Algebra 1 Semester 2 Instructional Materials...Algebra 1 Semester 2 Instructional Materials...
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Algebra 1 Semester 2 Instructional Materials 2015-2016
Released 12/17/15
2015-2016
Algebra 1 Semester 2
Instructional Materials for the WCSD Math Common Finals
The Instructional Materials are for student and teacher use and are aligned to the
Math Common Final blueprint for this course. When used as test practice, success
on the Instructional Materials does not guarantee success on the district math
common final.
Students can use these Instructional Materials to become familiar with the format
and language used on the district common finals. Familiarity with standards
vocabulary and interaction with the types of problems included in the Instructional
Materials can result in less anxiety on the part of the students.
Teachers can use the Instructional Materials in conjunction with the course guides
to ensure that instruction and content is aligned with what will be assessed. The
Instructional Materials are not representative of the depth or full range of learning
that should occur in the classroom.
Algebra 1 Semester 2 Instructional Materials 2015-2016
Released 12/17/15
1. Which of the following graphs represents π(π₯) =1
2|π₯ β 3| β 2 ?
A.
C.
B.
D.
2. Which of the following functions represent π(π₯) and β(π₯) based on the following information:
π(π₯) is the result of reflecting the graph of π(π₯) = |π₯| over the x-axis, then translating
the function up one unit.
β(π₯) is the result of translating the graph of π(π₯) = |π₯| up one unit, then reflecting the
function over the x-axis.
A. π(π₯) = β|π₯| + 1
β(π₯) = β|π₯| + 1
C. π(π₯) = β|π₯ + 1| β(π₯) = β|π₯ β 1|
B. π(π₯) = β|π₯| β 1
β(π₯) = β|π₯| + 1
D. π(π₯) = β|π₯| + 1
β(π₯) = β|π₯| β 1
3. Which of the following is the solution for x in the equation β2|π₯ + 3| + 6 = 10 ?
A. ππ π πππ’π‘πππ C. π₯ = 1
B. π₯ = β5, π₯ = β1 D. π₯ = β5
Algebra 1 Semester 2 Instructional Materials 2015-2016
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4. Which of the following is the solution for x in the equation β3|π₯ + 4| = β6 ?
A. π₯ = β2 C. π₯ = β2 and π₯ = 6
B. π₯ = β6 and π₯ = β2 D. ππ π πππ’π‘πππ
5. If π(π₯) = 2|π₯ + 3| β 4 and π(π₯) =1
2π₯ + 5, use the tables below find the x-value(s) where
π(π₯) = π(π₯).
π(π₯) = 2|π₯ + 3| β 4
π₯ π(π₯) β7 4 β6 2 β5 0 β4 β2 β3 β4 β2 β2 β1 0 0 2 1 4 2 6 3 8 4 10
π(π₯) =1
2π₯ + 5
π₯ π(π₯) β7 1.5 β6 2 β5 2.5 β4 3 β3 3.5 β2 4 β1 4.5 0 5 1 5.5 2 6 3 6.5 4 7
A. π₯ = 2, 4, 6 C. π₯ = β6, 2
B. π₯ = 2, 6 D. ππ π πππ’π‘πππ
Algebra 1 Semester 2 Instructional Materials 2015-2016
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6. Which graph below models the solutions to the equation β3|π₯ + 2| + 4 = β2π₯ ?
A.
C.
B.
D.
7. What is the simplified form of (4πβ3β4)β3 ?
A.
β12π6
β12 C.
12π9
β
B. β64π9
β12 D.
π9
64β12
8. Let π(π₯) = β3π1/2 and π(π₯) = 2π15/2πβ8. Find β(π₯) = π(π₯) β π(π₯).
A. β(π₯) =
β6π8
π8 C. β(π₯) =
β5π7
π8
B. β(π₯) =6π8
π8 D. β(π₯) = β6ππ
Algebra 1 Semester 2 Instructional Materials 2015-2016
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9. What is the simplified form of 36πβ4π6
4ππβ2πβ4 ? (Assume that π β 0, π β 0, and π β 0)
A. 9π4π4
π3 C.
9π8π4
π5
B. 9π8
π5π4 D.
9π5
π8π4
10. Simplify: β18
42
A. β21
7 C. 3
B. β63
7 D. β3
11. Find the simplified form of the following expression, assuming π₯ β 0, π¦ β 0, and π§ β 0:
(2π₯β4π¦5π§3
π₯7π¦π§0)
β2
A. β4π§6
π₯6π¦8 C.
π₯6
4π¦8π§6
B. π₯22
4π¦8π§6 D.
π¦5π§3
4π₯11
Algebra 1 Semester 2 Instructional Materials 2015-2016
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12. Which of the following expressions is equivalent to (3β1π₯0)β2 + (2π¦0)β3 β 5 [3 (1
3π₯3)
0
]?
A. π’ππππππππ C. β57
8
B. 41
8 D. β6
7
8
13. A moving company sells boxes for packing items. The large box has a volume of
6π₯3 + 2π₯2 + 3 cubic units. The medium box has a volume of 2π₯3 + 8π₯ β 5 cubic units. A
customer purchases two large boxes and one medium box. What is the total volume of the
purchased boxes?
A. 14π₯6 + 12π₯3 + 1 cubic units C. 14π₯3 + 2π₯2 + 8π₯ β 2 cubic units
B. 14π₯6 + 4π₯2 + 8π₯ + 1 cubic units D. 14π₯3 + 4π₯2 + 8π₯ + 1 cubic units
14. What is the product of the binomials: (π β 8)(π + 5) ?
A. π2 β 40 C. π β 3
B. π2 + