [1] Best Cable Company and anappropriate explanation is given.b (2) [1] $24 and an appropriate explanationis given.b (l) and b (2) [1] Best Cable Company and$24 and no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[259]

[3] 720


appropriate work is shown, such as 1525

1424

•

or 15 2

25 2

CC

.

[2] 1525

1424

• or 15 2

25 2

CC

is shown, but one

computational error is made or no furtherwork is shown.or [2] 15 2C and 25 2C are computed correctly,but no further work is shown.or [2] Appropriate work is shown, but onecomputational error is made.[1] The correct probabilities are found, butthey are added instead of multiplied.or [1] Only one of the two parts of theprobability is correct.or [1] Appropriate work is shown, but morethan one error is made.

or [1] 720

or an equivalent answer, but no

work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[260]

[2] 77, and appropriate work is shown, suchas (76 + 78) ÷ 2.[1] 76 and 78 are identified.or [1] 77, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[261]

[3] 120, and appropriate work is shown, suchas 6t + 30 + 8t – 60 = 180.[2] The student finds correctly the unknown, t= 15, but does not find the measure of angle4.or [2] Appropriate work is shown, but onecomputational error is made.[1] The student forms an incorrect equation,such as setting the two angles equal, andarrives at t = 45 and an angle of 300.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[262] D

[263] D

[264] C

[265]

a [2] 15 and an appropriate method is shown,such as finding GB = JC = 2x and FC = ED =HJ = 3.[1] 15 and no work is shown.or [1] At least one of the values is correct, asshown above, and the area is calculated basedon the incorrect value.b [1] Any form equivalent to (2x + 5)(x + 3)is shown, such as 5 2 6 152x x x+ + + .or [1] Any correct total area based on thestudents incorrect answer in part a is found.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[266] D

[267] C

[268] D

[269]

[2] 0, and an appropriate explanation is given,such as 0 is the number that when added toany number results in that number or does notchange it, or 1 + 0 = 1, 2 + 0 = 2, and 3 + 0 =3.[1] 0, but no explanation or an incorrectexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[270] C

[271] D

[272]

[3] 135 and appropriate work is shown.[2] The two correct angles of 65° and 70° arefound, but their sum is not identified as theanswer to the question.or [2] 65° or 70° and an appropriate sum isfound.[1] Either the 65° or the 70° is correctlyidentified.or [1] Two incorrect angle measures arefound, but they are added correctly.or [1] 135 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[273]

[2] 117.6, and appropriate work is shown,

such as tan .7825

°=x

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function, but anappropriate solution is found.or [1] A correct trigonometric equation iswritten, but no further correct work is shown.or [1] 117.6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[274] C

[275]

[4] 10 and y x− = − −1 34

2( ) or an equivalent

equation, and appropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Appropriate work is shown, but oneconceptual error is made in determining thedistance or the equation of the line.or [2] The length, the midpoint, and the slopeof AB are found correctly, but no equation oran incorrect equation is given for theperpendicular bisector.or [2] Only a correct equation of theperpendicular bisector is found.[1] The correct distance is found, but noattempt is made to find the equation of theperpendicular bisector.or [1] The midpoint and slope of AB arefound correctly, but no further correct work isshown.or [1] The slope of AB and the slope of theperpendicular bisector are calculatedcorrectly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[276] D

[277] D

[278]

[2] 20,349, and appropriate work is shown,such as 21 5 20 349C = , .[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as determiningthe value of 21 5P .or [1] 20,349, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[279]

[2] 8, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 8, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[280]

[3] 345, and appropriate work is shown, suchas solving the inequality 1450 500 000x > , ,solving an equation, or trial and error with atleast three trials and appropriate checks.[2] Appropriate work is shown, but onecomputational or rounding error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct inequality or equation iswritten, but no further correct work is shown.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 345, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[281] C

[282] B

[283] A

[284] D

[285] C

[286] B

[287]

[4] 114" (9 feet 6 inches) and 37" (3 feet 1inch) and appropriate work is shown, such as

sin cos7210

7210

°= °=x and y or use of the

Pythagorean theorem.[3] An incorrect diagram is drawn, butappropriate work and an appropriate solutionfor that diagram are shown.or [3] Appropriate work is shown, but theanswers are rounded to the nearest foot andthen converted to inches, arriving at 120" and36".or [3] The setup is correct, but the answers arenot converted to the nearest inch.[2] One correct dimension is shown, such as114" (9 feet 6 inches) or 37" (3 feet 1 inch).or [2] Only one error involving interchangingsine and cosine is made.or [2] An incorrect diagram is drawn, and thesolution is appropriate for the diagram but isnot rounded to the nearest inch.[1] The student switches sine and cosine anddoes not round to the nearest inch.or [1] The student uses the correcttrigonometric function to compute one sidecorrectly but does not convert it to the nearestinch.or [1] 114" (9 feet 6 inches) and 37" (3 feet 1inch) but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[288]

[2] 6, and a correct tree diagram is drawn orsample space is listed.[1] A correct tree diagram is drawn or samplespace is listed, but no answer or an incorrectanswer is found.or [1] An appropriate answer is found, basedon an incorrect tree diagram or sample space.or [1] 6, but no tree diagram is drawn orsample space is listed.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[289]

[2] 319, and appropriate work is shown.[1] A correct proportion is shown, but nosolution or an incorrect solution is found.or [1] An incorrect proportion of equaldifficulty is solved appropriately.or [1] Appropriate work is shown, but onecomputational error is made.or [1] 319, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[290] D

[291] C

[292]

[4] The student draws a histogram, a stem-and-leaf plot, or any other acceptablestatistical graph, with proper labels and a title.[3] The student makes one or two minorerrors, such as a lack of label, title, orconnected dots.[2] The student makes several minor errors orone major error, such as not accounting for all20 scores.[1] The student draws just the beginning of agraph.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[293] D

[294]

[3] Jerry, and appropriate work is shown,such as the following explanation: Jerrytraveled 7 miles at a rate of 5 miles per hour

and his time was 125

hours; Jean traveled 5

miles at a rate of 3 miles per hour for a time

of 123

hours.

[2] The time for each jogger is calculatedappropriately, but an error is made indetermining one of the distances, but anappropriate answer is found.or [2] The time for each jogger is calculatedcorrectly, but the question of which personreached C first is not answered.or [2] Both distances are calculated correctly,but an error is made in determining times, butan appropriate answer is found.[1] Only the distances are calculatedcorrectly. No answer to the question is foundor an answer is found based on distance only.or [1] The time for only one jogger iscalculated correctly, and the question ofwhich person reached C first is not answered.or [1] The time for both joggers is calculatedappropriately, but multiple computationalerrors are made.

or [1] Jerry and 125

hours and 123

hours, but

no work is shown.[0] Jerry, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[295] D

[296] D

[297] C


[298]

[4] 112.5, and appropriate work is shown,such as solving the equation 5 20 50x x− = + .[3] Appropriate work is shown, but onecomputational error is made.or [3] m BED∠ = 67 5. or m AEC∠ = 67 5. , butno further correct work is shown.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, but an appropriatemeasure for ∠CEB is found.or [2] A correct equation is written and solvedfor x, but no further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] 112.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[299]

[2] Kerry is incorrect and an explanation isgiven that the original area is 24 2ft and thearea of the rose plot is 6 2ft , which is not halfof 24 2ft .or [2] Kerry is incorrect and an explanation isgiven that since the original area is 24 2ft ,the area of the rose plot should be 12 2ft , sothe new dimensions should multiply to 12,such as 3 4 4 3 2 6 2 6× × × ×, , , .or [2] Kerry is incorrect and a diagram is usedto show the original area is 24 2ft and thearea of the rose plot is 6 2ft .[1] Kerry is incorrect but the work or diagramshows one error.or [1] Appropriate work is shown, but theincorrect conclusion is found.[0] Kerry is incorrect or correct but noexplanation is given.

or [0] Kerry is correct and 12

4 2( ) = or

12

6 3( ) = is shown.

or [0] Kerry is correct and the student uses theperimeter.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[300] C

[301] D

[302]

[2] 6, and appropriate work is shown, such as0.70x + 0.30 ≤ 5.00 or trial and error withthree trials and appropriate checks.[1] The inequality is solved correctly, but thenumber of doughnuts is not found.or [1] The trial-and-error method is used tofind a correct solution, but fewer than threetrials are shown.or [1] 6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[303] D

[304]

[2] 10, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] Appropriate work is shown, but thelength of the ladder is found.or [1] 10, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[305]

[3] 48100

or any equivalent fraction or 0.48 or

48% and appropriate work is shown, such as

on Monday 210

have power, 810

lost power;

on Tuesday 12

810

410

( ) = have been restored,

therefore 210

410

610

+ = have power; on

Wednesday 210

lose power, therefore

( )( )810

610

48100

= have power.

[2] Appropriate work is shown, but onecomputational error is made, leading to afractional answer.or [2] One error of having or losing power is

made, such as taking 20% of 410

.

[1] Appropriate work is shown, but multiplecomputational errors are made.or [1] The correct answer is found, but nowork is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[306]

a [1] Either (x – 2)(x + 1)(2x) = V or the sameexpression without “= V” is shown.or [1] 2 2 43 2x x x− − or an equivalentexpression is shown.b [1] 864or [1] The student substitutes appropriatelyinto an incorrect part a equation.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[307] D

[308] C

[309] B


[310]

[4]A correct circle graph is drawn andlabeled, and appropriate work is shown, suchas using proportions. [A correct graph willshow 150° for brown, 120° for black, 60° forblond, and 30° for red.][3] Appropriate work is shown, but onecomputational error is made, but anappropriate graph is drawn.or [3] Appropriate work is shown, but onegraphing error is made.or [3] Appropriate work is shown and acorrect graph is drawn, but the sectors are notlabeled or are labeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made, but anappropriate graph is drawn.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] Correct numbers of degrees or correctproportional values are found, but two ormore graphing errors are made.or [2] Correct numbers of degrees or correctproportional values are found, but no graph isdrawn.or [2] A correct circle graph is drawn andlabeled, but no work is shown.[1] Appropriate work is shown and a graph isdrawn, but two or more computational errorsand two or more graphing errors are made.or [1] At least two numbers of degrees orproportional values are found correctly, butno graph or an incorrect graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[311]


as ( ) ( ).12

13 12

10 242π − ⋅ ⋅

[3] Appropriate work is shown, but onecomputational or rounding error is made orthe answer is expressed in terms of π .or [3] Appropriate work is shown, but thearea of the entire circle is used to calculate thearea of the shaded region.or [3] The areas of the semicircle and triangleare found correctly, but they are notsubtracted to find the shaded area.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] An incorrect formula is used to find thearea of the triangle or the semicircle, but anappropriate shaded area is found.or [2] Only the area of the semicircle or thearea of the triangle is found correctly, and nofurther correct work is shown.[1] Both the areas of the semicircle and thetriangle are found incorrectly, but they aresubtracted to find an appropriate shaded area.or [1] Only the length of AC is foundcorrectly.or [1] 145, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[312]

[4] Width = 20 and length = 25 and anappropriate algebraic equation is shown, suchas x x2 5 500 0+ − = .[3] A correct quadratic equation is shown, butone error is made.or [3] A correct quadratic equation is shown,but solved for only one dimension.[2] An appropriate solution is shown, but thestudent fails to reject the negative root andfinds two sets of dimensions.or [2] The quadratic equation (5x)(x) = 500 issolved appropriately for both dimensions, x =10 and 5x = 50.[1] The student writes only the correctquadratic equation or only the equation x(x +5) = 500 or fails to solve the equationcorrectly.or [1] The student writes a linear equationfrom x(x + 5) = 500, such as 2x + 5x = 500,but solves that equation appropriately.or [1] A correct equation is shown for theperimeter and solved appropriately.or [1] (5x)(x) = 500 is solved correctly foronly one dimension.or [1] 20 and 25 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[313]

[2] The four correct lines of symmetry aredrawn.[1] At least two correct lines of symmetry aredrawn, and no inappropriate lines are drawn.or [1] All four correct lines of symmetry aredrawn, but one or more inappropriate lines arealso drawn.[0] At least one of the correct lines ofsymmetry is missing, and one or moreinappropriate lines are drawn.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[314] D

[315] C

[316]

[4] (3,14) and (–2,–1) and either an algebraicor a graphic solution is shown.[3] An appropriate method is shown, but onlyone correct ordered pair is identified.or [3] An appropriate method is shown, butone computational mistake is made.or [3] An appropriate method is shown, butvalues are given only for x.[2] The substitution is correct, but thequadratic produced is not factored correctly.or [2] Both equations are graphed correctly,but neither ordered pair is identified.[1] Only one equation is graphed correctly.or [1] The substitution is incorrect, but itproduces a linear equation that is solvedcorrectly.or [1] Only the substitution is correct.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[317]

[3] 78.5 square feet or 25π or an equivalentanswer, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but themeasure of one side of the square is used asthe radius of the circle.or [2] Appropriate work is shown, but theperimeter is used to find a side of the square.[1] The correct length of the side of thesquare is shown, but further work is missingor is incorrect.or [1] The equation for the circumference ofthe circle instead of the equation for the areaof the circle is solved appropriately.or [1] Appropriate work is shown, but morethan one error is made.or [1] 78.5 square feet or 25π , but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[318] A


[319]

[4] 2,050, and appropriate work is shown,such as finding the length of one side of thefield, finding the perimeter, and calculating(2.50 • 800) + 50.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but theinstallation fee is not added to the cost of thefencing.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] 2,050, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[320] B

[321] A

[322]

[2] 24 feet and appropriate work is shown,

such as 1015

16=

x or = 10

1615

=x

.

[1] An appropriate proportion is shown, butan incorrect solution or no solution is found.or [1] An incorrect proportion of equaldifficulty is shown, but an appropriatesolution for the proportion written is found.or [1] 24 feet but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[323] C

[324] B

[325]

[2] 2.1, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 2.1, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[326] C

[327] B

[328] A

[329] D

[330]

[2] 72 and an appropriate method, such as3 6 4× × , is shown.[1] 72 and no explanation is given.or [1] An appropriate method is shown, butthe student has one computational mistake oran incomplete listing, such as 2 of the 3clothing categories.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[331]

[3] Option 2 will yield 82,576,000 morepossibilities, and appropriate work is shown,such as 26 103 4• and 26 4 10 3P P• .[2] Appropriate work is shown, but onecomputational error is made, but theappropriate option is identified.or [2] The correct numbers of arrangementsare found for both Option 1 and Option 2, butthe question of which option will yield morearrangements is not answered or is answeredincorrectly.[1] Appropriate work is shown, but more thanone computational error is made, but theappropriate option is identified.or [1] Appropriate work is shown, but oneconceptual error is made, but the appropriateoption is identified.or [1] Either Option 1 or Option 2 is foundcorrectly, but no further correct work isshown.or [1] Option 2 will yield 82,576,000 morepossibilities, but no work is shown.[0] Option 2, but no work or inappropriatework is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[332] B

[333] A

[334] D

[335] D

[336] C

[337] C

[338] B

[339] A

[340] A

[341] A

[342]

[2] (5,1), and appropriate work is shown, such

as a graph using the slope or 2 12

=−x and

3 52

=+y .

[1] Both (2,3) and (-1,5) are plotted correctly,but one graphing error is made in finding theother endpoint.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but only x= 5 or y = 1 is found.or [1] Appropriate work is shown, and thecorrect endpoint is designated, but thecoordinates are not stated.or [1] (5,1), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[343]

a [1] A correct tree diagram or listing of all 8possibilities is shown.

b [1] 18

or [1] An appropriate answer is given for anincorrect part a tree diagram or listing.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[344] B

[345] A

[346]

[2] 210, and appropriate work is shown, suchas 7 • 6 • 5 or 7 3P .[1] Appropriate work is shown, but no answeror an incorrect answer is found.or [1] 210, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[347] D


[348] D

[349] D

[350] C

[351]

[3] 3, and appropriate work is shown, such asusing a 3:4:5 right triangle, correctproportions, or the Pythagorean theorem witha proportion.[2] Appropriate work is shown, and the valueof the side is determined to be 5, but n = 3 isnot found.[1] A correct proportion is set up, but noanswer or an incorrect answer is found.or [1] 3, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[352] D

[353] D

[354] C

[355] A

[356]

[2] 2.8, and appropriate work is shown, suchas 3 12 2 2= + ( ) .BC[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The length of BD is found to be 3, butno further correct work is shown.or [1] 2.8, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[357]

[3] 12 and the equation tan x = 4202000

= .21 is

shown.or [3] 12 and the Pythagorean theorem and anappropriate trigonometric function arecorrectly used.[2] Tan function is correctly used, but theanswer is not rounded, such as 11.859.or [2] The setup is correct, but onecomputational mistake is made, and anappropriate angle is found.or [2] The answer is incorrectly expressed,such as tan x = 12.[1] The tan function is set up correctly, butthe angle is not computed.or [1] 12 and no work is shown.

or [1] 12 and sin x = 4202000

is used.

or [1] 78 and cos x = 4202000

is used.


[358] A

[359] A

[360]

[2] 78.6%, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 78.6%, but no work is shown.[0] A zero response is completely incorrect,irrelevant, incoherent or is a correct responsethat was obtained by an obviously incorrectprocedure.


[361]

[2] The student draws a parallelogram, whichis not a rectangle, with four sides and fourangles labeled, such as angles of 60, 120, 60,and 120 and sides of 4, 6, 4, and 6.[1] A parallelogram or rhombus, not a square,is drawn, which does not have measures forall lengths or angles.[0] Angles and/or lengths are not appropriatefor a parallelogram.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[362] B

[363] A

[364]

[2] y x= −2 3 or an equivalent equation, andappropriate work is shown, or an appropriateexplanation is given, such as the slope is 2and the y-intercept is -3.[1] y x= −2 3, but the slope and intercept areincorrect, or the explanation is not given or isincorrect, such as m = 2 and b = -3.or [1] The slope and intercept are explainedcorrectly, but the equation is incorrect.or [1] y x= −2 3, but no work is shown andno explanation is given.[0] The equation is incorrect, and theexplanation of slope and intercept is not givenor is incorrect.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[365] A

[366]

[3] 2.6, and appropriate work is shown, suchas ( ) ( ) .5 5 5 7 7• • = • h[2] Appropriate work is shown, but onecomputational or rounding error is made.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect formula.or [1] The volume of both of the cubes isfound correctly, but no further correct work isshown.or [1] 2.6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[367] C

[368] B

[369] A

[370] B

[371]

[4] All lines are graphed and labeled correctlyand area = 10, and appropriate work is shown.[3] The lines are graphed and labeledcorrectly, but the area of the triangle ismissing or is incorrect.or [3] One of the lines is graphed incorrectly,but the area for the given triangle is foundappropriately.[2] One of the lines is graphed incorrectly,and the area of the triangle is missing or isincorrect.[1] Only one line is graphed and labeledcorrectly, and no further correct work isshown.or [1] All three lines are graphed incorrectly,but the area for the given triangle is foundappropriately.or [1] Area = 10, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[372] A

[373] D

[374] C

[375]

[4] 7 98 106. × or 7,980,000 and appropriatework is shown, such as 8 10 2 106 4× − × .[3] Appropriate work is shown, but onecomputational error is made.or [3] The student uses 1–9 instead of 0–9 asthe number of digits in 8 9 2 96 4× − × .[2] The student correctly produces only onepart, 8 106× or 2 104× , but carries theprocess to an appropriate result.or [2] Appropriate work is shown, but morethan one error is made.[1] The student produces only one part, 8 96×or 2 94× .or [1] 7,980,000 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[376] A

[377] D

[378]

[2] A correct stem-and-leaf plot is drawn,including a key.[1] The data are arranged correctly, butincorrect labels are written on the stem-and-leaf columns. [Columns do not need to belabeled for a full-credit response, but fullcredit may not be awarded if the columns arelabeled incorrectly.]or [1] The data are listed in the stem-and-leafplot, but not in ascending order.or [1] One or two of the scores are left out ofthe stem-and-leaf plot.or [1] Duplicate values are left out of thestem-and-leaf plot.[0] Incorrect labels are written on the stem-and-leaf columns, and scores are left out ofthe plot.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[379]

a [2] An appropriate equation or system isshown, such as x + y = 148 and 12x + 9y =1410 or one equation such as 12(148 - x) + 9x= 1410 with variables identified.[1] The student shows appropriateequation(s), but variables are not defined.or [1] One mistake in equation(s) is made, oronly one equation with two variables isshown, but variables are defined.b(1) [1] 26 and an appropriate method isshown, such as solving the equation ormaking a table.or [1] An appropriate answer is found basedon incorrect equation(s) obtained in part a.b(2) [1] 122 and an appropriate method isshown, such as 148 - 26.or [1] An appropriate answer is found basedon incorrect equation(s) obtained in part a.b (l) and b (2) [1] 26 and 122 and no work isshown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[380] D


[381] C

[382]

[3] 10.6 and the Pythagorean theorem,C2 2 28 7= + , or any other appropriate methodis shown.[2] Appropriate work is shown, but theanswer is left as 113 or is roundedincorrectly.or [2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but multipleerrors are made.or [1] The only correct work shown is acorrectly drawn diagram with three distanceslabeled.or [1] 10.6 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[383] A

[384] B

[385] A

[386] D

[387] C

[388]

[2] A correct construction is drawn to find themidpoint of BC , showing both sets of arcsand a line connecting A with the midpoint.[1] A correct construction is drawn to find themidpoint of BC , but the median is not drawn.or [1] The construction is appropriate, but acompass and a straightedge are not used.[0] No construction arcs are shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[389] B

[390] A

[391]

[3] 47, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational or rounding error is made.or[2] The correct numerical value of the volumeof the cup ( 20π or its equivalent) and thevolume of the tank (3,000) are shown, but thesolution is not completed.[1] The correct volume of only the cup oronly the tub is shown.or[1] 47, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[392] C

[393] B


[394]

[4] S U N' ( , ), ' ( , ), ' ( , ),0 6 3 5 3 0− − and thecorrect graphs of both triangles are shown.[3] The correct graphs of both triangles areshown, but the coordinates of ΔS U N' ' ' arenot stated correctly.or [3] ΔSUN is graphed and labeledcorrectly, and the coordinates of ΔS U N' ' ' arestated correctly but not graphed correctly.or [3] The coordinates of ΔS U N' ' ' aregraphed and stated correctly, but ΔSUN isnot graphed or labeled.or [3] ΔSUN is graphed incorrectly, but thegraph and the coordinates of ΔS U N' ' ' areappropriate, based on that error.[2] ΔS U N' ' ' is graphed correctly, but thecoordinates of ΔS U N' ' ' are not stated, andΔSUN is not graphed.or [2] ΔSUN is graphed and labeledcorrectly, but ΔS U N' ' ' is reflected in the x-axis, and the coordinatesS U N' ( , ), ' ( , ), ' ( , )0 6 3 5 3 0− − are stated.or [2] ΔSUN is graphed incorrectly, butΔS U N' ' ' is graphed appropriately, based onthat error, but the coordinates of ΔS U N' ' ' arenot stated.[1] ΔSUN is graphed and labeled correctly,but no other work or completely incorrectwork for ΔS U N' ' ' is shown.or [1] ΔS U N' ' ' is graphed correctly, but thecoordinates of ΔS U N' ' ' are not stated, andΔSUN is not graphed or is graphedincorrectly.or [1] S U N' ( , ), ' ( , ), ' ( , ),0 6 3 5 3 0− − but nowork or graph is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure. [395]

[4] Length of ladder =11 and distance fromthe base of the ladder to the wall = 4, andappropriate work is shown, such as using sineand then tangent or the Pythagorean theorem.[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown, but thecorrect answers are not labeled or are labeledincorrectly.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as using oneincorrect trigonometric ratio.or [2] Appropriate work is shown, but onlythe length of the ladder or the distance fromthe base of the ladder to the wall is found.or [2] Two correct trigonometric equationsare written, but no further correct work isshown.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] Only one correct trigonometricequation is written, and no further correctwork is shown.or [1] Length of ladder = 11 and distancefrom the base of the ladder to the wall = 4, butno work is shown.[0] Length of ladder = 11 or distance from thebase of the ladder to the wall = 4, but no workis shown.or [0] 11 and 4, but no work is shown, and thesolutions are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[396] B

[397] D


[398]

[2] 3(x + 7)(x - 2), and appropriate work isshown.[1] Appropriate work is shown, but onecomputational error is made.or [1] A conceptual error is made, such asincomplete factoring.or [1] 3(x + 7)(x - 2), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[399] C

[400] B

[401] A

[402] A

[403]

[3] Mean = 79, median = 79, and mode = 78,and appropriate work is shown.[2] Appropriate work is shown, but only twoof the three measures of central tendency aredetermined and identified correctly.or [2] Appropriate work is shown and allthree measures of central tendency aredetermined correctly, but the measures are notidentified or are identified incorrectly.[1] Appropriate work is shown, but only oneof the three measures of central tendency isdetermined and identified correctly.or [1] Mean = 79, median = 79, and mode =78, but no work is shown.[0] 79, 79, and 78, but no work is shown, andthe answers are not identified or are identifiedincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[404] A

[405] D

[406]

[4] 260, and appropriate work is shown, suchas applying the appropriate area formula,

or A bh=12

or A h b b= +12 1 2( ), to find the

length of AE and using the Pythagoreantheorem or stating the Pythagorean triple todetermine AB.[3] 300, because BE is added to theperimeter.or [3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Only AB and AE are determinedcorrectly.[1] Only AB or AE is determined correctly.or [1] 260, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[407] B

[408] C

[409] B

[410]

a [2] The student draws a circle with its centerat (0,0) and a radius of 3.[1] The student draws a circle, but it has anincorrect center or radius.b [2] 28, and appropriate work or theexpression 9π is shown, which rounds to 28.or [2] An appropriate area is shown for theincorrect figure in part a.[1] The correct expression is shown, but theanswer is left as 9π , not rounded, or notrounded correctly.or [1] An incorrect radius is used, but the areais rounded appropriately.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[411]

[2] 75, and appropriate work is shown, suchas 3x + 15 = 4x – 5.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as showingAC and BD as congruent opposite sides.

or [1] A correct equation is written, but nofurther correct work is shown.or [1] A correct equation is written and solvedfor x, but the length of AC is not found.or [1] An incorrect equation of equaldifficulty, such as 3x + 15 + 4x – 5 = 180, issolved appropriately, and an appropriatelength of AC is found.or [1] 75, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[412] B

[413] A

[414] B

[415] A

[416]

[3] Yes, A' ' is (1,–3) and B' ' is (2,–1) andappropriate work is shown, algebraically orgraphically.[2] Correct coordinates for A' ' and B' ' arefound, but no conclusion is shown.or [2] Either A' ' or B' ' is correct, and anappropriate conclusion is shown.or [2] One transformation is correct and one isincorrect, such as the reflection in y, but anappropriate conclusion is shown.[1] Neither transformation is correct, but anappropriate conclusion is shown.or [1] One transformation is correct.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[417] D

[418] C

[419]

[3] $16,400, and appropriate work is shown,such as200 tickets sold at the door $32 = $ 6,400400 tickets sold in advance $25 = $10,000 $16,400[2] The correct number of tickets is shown,but one computational error is made incomputing the total amount of moneycollected.or [2] $6,400 and $10,000 are calculatedcorrectly, but they are not added to obtain thetotal.[1] The numbers of tickets, 200 and 400, arecalculated correctly.or [1] An appropriate solution is found, but itis based on incorrect numbers of tickets.or [1] $16,400, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[420]

[4] Correct cumulative frequencies of 7, 14,24, and 30 and a fully labeled correcthistogram are shown.[3] Incorrect cumulative frequencies areshown, but the histogram is appropriate forthe data.or [3] Correct cumulative frequencies areshown, but a partially incorrect histogram isshown, such as the axes not being labeled,having nonequal intervals, or the x-axisstarting at 50.[2] Only a frequency histogram is completedcorrectly.or [2] Only a correct cumulative frequencytable and a correct bar graph are shown.[1] An appropriate bar graph is shown, but itis based on frequencies, not the cumulativefrequency.or [1] Only a correct cumulative frequencytable is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[421] B

[422] A

[423] D

[424] D

[425] D

[426] D

[427]

[2] 42.85714286 or an equivalent answer, andappropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] An answer of 30 is found by dividing1.8 by 6.or [1] An answer of 70 is found by dividing4.2 by 6.or [1] 42.85714286 or an equivalent answer,but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[428] D

[429] C

[430] B

[431] A

[432] C

[433] B

[434] A

[435] C

[436] B

[437]

[4] $1.50 for one slice of pizza and $0.75 forone cola, and appropriate work is shown, suchas 3x + 2y = $6 and 2x + 3y = $5.25.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlythe price of one slice of pizza or the price ofone cola is found correctly.[2] Appropriate work is shown, but more thanone computational error is made.or [2] An incorrect system of equations ofequal difficulty is solved appropriately tocalculate the cost of one slice of pizza andone cola.[1] $1.50 for one slice of pizza and $0.75 forone cola, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[438] A


[439]

[3] Seth had 101, Jason had 51, and Raoul had104, and appropriate work is shown,such as x + 25 = (2x - 1) - 25 or trial and errorwith at least three trials and appropriatechecks.[2] Appropriate work is shown, but onecomputational error is made.or [2] 101, 51, and 104, and appropriate workis shown, but the solutions are not labeled orare labeled incorrectly.or [2] A correct equation is solved, but thenumber of CDs for only one boy is found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, but an appropriatenumber of CDs is found for each boy.or [1] A correct equation is written, but nofurther correct work is shown.or [1] Seth had 101, Jason had 51, and Raoulhad 104, but no work or only one trial with anappropriate check is shown.[0] Seth had 101 or Jason had 51 or Raoul had104, but no work is shown.or [0] 101, 51, and 104, but no work is shownand the solutions are not labeled or arelabeled incorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[440] D

[441] D

[442] D

[443] C

[444]

[2] 4, and appropriate work is shown, such asa Venn diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[445]

[4] $5 for the sprayer and $10 for thegenerator, and appropriate work is shown,such as x = hourly cost of sprayer and y =hourly cost of generator, and an appropriatesystem of equations is solved or a trial-and-error method is used, showing at least twotrials with appropriate checks.[3] Both correct equations are shown or anappropriate chart or trial-and-error method isused, but one computational error is made.or [3] Both correct equations are shown, andthey are solved for one value, but no furtherwork is shown.[2] Only one of the two equations is correct,but they are solved appropriately for bothvalues.or [2] Both correct equations are shown, butmore than one computational error is made.or [2] $5 for the sprayer and $10 for thegenerator, but only one trial is shown withappropriate checks.[1] Both equations are incorrect, but they aresolved appropriately for both values.or [1] Both correct equations are shown, butthey are not solved.or [1] $5 for the sprayer and $10 for thegenerator, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[446] A

[447] C


[448]

[4] 2 and –3, and a correct quadratic equationis shown, such as x(x + 1) = 6, and solvedalgebraically.[3] The student shows a correct quadraticequation but makes one algebraic error andcarries it to solution or no solution for theequation generated.or [3] Correct work is shown, but only oneroot is found as the answer.[2] A correct quadratic equation is used, buttwo or more errors are made.or [2] An incorrect quadratic equation ofequal difficulty is shown and solvedappropriately.[1] The student cross multiplies but producesonly a linear equation that is solvedappropriately.or [1] 2 and –3, but no algebraic work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[449] C

[450] B

[451] A

[452] B

[453] D

[454] C

[455]

[3] 224

or an equivalent answer, and an

appropriate explanation is given orappropriate work is shown, such as a treediagram, sample space, or permutations.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but only anumerator or a denominator is determinedcorrectly.

or [2] 224

or an equivalent answer, but only

work for either the numerator or thedenominator is shown.[1] The probability of the tallest or theprobability of the shortest student being in theproper position is correct, such as .or [1] Only a tree diagram, sample space, orpermutations are shown.

or [1] 224


work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[456]

[3] 1,344, and appropriate work is shown,such as 8 • 7 • 6 • 4.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made, such as basing theanswer on ordering an appetizer and a soup,using 5 • 3 • 7 • 6 • 4.or [1] 1,344, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[457]

[3] 162, and appropriate work is shown.[2] The Pythagorean theorem is used correctlyto find the hypotenuse, but the result is notmultiplied by 6.or [2] Appropriate work is shown, but onecomputational or rounding error is made.[1] Appropriate work is shown, but more thanone computational or rounding error is made.or [1] 162, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[458] C

[459]

[2] A correct triangle with the longest side onPQ and a vertex at P is drawn, and threeappropriate arcs are shown.[1] A correct triangle is constructed on PQ ,but P is not a vertex.or [1] A correct triangle is constructed withno sides on PQ .[0] A triangle that is not congruent to thecorrect solution or a triangle with less thanthree arcs is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[460] A

[461] B

[462] B

[463]

[2] Bob, and appropriate work is shown, suchas using the distance formula to calculate thetwo travel times or setting up a proportion.[1] Appropriate work is shown, but onecomputational or conceptual error is made,but an appropriate answer is found.or [1] Appropriate work is shown, but noanswer or an incorrect answer is found.[0] Bob, but no work or inappropriate work isshown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[464] D

[465] D

[466] D

[467]

[3] $800, and appropriate work is shown,such as 0.15x + 50 = 170 or a table of valuesor trial and error with at least three trials andappropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but the $50per day is not included in his pay, resulting inan answer of $1,133.33.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] $800, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[468]

[2] 120, and appropriate work is shown, suchas 1 • 5 • 4 • 3 • 2 • 1.[1] Appropriate work is shown, but onecomputational error is made.or [1] 720 and 6 6P or 6! is shown.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[469] B

[470] C

[471]

a [3] A parabola is correctly graphed through(0,0), (1,5), (2,8), (3,9), (4,8), (5,5), and (6,0).[2] The correct table of values is shown but isnot graphed through the entire domain.or [2] The correct points are graphed but as abroken line graph not a curve.or [2] At least three values are correctlycalculated and graphed.[1] At least two of the values are correctlycalculated, and the student tried to graph allpoints.b [1] 3or [1] The correct time, x, for an incorrectgraph in part a is found.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[472] A

[473] C

[474] B

[475] D

[476] C

[477]

[3] 63, and appropriate work is shown, suchas 400 - (81 + 88 + 88) and determining thehighest and lowest possible scores remainingthat total 143.[2] Appropriate work is shown, but onecomputational error is made.[1] A total of 400 is shown, but oneconceptual error is made, such as 257 issubtracted, and then 143 is split into 72 and71, resulting in an answer of 71.or [1] Appropriate work is shown, but morethan one computational error is made.or [1] No answer or an incorrect answer isfound, but a list such as ___, ___, 81, 88, 88is shown.or [1] 63, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[478]

[2] 20, and appropriate work is shown, suchas (180 ÷ 0.9) - 180.[1] A partial answer is found, such as 200students are enrolled, but 180 is notsubtracted from the answer.or [1] An appropriate equation is shown, butone computational error is made, but 180 issubtracted.or [1] An answer of 18 is found by subtracting180 x 0.9 from 180.or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[479]

[4] y = 2x - 40, a correctly drawn graph with aslope of 2 and a y-intercept of -40, and 20,and appropriate work is shown.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] The equation and graph are correct, butthe breakeven point is missing or is incorrect.[2] Appropriate work is shown, but more thanone computational or graphing error is made.or [2] An incorrect equation is written, but anappropriate graph is drawn, and anappropriate breakeven point is identified.[1] An incorrect equation is written, but anappropriate graph is drawn, but the breakevenpoint is missing or is incorrect.or [1] A correct equation is written, but thegraph is incorrect, and the breakeven point isnot identified.or [1] y = 2x - 40 and 20, but no work isshown and no graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[480] C

[481] B

[482] A

[483] C

[484] B

[485] A

[486] D

[487] C

[488]

[2] xx+−

15

, and appropriate work is shown.

[1] Only one expression is factored correctly,such as (x + 5)(x + 1) or (x + 5)(x - 5), but anappropriate simplification is done.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[489]

[2] 23, and appropriate work is shown.[1] Appropriate work is shown, but no answeror an incorrect answer is found.or [1] 23, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[490]

[4] 3, 5, and 7, and appropriate work isshown, such as an appropriate quadraticequation or trial-and-error method.[3] An appropriate equation is written andsolved, but one computational error is made.or [3] An appropriate equation is written andsolved, but the even solutions are also listed.[2] An incorrect quadratic equation is shown,but it is solved appropriately.or [2] Integers are misrepresented, but thesubsequent quadratic equation is solvedappropriately.or [2] An appropriate equation is written andsolved, but more than one computational erroris made.or [2] The correct solution is given, but onlyone trial is shown with appropriate checkswhen a trial-and-error method is used.[1] A linear equation is solved appropriately.or [1] 3, 5, and 7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[491]

[3] 4 and an appropriate method is shown,such as calculating A at 6 mph and B at 2mph through arithmetic, formula, orextending the graph to 60 minutes.[2] The speeds of 6 and 2 are found but nottheir difference.or [2] Their difference is found but not inmiles per hour.[1] Only distances of 4.5 miles and 1.5 milesare found.or [1] The speeds found are incorrect but thenare subtracted appropriately.or [1] 3 times as fast and no appropriateexplanation is given.or [1] 4 and no appropriate explanation isgiven.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[492] A

[493] A

[494]

[2] $178.50, and appropriate work is shown,such as solving a proportion, using a table, ortrial and error with at least three trials andappropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] An appropriate proportion is set up, butno solution or an incorrect solution is found.or [1] An incorrect proportion is set up, but anappropriate solution is found.or [1] $178.50, but no work is shown or fewerthan three trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[495] A

[496] C

[497] B

[498] B

[499] A

[500] D

[501] D

[502] C

[503] B

[504]

[4] 116 and an appropriate method is shown.[3] An appropriate method is shown, but theanswer is left in an inappropriate form, suchas 116.2.or [3] An appropriate method is shown, but 3feet is not added, and the answer is left 113.or [3] Tangent function is used, butcomputational mistakes are made, but 3 feet isadded to the incorrect value and the answer isfound correctly.[2] An incorrect trigonometric function isused, 3 feet is added, and the answer isrounded correctly.or [2] Tangent function is used, butcomputational mistakes are made, and 3 feetis not added to an incorrect answer.[1] 116 and no work is shown.or [1] An incorrect trigonometric function isused, and 3 feet is added to the incorrectanswer, but the answer is rounded incorrectly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[505] B

[506] C

[507] B

[508] B


[509]

[3] Juliet and an explanation is given of howthe identification was reached, such as by anarrative or table.[2] One error is made in the logic statementsor the table, but appropriate results are found.[1] More than one error is made in the logicstatements or the table, but appropriate workis shown.or [1] Juliet but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[510] B

[511] A

[512] B

[513] C

[514] B

[515] A

[516] C

[517] C

[518] C

[519] C

[520]

[4] Two Xs are indicated at the intersectionsof the angle bisector and the parallel lines inthe correct sketch of the loci.[3] All loci are drawn correctly, but no Xs aredrawn to indicate the locations, or only one Xis drawn.or [3] The angle bisector is drawn correctly,but only one line is drawn parallel to thewalkway, but an X is indicated appropriately.[2] Only one correct locus is drawn, but Xsindicate the two appropriate locations of theintersection of the loci.[1] Xs are drawn in the correct locations, butno loci are shown.or [1] Only one correct locus is drawn, and noXs are indicated.or [1] Both loci are drawn incorrectly, but Xsare drawn on the appropriate points ofintersection.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[521] A


[522]

[4] m A m B and m C∠ = ∠ = ∠ =20 59 101, , ,and appropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made.or [3] A correct equation is written andsolved, and the correct measures for theangles are found, but they are not labeled orare labeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct equation is written and solvedfor x, but the measures of the angles are notfound.or [2] An incorrect equation of equaldifficulty is solved appropriately, and thethree angles are found.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1]m A m B and m C∠ = ∠ = ∠ =20 59 101, , ., butno work is shown.[0] m A or m B or m C∠ = ∠ = ∠ =20 59 101,but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[523]

[3] A correct graph is shown, and an answerbetween -6° and -2° is found.[2] A correct formula is used, and -4°C or anequivalent answer is found, but no graph isshown.or [2] An appropriate graph is shown, and thecorrect answer is marked, but it is statedincorrectly, such as 5°C instead of -5°C.or [2] An appropriate graph is shown, butanswers outside the given range are found.or [2] The line graph passes through at leastone correct point, and an appropriate answeris found.[1] The formula is used correctly, but theanswer is not in the range, and no graph isshown.or [1] An answer between -6° and -2° isfound, but no graph is shown.[0] A completely incorrect graph is shown.or [0] No graph is shown and the formula isused incorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[524] B

[525] A


[526]

a [2] The student writes an appropriate systemof equations, such as b = f + 100 and 4b + 12f= 3,056, and defines the variables.or [2] The student writes an appropriateequation, such as 4(100 + x) + 12x = 3,056,and defines the variable.[1] A correct equation or correct equations areshown, but the variables are not defined.or [1] One error is made in the setup, such asb+ f = 100.[0] The student only defines the variables.b [2] 266, and appropriate work is shown,using an algebraic solution or a correct trial-and-error method.or [2] Appropriate work is shown for anincorrect part a equation or system ofequations.[1] Work is shown, but the answer isinappropriate, such as $1,064.or [1] 266, but no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[527] D

[528] D

[529] C

[530]

[2] 44, and appropriate work is shown, suchas 0.8(200 - 145).[1] Appropriate work is shown, but onecomputational or conceptual error is made.or [1] 44, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[531] B

[532] A

[533]

[4] 36 T-shirts and 12 caps, and appropriatework is shown, such as an appropriate systemof equations or a correct trial-and-errormethod with at least two trials andappropriate checks.[3] Appropriate work is shown, but only thecorrect number of T-shirts or the correctnumber of caps is determined.or [3] One error is made, resulting in anincorrect number of T-shirts or caps, but thecorresponding number of the other item isdetermined appropriately.[2] An appropriate method is shown, but noanswer is found.or [2] The variables are represented correctly,and a correct equation or system of equationsis written, but the process is not completed.or [2] 36 T-shirts and 12 caps, but only onetrial and appropriate checks are shown.or [2] The variables are represented correctly,but an incorrect equation is written, but thesolution is completed appropriately.[1] 36 T-shirts and 12 caps, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[534] A


[535]

[3] 14 2 , and appropriate work is shown,such as using the Pythagorean theorem ordrawing a correctly labeled diagram thatshows the isosceles right triangle.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but theanswer is expressed as a decimal or theradical is not simplified.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but onecomputational error is made, and the answeris not expressed as a radical in simplest form.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 14, the side of the square is foundcorrectly, but no further correct work isshown.or [1] 14 2 , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[536]

[2] 21 and the student shows an appropriatesolution, such as the equation x + x + 1 + x +2 = 63 or trial and error.[1] Appropriate work is shown, but anincorrect answer is found.or [1] An incorrect equation is shown, but it issolved appropriately to find an answer, suchas x + x + 2 + x + 4 = 63.or [1] 21 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[537]

[4] A correct diagram is drawn, two X pointsare marked, a numerical 2 is given for theplaces to dig, and appropriate work is shown.[3] The diagram is correct including two Xpoints, but an incorrect answer or no answeris found.[2] One correct locus situation and oneincorrect locus situation are drawn, but theanswer is appropriate according to thediagram.or [2] Each locus situation is correctly drawn,but no X points are marked, and no numericalanswer is found.[1] Only one locus situation is correctlydrawn and an incorrect conclusion or noconclusion is shown.or [1] 2 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[538]

[2] 16, and appropriate work is shown, suchas the Pythagorean theorem, the Pythagoreantriple, or trigonometry.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] 16, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[539] A

[540] D


[541]

[2] 100 and an appropriate method is shown,

such as 360 – 300 = 60 degrees, which is 16

of the circle so 16

of 600 is 100.

[1] 100 and no explanation is given.or [1] An incorrect degree measure is used todevelop a fraction by which to multiply 600,obtaining an appropriate answer.or [1] A correct degree measure is used to

develop 16

.

or [1] 60 degrees is used, but an incorrectnumber of people is found.[0] Only 60 degrees is found.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[542]

[4] No, and an appropriate explanation is

given, such as P P( ) ( ) .15 656

2 1256

= < =

[3] One of the two probabilities is foundcorrectly, but one computational error is madein finding the other, but an appropriateconclusion is drawn, based on the valuesfound.or [3] Replacement is used to conclude

P P( ) ( ) .15 664

2 1264

= < =

or [3] The two probabilities are foundcorrectly, but no conclusion or the incorrectconclusion is drawn.[2] One of the probabilities is found correctly,but one computational error is made infinding the other, and no conclusion or theincorrect conclusion is drawn.[1] An appropriate method is used, such as atree diagram or sample space, but theprobabilities are not determined or aredetermined incorrectly.

or [1] P P( ) ( ) ,15 656

2 1256

= < = but no work

is shown.[0] No, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrectresponse that was obtained by an obviouslyincorrect procedure.

[543] D

[544] C

[545] B

[546] A

[547] B


[548]

[2] 70.92, and appropriate work is shown,such as a proportion.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 70.92, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[549]

[4] 410

and appropriate work is shown, such

as the following illustration or any othercorrect method:

[3] Appropriate work is shown, but onecomputational error is made.

or [3] Appropriate work and complement 610

are shown.or [3] Appropriate work is shown, but theanswer is incomplete.[2] 5 2C and the work is appropriate butincomplete.or [2] 10 but appropriate work is shown.or [2] A correct sample space or tree diagramis shown.[1] Incorrect work leading to 0 1≤ ≤fractionor 0 100≤ ≤percent is shown.

or [1] 410

but no work is shown.


[550]

[2] 20, and appropriate work is shown, suchas 3 360 14 12, ( ).÷ ×[1] Appropriate work is shown, but onecomputational error is made.or[1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[551]

[2] 3a(x – 3)(x + 3), and appropriate work isshown.[1] Appropriate work is shown, but onefactoring error is made, or the expression isnot factored completely.or [1] 3a(x – 3)(x + 3), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[552]

[4] One doughnut is $0.75 and one cookie is$0.60, and appropriate work is shown, such asa system of equations, trial and error with atleast three trials and appropriate checks, or atable.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlyone correct answer is found, or two correctanswers are found, but they are not identifiedclearly as doughnuts or cookies, or thedoughnuts and cookies are labeledincorrectly.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Two equations are written, one correctand one incorrect, but two appropriateanswers are found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Two correct equations are written, but nofurther correct work is shown.or [1] One doughnut is $0.75 and one cookieis $0.60, but no work or only one trial with anappropriate check is shown.[0] One correct equation is shown, and noanswer or only one appropriate answer isfound.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[553] B

[554] C

[555] B

[556] A

[557] A

[558]

[3] 65, and appropriate work is shown, suchas setting the given angles equal to each otherand determining the value of x to be 16, andcorrect substitution is shown.[2] The given angles are set equal to eachother, the correct value of x is determined, butno substitution is shown.or [2] The given angles are set equal to eachother, and substitution is shown, but onecomputational or substitution error is made.[1] The given angles are set equal to eachother, but no further work is shown.or [1] An incorrect equation is solvedappropriately, such as 5x – 15 + 2x + 33 =180.or [1] 65, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[559] A

[560] C

[561] C


[562]

[4] 836

or 29

or 2:9, and all three lines are

graphed correctly and the triangle’s area isshown to be 8 and the square’s area is shownto be 36.[3] The three lines are graphed correctly, butone area is incorrect, but the probability isappropriate, based on this error.or [3] The graphs and areas are correct, butthe probability is incorrect, based on onecomputational error.or [3] The three lines are graphed correctlyand both areas are calculated correctly, butthe probability is not found.or [3] One equation is graphed incorrectly,but the area is appropriate, based on thegraph, and the probability is appropriate,based on the areas.[2] The three lines are graphed correctly, butthe area of the smaller triangle is used, but the

probability is appropriate, such as 236

.

or [2] Two or three lines are graphedincorrectly, but the areas and the probabilityare appropriate.or [2] The lines are graphed correctly, but theareas are incorrect, but the probability isappropriate, based on the errors.[1] All graphs and the areas are incorrect, butthe probability is appropriate.

or [1] 836

or 29

or 2:9, but no work is shown.


[563] A

[564] B

[565] A

[566] C

[567] B

[568] A

[569] B

[570] A

[571] A

[572] A

[573] C

[574]

[3] –8 and 5 and appropriate work is shown,such as factoring or trial and error.[2] The student shows correct factoring into(x + 8)(x – 5) or correct use of the quadraticformula but finds only one correct value for x.[1] Correct factoring is shown, but no valuesare found.or[1] Incorrect factoring is shown, but twoappropriate values are found.or[1] Either –8 or 5 is arrived at by trial anderror.or[1] –8 and 5 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[575] A

[576] B

[577] B

[578] A

[579]

[2] A correct construction is drawn to find themidpoint of BC , showing both sets of arcsand a line connecting A with the midpoint.[1] A correct construction is drawn to find themidpoint of BC , but the median is not drawn.or [1] The construction is appropriate, but acompass and a straightedge are not used.[0] No construction arcs are shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[580] D

[581] B

[582] A

[583] A

[584] C

[585] D

[586]

[3] 5, and appropriate work is shown, such asthe equation 60 + 5x = 135 - 10x, or trial anderror with at least three trials and appropriatechecks, or a graph.[2] Appropriate work is shown, but onecomputational or graphing error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but more thanone computational or graphing error is made.or [1] 5, but no work or only one trial with anappropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[587] D

[588] C

[589]

[2] 1,225, and appropriate work is shown,such as solving an equation or writing anexplanation.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but theconversion from years to months is incorrect,but an appropriate solution is found.or [1] 1,225, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[590] A

[591] B

[592] A

[593] C

[594] B

[595] A

[596]

[2] 14 and 42, and appropriate work is shown,such as x + 3x = 56, a table, or trial and errorwith at least three trials and appropriatechecks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but onlyone of the two lengths is found.or [1] A correct equation is written andsolved, but the lengths are not stated.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 14 and 42, but no work or fewer thanthree trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[597]

[3] The circle is graphed correctly, andappropriate work shows that (5,–2) does notlie on the circle.[2] The circle is graphed correctly, but thework fails to show that (5,–2) does not lie onthe circle.[1] The circle is graphed incorrectly, but thelocation of (5,–2) is determined appropriately,based on the incorrect graph.[0] Yes or no, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[598] A


[599]

[4] The table is completed correctly, and anappropriate cumulative frequency histogramis drawn and labeled.[3] The table is completed correctly, but oneerror is made in drawing the cumulativefrequency histogram or one or more labelingerrors are made.or [3] The table is not completed correctly,but an appropriate cumulative frequencyhistogram is drawn, based on the table.[2] One error is made in completing the table,and one graphing error is made in drawing thecumulative frequency histogram.or [2] The table is completed correctly, butone conceptual error is made, such as drawinga frequency histogram or a cumulativefrequency bar graph.[1] The table is completed correctly, but nohistogram is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[600]

[3] 7, and appropriate work is shown or anappropriate explanation is given.[2] Appropriate work is shown, but onecomputational error is made.or [2] No answer or an incorrect answer is

found, but 14

of 28 and 13

of 21 are

calculated correctly to arrive at 14.[1] Appropriate work is shown, but more thanone computational error is made.or [1] No answer or an incorrect answer is

found, but 14

of 28 is calculated correctly to

arrive at 21.or [1] 7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[601] D

[602]


as a diagram or 122 75.=

x .

[1] Appropriate work is shown, but no answeror an incorrect answer is found.or [1] 45, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[603] B

[604] B

[605] A

[606] C

[607]

[3] 7,625 and 66.7%, and appropriate work isshown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Only the number of votes for candidateB is found correctly, but appropriate work isshown.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The percent of votes cast for candidateA is found correctly, but no further correctwork is shown.or [1] 7,625 and 66.7%, but no work isshown.[0] 7,625 or 66.7%, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[608] A

[609] B

[610] D


[611]

[2] 2 45

8 3 1 2 3, , . , ,π and appropriate

work is shown, such as converting each valueto a decimal equivalent.[1] All values are correctly converted todecimal equivalents, but the order is notindicated or is indicated incorrectly.or [1] One or two computational errors aremade in finding decimal equivalents, butthe appropriate order is indicated.or [1] Appropriate work is shown, but oneconceptual error is made, such as indicatingthe order from greatest to least.

or [1] 2 45

8 3 1 2 3, , . , ,π , but no work is

shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[612]

[4] ABCD and its image A’B’C’D’ aregraphed and labeled correctly and 29, andappropriate work is shown.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] A’B’C’D’ is graphed and labeledcorrectly and 29, but ABCD is not graphed.or [3] ABCD is graphed incorrectly, but anappropriate image is graphed and labeled, andan appropriate area is found.or [3] ABCD and A’B’C’D’ are graphedcorrectly and 29, but neither quadrilateral islabeled.[2] Appropriate work is shown, but two ormore computational or graphing errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as an incorrecttransformation, but the graphs are labeled,and an appropriate area is found.or [2] Both ABCD and A’B’C’D’ are graphedand labeled correctly, but the area is notfound.or [2] 29, and appropriate work is shown,such as using the distance formula andfinding the area, but neither ABCD norA’B’C’D’ is graphed.[1] Appropriate work is shown, but oneconceptual error and one computational orgraphing error are made.or [1] Either ABCD or A’B’C’D’ is graphedand labeled correctly, but no further correctwork is shown.or [1] 29, but no work is shown and no graphis drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[613] D


[614]

[4] Angelo is 66, Brandon is 26, and Carl is31, and appropriate work is shown, such assolving an equation or trial and error with atleast three trials and appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] 66, 26, and 31, and appropriate work isshown, but the solutions are not labeled or arelabeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] Carl is 31, and appropriate work isshown, but the ages of the other men are notfound.or [2] An incorrect equation of equaldifficulty is solved appropriately.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] Angelo is 66, Brandon is 26, and Carl is31, but no work or only one trial with anappropriate check is shown.[0] Angelo is 66 or Brandon is 26 or Carl is31, but no work is shown.or [0] 66, 26, and 31, but no work is shown,and the answers are not labeled or are labeledincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[615] D

[616]

[4] The student draws parallelogram ABCDcorrectly, identifies D(1,3), and justifies thecoordinates of D by using any appropriatemethod to show ABCD is a parallelogram.[3] The student draws parallelogram ABCDincorrectly but justifies D appropriately.or [3] The student draws parallelogramABCD correctly and identifies D(1,3), but thejustification is incomplete.[2] The student draws parallelogram ABCDcorrectly and identifies D(1,3), but nojustification is shown.[1] The student either draws parallelogramABCD correctly or identifies D(1,3)correctly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[617] B

[618] A

[619] D

[620] C

[621] D

[622] D

[623]

a [2] A correct circle is sketched with itscenter at (2,1) and a radius of 3 and the line2 8x y+ = is drawn.[1] Only one of the graphs is sketchedcorrectly.b [1] 2or [1] The correct number of intersections isfound, based on the incorrect graphs drawn inpart a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent of is acorrect response that was obtained by anobviously incorrect procedure.


[624]

[3] 59 or 59º, and appropriate work is shown,

such as 63 2565

=+ x or

56 + 72 + 67 + 61 = 256, 63 x 5 = 315, and315 – 256 = 59.[2] Appropriate work is shown, but onecomputational error is made.or [2] A value is chosen for Friday’stemperature that rounds to 63, such as 57 or61,but whose mean is not exactly 63, andappropriate work is shown.[1] A limited understanding of the concept ofthe mean is shown, such as the sum ofthe temperatures must be 315, but the giventemperatures are not subtracted.or [1] The correct mean of the four giventemperatures is calculated.or [1] 59 or 59º, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[625] A

[626]

[2] The points D and M are plotted, the graphof the line x = 3 is drawn, and its equation isstated.[1] One graphing error is made, but anappropriate equation is stated for the locus ofpoints.or [1] A correct graph is drawn, but theequation is not stated or is stated incorrectly.or [1] x = 3, but no graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[627] B

[628] A

[629]

[2] The statements 7 + 8 = 15 and “15 is notgreater than 16” are written or the explanationis given that the sum of any two sides of atriangle must be greater than the third side.[1] An explanation is written that includes areference to the triangle inequality, but theexplanation is not complete or an incorrectconclusion is stated.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[630] D

[631]

[2] 800900


appropriate work is shown, such as findingthe areas of the two squares, subtracting thearea of the smaller square from the area of thelarger square, and setting up a correct ratio.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as calculatingthe perimeters of the squares instead of theareas.

or [1] Appropriate work is shown, but 100900

or

an equivalent answer (the complement of thecorrect answer) is found.or [1] The areas of the squares are calculatedincorrectly, but an appropriate probability isfound.

or [1] 800900


work is shown.[0] The areas of the squares are calculatedcorrectly, but no probability is stated.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[632] D

[633] D


[634]

[3] Four 20-cent and eight 32-cent stamps,and appropriate work is shown, such as asystem of equations, or a linear equation suchas 2x(.32) + .20x = 3.36, or trial and errorwith at least three trials and appropriatechecks.[2] Appropriate work is shown, but onecomputational error is made, but appropriatequantities are found for each stamp.or [2] Appropriate work is shown, but thequantity for only one of the stamps is found.or [2] Appropriate work is shown, but thesolutions are not labeled or the labels arereversed.or [2] The trial-and-error method is used tofind correct solutions, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made, butappropriate quantities are found for eachstamp.or [1] The trial-and-error method isattempted, and at least six systematic trialsand appropriate checks are shown, but nosolution is found.or [1] An incorrect equation or system ofequations of equal difficulty is solvedappropriately for both solutions.or [1] A correct equation or system ofequations is written, but no further correctwork is shown.or [1] Four 20-cent and eight 32-cent stamps,but no work or only one trial with anappropriate check is shown.[0] Four and eight, but no work is shown, andthe solutions are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[635] B

[636] D

[637] C

[638] B

[639] A

[640]

[2] 5 and appropriate work is shown, such assubstituting $18.11 for p and solving theequation correctly, or trial and error with atleast three trials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 5, but no work or fewer than three trialswith appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[641] C

[642] B

[643] A

[644] B

[645] A


[646]

[3] Perimeter = 4x + 4 or 4(x + 1) and area =x x2 2 24+ − , and appropriate work is shown.[2] 4x + 4 and x x2 2 24+ − , and appropriatework is shown, but the answers are notlabeled or are labeled incorrectly.or [2] Appropriate work is shown, but onecomputational error is made.or [2] Area = x x2 2 24+ − , and appropriatework is shown, but the perimeter is not foundor is found incorrectly.or [2] The area and perimeter are representedcorrectly, but only one of them is expressed insimplest form.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Perimeter = 4x + 4, and appropriatework is shown, but the area is not found or isfound incorrectly.or [1] The area and perimeter are representedcorrectly, but neither is expressed in simplestform.or [1] Perimeter = 4x + 4 or 4(x + 1) and area= x x2 2 24+ − , but no work is shown.[0] Perimeter = 4x + 4 or area = x x2 2 24+ − ,but no work is shown.or [0] 4x + 4 and x x2 2 24+ − , but no work isshown and the answers are not labeled or arelabeled incorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[647]

[3] 27 and an appropriate method orexplanation is shown, such as

( )( )( )16

13

23

127

= of a cubic foot, thus 27

bricks needed or, in inches, 172864

27= . A

labeled drawing is an acceptable explanation.[2] An appropriate method for finding volumeis shown, but one computational mistake ismade.[1] Correct conversion into feet is shown.or[1] The volume of 64 cubic inches is found.or[1] 27 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[648] A

[649]

[2] 2, and appropriate work is shown, such asa Venn diagram, a listing, or an explanation.[1] Appropriate work is shown, but onecomputational or conceptual error is made.or [1] 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[650] D

[651] D

[652] C


[653]

[4] The inequalities x ≤ 10, y ≤ 12, and x + y≤ 16 are graphed and shaded correctly on thegiven set of axes.[3] All inequalities are graphed and shadedcorrectly, but one incorrect type of line(dashed or broken) is used.or [3] All three inequalities are graphedcorrectly, but one inequality is not shaded oris shaded incorrectly.or [3] The inequality x + y ≤16 is graphedcorrectly, but an error is made in graphingeither the horizontal or vertical line, but theyare shaded appropriately.or [3] Only two of the three inequalities aregraphed correctly, but all three are shadedappropriately.[2] All three inequalities are graphedcorrectly, but two are shaded incorrectly.or [2] Only two of the three inequalities aregraphed and shaded correctly.[1] Only one of the three inequalities isgraphed and shaded correctly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[654]

[2] Both correct lines of symmetry are drawn:one horizontal, one vertical.[1] Only one correct line is drawn.or [1] Two correct and one or two incorrectlines, such as the diagonals, are drawn.[0] More than two incorrect lines are drawn.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[655] B

[656] D

[657] C

[658] D

[659] B

[660] A

[661] D

[662] C

[663] C

[664] D

[665] D

[666] D

[667]

[3] A' (-2,0), B' (-1,7), and C' (-5,1) aregraphed, labeled, and stated correctly.[2] Appropriate work is shown, but onegraphing or labeling error is made.or [2] A' (-2,0), B' (-1,7), and C' (-5,1), but nograph is drawn.[1] Appropriate work is shown, but two ormore graphing or labeling errors are made.or [1] Appropriate work is shown, but oneconceptual error is made, such as reflectingover the x-axis.or [1] The three points are plotted correctly,but the coordinates A' , B' , and C' are notstated.[0] (-2,0), (-1,7), and (-5,1), but no furthercorrect work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[668] A

[669]

[2] 2 and an appropriate sketch of two circlesintersecting in two points is shown.[1] 2 and no sketch is shown.or [1] An appropriate sketch is shown,without indicating 2 as the possibilities.or [1] An appropriate number is found, basedon an inappropriate sketch.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[670]


as 15150

2=

x.

[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as expressing

the answer as 13

hour.

or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[671] B

[672]

[3] 1,095 and 1,209, and appropriate work isshown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but awhole-number solution is not found.or [2] 5% of CD cases is rounded to 58, but58 is added to or subtracted from 1,152appropriately.or [2] Appropriate work is shown, but onlyone correct solution is found.[1] Appropriate work is shown, but more thanone computational error is made.or [1] 5% of CD cases is rounded to 58, but58 is added to or subtracted from 1,152, butone computational error is made.or [1] 5% of 1,152 is found, but no furtherwork is shown.or [1] 1,095 and 1,209, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[673] A

[674] D

[675]

[4] 3 and –5, and appropriate work is shown,such as x(x + 7) = 5(x + 3) or trial and errorwith at least three trials and appropriatechecks for each solution.[3] Appropriate work is shown, but onecomputational or factoring error is made.or [3] Appropriate work is shown, but onlyone correct solution is found.or [3] The trial-and-error method is used tofind both correct solutions, but only two trialsand appropriate checks are shown for eachsolution.[2] Appropriate work is shown, but two ormore computational or factoring errors aremade.or [2] A correct quadratic equation is writtenand factored, but no further correct work isshown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but neithersolution is found.[1] A correct quadratic equation is written,but no further correct work is shown.or [1] 3 and –5, but no work or only one trialwith an appropriate check is shown.[0] 3 or –5, but no work or only one trial withan appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[676] C

[677] B

[678] A

[679] B


[680]

a [2] 10 and an appropriate tree diagram, list,sample space, or 5 3 10C = is shown.[1] 10 and no work is shown.or [1] An appropriate method is shown, butnot all 10 possible combinations are listed

b [1] 110

or [1] An appropriate answer is found for anincorrect response in part a.

c [1] 410

25

0 4or or .

or [1] An appropriate answer is found for anincorrect response in part a.a and b and c [0] A zero response iscompletely incorrect, irrelevant, or incoherentor is a correct response that was obtained byan obviously incorrect procedure.

[681]

a [2] 56, and appropriate work is shown, such

as tan A =64

or finding the hypotenuse and

then using sine or cosine or usingproportional sides of similar triangles.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The length of the hypotenuse is foundcorrectly, but no further correct work isshown.or [1] 56, but no work is shown.b [2] 12, and appropriate work is shown, such

as sin5615

=h .

or [2] An appropriate answer is found basedon an incorrect angle found in part a.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 12, but no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[682]


as 12 162 2 2+ = r , 50− =r s , and sin x = 1630

.

[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown to find r =20 and s = 30 and the trigonometric equation

sin x = 1630

is written, but it is not solved or is

solved incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function to find theangle.or [2] The lengths of rand s are foundcorrectly, but no further correct work isshown.or [2] Incorrect lengths are found for rand s,but the sine function is used correctly to findan appropriate angle.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The length of r is found correctly, butno further correct work is shown.or [1] 32, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[683] D

[684] C

[685] B


[686]


as solving the equation 10 59

32= −( ).F

[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Correct substitution is made into theequation, but no further correct work isshown.or [1] 50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[687] B

[688] A

[689] C

[690] B

[691]

[3] All three examples are illustrated underdivision correctly, such as2 0 2 4 2 4÷ − ÷ − ÷ −, , , and correctexplanations are given.[2] Only two of the three examples areillustrated and explained correctly.or [2] All three examples are illustratedcorrectly, but only one explanation is given oris correct.or [2] The division examples and explanationsare correct, but at most two incorrectexamples are also shown, such as examplesfor addition, subtraction, or multiplication.[1] The division examples and explanationsare correct, but more than two incorrectexamples are shown, such as examples foraddition, subtraction, or multiplication.or [1] All three examples are illustratedcorrectly, but no correct explanation is given.or [1] Only one correct example with acorrect explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[692] C

[693] B

[694] C

[695]

[4] (–3,–5) and (1,3), and appropriatealgebraic work is shown.[3] Appropriate algebraic work is shown, butx = –3 and x = 1 are given as the solution.or [3] Appropriate algebraic work is shown,but only one correct solution is given, such as(1,3).[2] (–3,–5) and (1,3), but a graphic solution isshown.or [2] Correct substitution and an algebraicequation set equal to zero are shown, but theresult is not factored, such as x x2 2 3 0+ − = .[1] Any correct substitution is shown, such as2 1 3 22x x x+ = + − .or [1] (–3,–5) and (1,3), but no algebraic workis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[696]

[2] ′A (0,-2) and ′B (4,-6) are stated, and anappropriate graph is drawn.[1] Only one endpoint, ′A or ′B , is graphedand stated correctly.or [1] Both endpoints are reflected in otherthan the x-axis, and the coordinates aregraphed and stated correctly, such as:y-axis ′A (0,2) and ′B (-4,6)y = x ′A (2,0) and ′B (6,4)Origin ′A (0,-2) and ′B (-4,-6)or [1] Both points ′A and ′B are statedcorrectly, but no graph is drawn.or [1] An appropriate graph is drawn, but nocoordinates or incorrect coordinates arelabeled.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[697] D


[698] D

[699] D

[700] D

[701]

[2] 29, and appropriate work is shown, suchas 92 – 63 = 29.[1] The correct application of the exteriorangle theorem is shown, but one or morecomputational errors are made.or [1] The correct application ofsupplementary angles and the sum of theangles of a triangle are shown, but one ormore computational errors are made.or [1] m BCA∠ is calculated incorrectly, butthe sum of the angles in a triangle is usedappropriately.or [1] 29, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[702]

[2] $390 or 390 and appropriate work isshown, such as a numerical table or theequation y = 30x + 90 or the expression 90 +30N.[1] Appropriate work is shown, but onecomputational error is made.or [1] $300 or 300 or a slope of 30 butappropriate work is shown.or [1] $390 or 390 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[703]

[2] 30, and appropriate work is shown or anappropriate explanation is given.[1] Angles of the equilateral triangle areshown to be 60°, but x is not determined or isdetermined incorrectly.or [1] 30, but no work is shown or noexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[704] C

[705]

a [3] The frequency table is completedcorrectly, and a histogram is drawn with acorrect scale and is labeled correctly.[2] One or two errors are made in thefrequency table, but an appropriate histogramis drawn.or [2] The frequency table is completedcorrectly, but one error is made in drawingthe histogram.[1] A correct histogram is drawn, but thefrequency table is not completed.b [1] The interval 91-100 is identified ascontaining the 75th percentile.or [1] The appropriate interval is identified,based on an incorrect frequency table in parta.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[706]

a [3] Two parallel lines, one 3 units above andone 3 units below AB , and a circle withits center at P with a radius of 5 units aredescribed correctly in words or drawn.[2] Only one parallel line 3 units above or 3units below AB and a correct circle aredescribed in words or drawn.or [2] Appropriate parallel lines are shown,but the circle is incomplete.[1] Both parallel lines and the circle haveincomplete descriptions or drawings.[0] Only one incomplete locus is described ordrawn.b [1] 4, and appropriate work is shown.or [1] An appropriate answer for an incorrectpart a is found.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrectresponse that was obtained by an obviouslyincorrect procedure.

[707] D


[708]

[3] 5-inch box and appropriate work is shown,including showing a diameter between 4 and5.[2] The correct diameter is shown, but thewrong box size is chosen.or[2] The correct radius is shown, but the 3-inchbox is chosen.[1] The correct diameter or radius is shown,but no box is chosen.or[1] An appropriate radius between 2 and 3 isshown, using the incorrect formula A r= π 2 ,and the 3-inch box is chosen.or[1] An appropriate diameter, using A r= π 2 ,is shown, but the appropriate box is chosen.or[1] An appropriate radius, using A r= π 2 , isshown, but no box is chosen.or[1] The 5-inch box is chosen, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[709] C

[710] B

[711] A

[712] C

[713] B

[714]

[4] 9.4, and appropriate work is shown, suchas the use of the Pythagorean theorem.[3] Appropriate work is shown, but onecomputational or rounding error is made.[2] Appropriate work is shown, but more thanone computational or rounding error is made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect diagonal of the base isfound, but an appropriate solution is found.or [2] Only the diagonal of the base is foundcorrectly, but appropriate work is shown, suchas 3 42 2 2+ = d or use of 3–4–5 righttriangles.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] The Pythagorean theorem is used tofind the length of the straw, but theappropriate legs are not used.or [1] 9.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[715] B

[716] A

[717] B

[718]

[2] 37,440 and appropriate work is shown,such as 2 x 26 x 10 x 9 x 8 or 2 1 26 1 10 3P P P× × .[1] Appropriate work is shown, but onecomputational or conceptual error is made.or [1] Appropriate work is shown for at leastone restriction, such as 2 x 26 or 10 x 9 x 8.or [1] 37,440 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[719] B

[720] A


[721]

[2] 20.7, and appropriate work is shown, such

as 141288683748 100

=x .

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 20.7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[722] C

[723] B

[724] D

[725] C

[726]

[3] 2,827.4, and appropriate work is shown,such as 50 402 2π π− .[2] The areas of both circles are foundcorrectly, but the two areas are not subtracted.or [2] Appropriate work is shown, but onecomputational error is made.[1] The correct area is found for only one ofthe circles.or [1] The circumference formula is used, butthe appropriate difference is shown, such as100 80 20π π π− = .or [1] 2,827.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[727]

[3] ΔABC and ΔA B C' ' ' , A’(–2,4), B’(0,12),C’(10,8), are graphed correctly.[2] ΔABC is graphed correctly, but only twoimage points are graphed correctly.or [2] ΔABC is graphed incorrectly, butΔA B C' ' ' , is graphed appropriately, based onan incorrect ΔABC .[1] Only ΔABC is graphed correctly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[728] B

[729] B

[730] A

[731] A

[732]

[4] $52,950, $35,300, and $88,250 and anappropriate method is shown, such as 3x + 2x+ 5x = $176,500.[3] A correct equation is set up or multiplied

by correct fractional values 310

, 210

, and 510

,

but a computational mistake is made, andthree appropriate values are found.or [3] An appropriate method is shown, butnot all three values are found.[2] The equation is set up correctly, butnumerous computational mistakes are made,and three appropriate values are found.or [2] An incorrect equation is shown, butthree appropriate values are found.or [2] An appropriate equation is shown but issolved only for x (17,650).[1] The equation is set up correctly, but noappropriate values are found.or [1] Three correct answers are found, andno work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[733] C


[734] C

[735]

[4] (10,0) and (1,9), and both graphs aredrawn correctly.[3] Both graphs are drawn correctly, but onlyone solution is stated correctly.or [3] One graph of equal difficulty is drawnincorrectly, but the solutions are appropriate,based on the graphs.[2] (10,0) and (1,9), but the problem is solvedalgebraically instead of graphically.or [2] One graph of equal difficulty is drawnincorrectly, and only one solution isappropriate, based on the graphs.[1] Both the parabola and the line are graphedincorrectly, but the solutions are appropriate,based on the graphs.or [1] Incorrect solutions result from analgebraic method.or [1] (10,0) and (1,9), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[736] C

[737] B

[738] A

[739] D

[740]

[2] 120, and appropriate work is shown, suchas m CDB∠ = − =180 130 150 andm CBA∠ = + =70 50 120 or correctly labeledangles in a diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] m CBD∠ = 60 is found, but no furthercorrect work is shown.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[741]

[4] 9, and appropriate work is shown.[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown, and theareas of the rectangle and one circle are foundcorrectly, but the area of the circle is notdoubled, but an appropriate number of bags isfound.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect formula for the area of a circle, butan appropriate number of bags is found.or [2] The areas of the rectangle and the circleare found correctly, but no further correctwork is shown.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] 9, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[742] A

[743] B


[744]

[2] 256, and appropriate work is shown, suchas finding the side of the square andcalculating the area.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but onlythe area of the circle is found.or [1] An incorrect value for the side of thesquare is determined, but an appropriate areais found.or [1] A correct value for the side of thesquare is determined, but the area is not foundor is found incorrectly.or [1] The area for the square inscribed in thecircle is found, resulting in an answer of 128.or [1] 256, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[745] B

[746] A

[747]

[3] 95 and an appropriate method is shownthat obtains an answer, such as 344 - 249 or asimilar equation or method.or [3] Four scores are tried that round off toan average of 86, such as 93 or 94. Round offto 86 must be shown.[2] An appropriate method is shown, but onecomputational mistake is made.[1] The student understands weighted averageand shows that the average of 83 for 3 tests isa total of 249 points.or [1] 95 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[748]

[2] 4.5 and an appropriate method is shown,such as the equation 3 2 20x x+ + = or sometrial and error or arithmetic process.[1] An appropriate method is shown, but thecorrect answer is not found.or [1] 4.5 and no work is shown.or [1] The student solves the equationx x+ − =3 2 20 and answers 5.5.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[749] A

[750] B

[751] A


[752]


as tan .5262

=x

[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] An incorrectly labeled diagram isdrawn, but the appropriate trigonometricfunction is used, and an appropriate answer isfound.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function or ratio.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] A correctly labeled diagram is drawn,but no further correct work is shown.or [1] A correct equation is written, but nofurther correct work is shown.or [1] An incorrectly labeled diagram isdrawn, but an appropriate equation is written,but no further correct work is shown.or [1] 79.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[753]

[4] 3, and an appropriate algebraic or graphicsolution is shown.[3] The equation is graphed correctly, but thetime to reach the ground is not identified.or [3] Appropriate work is shown for analgebraic solution, but either no solution isfound or the negative root is not rejected.or [3] An appropriate algebraic solution isshown, but one computational error is made.[2] The equation is graphed incorrectly, butan appropriate time to reach the ground isidentified.or [2] The equation is factored incorrectly, butan appropriate solution is found.[1] 3, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[754] B

[755] A

[756] B

[757] D

[758] D

[759] C


[760]

[3] No, it will not differ and the student showsthat both methods lead to $47.08, such as $55x .80 = $44, $44 x 1.07 = $47.08, $55 x 1.07= $58.85, and $58.85 x .80 = $47.08.[2] Both ways are computed, onecomputational mistake is made, and anappropriate answer is found.or [2] Both ways are computed correctly, butno comparison is found.[1] At least one way is computed correctly,but no comparison is found.or [1] Both ways are computed incorrectly,but an appropriate comparison is found.[0] Both ways are computed incorrectly, andno comparison is found.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[761] A

[762] D

[763] C

[764] C

[765]

[2] 1, and an appropriate explanation is given,such as when 1 is added to 3, the result is theidentity element, 4; therefore 1 is the inverseof 3.[1] 1 + 3 = 4, but the identity element is notidentified.or [1] 4 is identified as the inverse becausethe identity element and inverse element areconfused.or [1] 1, but no explanation or an incorrectexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[766]

[2] 6 23

or 6 hr 40 min or 6 66. or an

equivalent answer, and appropriate work isshown.[1] 400 min, but the answer is not convertedinto hours.or [1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but theanswer is rounded to the nearest hour.or [1] 6 or 6 hr 40 min or 6 66. or anequivalent answer, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[767]

[2] 5, and appropriate work is shown, suchas the distance formula, the Pythagoreantheorem, or a Pythagorean triple.[1] Appropriate work is shown, but onecomputational or graphing error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[768] B

[769] B


[770]

[3] 7, 11, 16, and yes, and appropriate work isshown, and an appropriate explanation of theTriangle Inequality theorem is given.[2] 7, 11, 16, and yes, and appropriate work isshown, but no explanation or an incorrectexplanation of the Triangle Inequalitytheorem is given.or [2] One computational error is made, butappropriate substitution is shown, and anappropriate explanation is given.or [2] The correct equation is written but notsolved, but the Triangle Inequality theorem isstated correctly.[1] Appropriate work is shown, and x = 4 isdetermined, but no further work is shown.or [1] The Triangle Inequality theorem isstated correctly but not evaluated for thesides, or the correct equation is written, butno further work is shown.or [1] 7, 11, 16, and yes, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[771] C

[772] B

[773] A

[774]

[2] $40, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] $40, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[775]

[2] 50, and appropriate work is shown, suchas using a proportion.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] An incorrect fractional part isdetermined, but an appropriate number ofstudents is found.or [1] 50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[776] C

[777] B

[778] A

[779]

[2] 10, and appropriate work is shown, suchas 5 2C or a diagram or a list.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 10, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[780] B

[781] A


[782]

[2] 20 and an appropriate explanation isgiven, such as the number cannot be writtenas a repeating or terminating decimal or itcannot be written as a fraction or it is not aperfect square.[1] 20 and an inappropriate explanation orno explanation is given.or [1] 20 and a correct explanation is given,but one other number is also identified asirrational.[0] All three numbers are identified asirrational.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[783] B

[784] A

[785]

[2] 22, 27 and 24.5, 24.5, or 22, 27, and 24.5,and appropriate work is shown, such as alabeled diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but onlyone of the two possible sets of numbers isfound.or [1] 22, 27 and 24.5, 24.5, or 22, 27, and24.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[786] D

[787]


as solving the equation sin .x = 37

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] A correct trigonometric equation iswritten, but no further correct work is shown.or [1] 25.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[788] B

[789] A

[790] D

[791]


as calculating ( )( )

36 1449 9××

or drawing a

labeled diagram.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but more thanone computational error is made.or[1] Appropriate work is shown, but oneconceptual error is made.or[1] 64, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[792] B

[793] A

[794] D


[795]

[3] 374 grasshoppers and 187 crickets, andappropriate work is shown.[2] An appropriate equation is solved orappropriate work is shown, but only onecorrect answer is found, or two correctanswers are found but they are not identifiedclearly as grasshoppers or crickets, or thegrasshoppers and crickets are labeledincorrectly.or [2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but more thanone computational error is made.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 374 grasshoppers and 187 crickets, butno work is shown.[0] 374 and 187, but no work is shown, andthe answers are not identified clearly asgrasshoppers or crickets.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[796] C

[797] B

[798] D

[799] D

[800] C

[801] B

[802] D

[803]

[2] 40, and appropriate work is shown, suchas a Venn diagram or (240 + 210) - 90 = 360and 400 - 360 = 40.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 40, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[804] D

[805]

[3] 3 hours and an appropriate method orequation is shown, such as 45(x + 1) = 60x.[2] An appropriate method is shown, but anincorrect answer is found, such as4 hours (the truck's time) or 180 milestraveled.[1] An appropriate equation or method isshown, but no answer is found, such asshowing an equation that reflects a one-hourdifference in time but it is not solved.or [1] 3 hours and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[806] B

[807] C

[808] B

[809]

[2] 12 and an appropriate explanation isgiven.[1| The student uses an appropriate method,

such as showing k −−

=2

3 15 or graphing of a

line through (1,2) having a slope of 5, but thecorrect answer is not found.or [1] 12 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[810]

[4] 16 and appropriate work is shown, such asW(W + 2) = 15.[3] Appropriate work is shown, but onecomputational error is made.or [3] L = 5, W = 3, and the perimeter = 16,but no work is shown.[2] Appropriate work is shown, but more thanone computational error is made.or [2] L = 5, W = 3, and appropriate work isshown, but the perimeter is not found.or [2] The length and width are incorrect, butthe perimeter is computed appropriately.[1] Length and width are appropriatelydefined in terms of a single variable.or [1] 16 but no work is shown.[0] L = 5 and W = 3 but no work is shown,and the perimeter is not found.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[811] A

[812] B

[813] B

[814] A

[815] A

[816] B

[817] A

[818]

[3] –7 and 4, and appropriate work is shown,such as factoring.[2] Correct factoring (x + 7)(x – 4) is shown,but only one correct value of x is found.or [2] Correct factoring is shown, but thenegative value of x is rejected.[1] Correct factoring is shown, but the valuesof x are not found.or [1] Incorrect factoring is shown, butappropriate values are found.or [1] Only one value is found by trial anderror.or [1] –7 and 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[819]

[4] (3,4) and (–3,–4), and a correct algebraicor graphic solution is shown.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] Appropriate work is shown for analgebraic or graphic solution, but only onecorrect ordered pair is found or the correctvalues are found only for x or for y.[2] Appropriate work is shown, but two ormore computational or graphing errors aremade.or [2] Both equations are graphed correctly,but neither ordered pair is identified.or [2] The line is graphed correctly, but thecircle is graphed as a semicircle, and only onecorrect solution is identified.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately, andan appropriate solution or solutions are found.or [2] The linear equation is graphed correctlyand correct points of the circle are graphed,but the points are connected to form aquadrilateral, but appropriate ordered pairsare identified.[1] Appropriate work is shown, but oneconceptual error and one computational orgraphing error are made.or [1] One equation is graphed correctly, butno further correct work is shown.or [1] An incorrect equation of a lesser degreeof difficulty, such as a linear equation, issolved appropriately, and an appropriatesolution or solutions are found.or [1] A correct quadratic equation is setequal to zero, but no further correct work isshown.or [1] (3,4) and (–3,–4), but no work isshown.[0] (3,4) or (–3,–4), but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[820] D

[821] C

[822] B

[823] A

[824]

[2] A correct construction is drawn, showingthe arcs intersecting above and below AB,and the perpendicular line is drawn.[1] All of the construction arcs are drawn, butthe perpendicular line is not drawn.[0] A drawing that is not an appropriateconstruction is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[825]

a [1] S + 243

or S3

8+

b [1] 11.5or [1] Correct substitution into an incorrectpart a is shown, and the answer is given to thenearest tenth of an inch.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[826]

[3] 5, and appropriate work is shown, such asthe quadratic equation (x + 7)(x - 3) = 24 ortrial and error with at least three trials andappropriate checks.[2] A correct quadratic equation is written,but one computational error is made infinding Tamara's age.or [2] 12 and 2 are found as the sisters' ages,but Tamara's age is not found.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct quadratic equation is written,but no further correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately for Tamara'sage.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 5, but no work or only one trial with anappropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[827] B

[828] D

[829] C

[830]

[3] 18, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, and thevalue of x is found, but no further correctwork is shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct expression is written for theperimeter of each figure, but no furthercorrect work is shown.or [1] 18, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[831] D

[832] C


[833]

[3] 109 meters and appropriate work is shownby using an appropriate trigonometric ratio,

such as tan 32175

°=y .

[2] 109 meters but one rounding error ismade.or [2] The student uses an appropriatetrigonometric function with an inverted ratio,

such as tan32 175°=

y, but completes the

calculation appropriately, such as showing280 meters.[1] The student uses an incorrecttrigonometric ratio but completes thecalculation appropriately.or [1] The student uses an inverted tangentratio and makes one computational orrounding error.or [1] The student uses the correcttrigonometric ratio but solves it incorrectly ordoes not solve it at all.or [1] 109 meters but no work or explanationis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[834] C

[835] B

[836] A

[837] A

[838]

[3] 50, and appropriate work is shown, suchas a Venn diagram.[2] Appropriate work is shown, but onecomputational error is made.or [2] 200, and appropriate work is shown tofind the number of students that have brownhair and/or brown eyes.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The numbers of students who havebrown hair only (40) and brown eyes only(70) are found, but no further correct work isshown.or [1] 50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[839] A

[840] B

[841] A

[842] B


[843]

[2] (-6,8) or -6,8 or x = -6 and y = 8 and anappropriate explanation is given, such asgraphing the line or doubling the coordinates.[1] One correct coordinate and one incorrectcoordinate are found.or [1] An appropriate method is shown, suchas algebraic or graphing, but computationalmistakes are made.or [1] (-6,8) or -6,8 or x = -6 and y = 8 and noexplanation is given.or [1] Substitutions are correct for themidpoint formula, but computational mistakesare made.or [1] The student properly locates point B onthe graph but does not state its coordinates.or [1] Point A and point M are reversed,resulting in B(3,-4), and an explanation isgiven.

[0] Only the midpoint of AM ( , )−32

2 is

found.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[844]

[2] 18 and correct substitution, F = 95

(-8) +

32, is shown.[1] A correct substitution method is shown,but one computational error is made.or [1] The answer is not rounded to thenearest integer, such as 17.6 or 17 .or [1] The student substitutes -8 for F, butthen solves appropriately for C.or [1] The student substitutes +8 for C, butthen solves appropriately for F.or [1] 18 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[845]

[2] 4 10 22x x+ + , and appropriate work isshown, such as ( ) ( ).9 3 4 5 7 62 2x x x x+ − − − −[1] The setup is correct, but the distribution ofthe negative sign is incorrect.or [1] 14 4 102x x− − , but appropriate work isshown.or [1] 4 10 22x x+ + , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[846]


as 64

24=

xor a labeled diagram.

[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] An incorrect proportion is written, butit is solved appropriately.or [1] 16, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[847] D

[848] D

[849]

[2] 24 miles and appropriate work is shown,such as using a proportion, showing doublingof the sides, or using any other appropriatemethod.[1] Appropriate work is shown, but onecomputational or substitution error is made.or [1] An incorrect proportion is appropriatelysolved.or [1] 24 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[850] B


[851]

[3] 150, and appropriate work is shown, suchas 5 2 6 2C C• .[2] Appropriate work is shown, but onecomputational error is made.or [2] All the possible combinations of twomystery books and all the possiblecombinations of two biographies arecalculated, but the answers are not multiplied.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as thecomputation 11 4 330C = .or [1] 150, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[852]

[4] $68,000, and appropriate work is shown.[3] $119,000 and $51,000, and appropriatework is shown, but the answers are notsubtracted to find the difference.or [3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.[1] The value for one share ($17,000) isfound, but no further correct work is shown.or [1] $68,000, but no work is shown.[0] $17,000 or $119,000 or $51,000, and nowork is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[853]

[3] 1.3 and appropriate work is shown, suchas calculating the circumference of the wheeland the length of the trail in feet, andconverting them to miles, such as2 11005

5280⋅ ⋅π . .

[2] The student correctly calculates thecircumference and length in feet but does notconvert them to miles.or [2] Correct calculations are shown, but theanswer is rounded incorrectly or is notrounded.or [2] Appropriate work is shown, but oneerror is made.[1] The correct circumference is calculated.or [1] Appropriate work is shown, but morethan one error is made.or [1] 1.3 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[854]

[4] 283.5 or 284 and appropriate work or anexplanation is shown, such as 4x + 12 = 96,21 27

2× , or trial and error.

[3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.or [2] 283.5 or 284 and only a check isshown.[1] Appropriate work is shown, but no answeris found.or [1] 283.5 or 284 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[855]

[4] 17 nickels and 15 dimes, and appropriatework is shown, such as the equation 0.05x +0.10(32 - x) = 2.35 or trial and error with atleast three trials and appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, and thecorrect answers are found, but they are notlabeled or are labeled incorrectly.or [3] Appropriate work is shown, but onlythe correct number of nickels or the correctnumber of dimes is found and labeled.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] An incorrect system of equations ofequal difficulty is solved appropriately forboth the number of nickels and dimes.or [2] A correct equation is solved for x, butno further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 17 nickels and 15 dimes, but no work oronly one trial with an appropriate check isshown.[0] 17 nickels or 15 dimes, but no work oronly one trial with an appropriate check isshown.or [0] 17 and 15, but no work is shown, andthe answers are not labeled or are labeledincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[856] C

[857] B

[858] A


[859]

[4] (-1,-2) and (2,13), and appropriate work isshown, such as an algebraic or graphicsolution or trial and error with at least threetrials and appropriate checks.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] Appropriate work is shown, but onlyone solution is found or only the x- or the y-values are found.[2] Appropriate work is shown, but two ormore computational or graphing errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind the correct solutions, but only two trialsand appropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] Both equations are graphed correctly,but neither ordered pair is identified.or [2] Only one equation is graphed correctly,but an appropriate solution is found.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately, andappropriate solutions are found.[1] Appropriate work is shown, but oneconceptual error and one computational orgraphing error are made.or [1] One equation is graphed correctly, butno further correct work is shown.or [1] An incorrect equation of a lesser degreeof difficulty, such as a linear equation, issolved appropriately.or [1] A correct substitution is made and thesystem of equations is simplified to a singlequadratic equation set equal to zero, but nofurther correct work is shown.or [1] (-l,-2) and (2,13), but no work or onlyone trial with an appropriate check is shown.[0] (-1,-2) or (2,13), but no work or only onetrial with an appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[860] B

[861] A

[862] D

[863]

[2] An irrational number is written, and anappropriate explanation is written, such as anirrational number cannot be written as afraction or as a repeating or terminatingdecimal.[1] An irrational number is written, such as πor the square root of a nonperfect square, butno explanation or an inappropriateexplanation is written.or [1] A correct definition of an irrationalnumber is written, but the example is missingor is inappropriate.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[864]

[2] No, and an appropriate explanation isgiven or the expression is evaluated correctly.[1] No, and the correct order of operations isused to evaluate 2(3)2 + 5, but onecomputational error is made.or [1] One conceptual error is made inevaluating the expression, but the question isanswered appropriately.or [1] Appropriate work is shown, but thequestion is not answered.[0] No, but no explanation or an inappropriateexplanation is given.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[865] B

[866] A

[867] C

[868] D


[869]

[2] 60, and appropriate work is shown, suchas 300 - 120 - 90 - 30 = 60.or [2] 60, and an appropriate Venn diagram toillustrate the answer is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] An appropriate Venn diagram is drawn,and 240 is determined to be the total numberof students given, but no further work isshown.or [1] 60, but no work is shown.[0] 240 is not subtracted from 300 and isgiven as the solution.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[870]

a [1] $50b (1) [1] 5(2) [1] $125c [1] $10a, b, and c [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[871] D

[872]

[3] 12, and appropriate work is shown, suchas calculating volume = 5 760 3, in anddividing by 500 3in .[2] Appropriate work is shown, but onecomputational or rounding error is made.or[2] The volume is found incorrectly bymultiplying 24 ? 16 ? 18, but it is divided by500 and rounded appropriately, resulting in ananswer of 14.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or[1] Appropriate work is shown, but oneconceptual error is made.or[1] The volume of 5,760 is found correctly,but no further correct work is shown.or[1] 12, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[873] B

[874] A

[875] A

[876] C

[877] B

[878] A

[879] A


[880]

a [2] An appropriate histogram is drawn withboth axes labeled with a correct numericalscale.[1] A correct bar graph is drawn.or [1] The parts of the histogram are notlabeled.or [1] Equal interval scales are not shown.or [1] One error on frequency calculation ismade.[0] Two or more mistakes on frequencycalculation are made.b [2] 60% and an appropriate explanation isgiven.[1] An appropriate method to find percent isshown, but a mistake is made in reading the

chart, such as 615

40% 915

= or is shown but

not given as a percent answer.or [1] 60% and no explanation is given.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[881] B

[882]

[2] (1,1), and appropriate work is shown, suchas a correct graph of AB and an appropriateexplanation of how point A is found or theuse of the midpoint formula.[1] Appropriate work is shown, but onecomputational or graphing error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as finding themidpoint of the given coordinates.or [1] The midpoint and points A and B aregraphed correctly, but the coordinates of pointA are not stated or are stated incorrectly.or [1] (1,1), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[883] D

[884] C

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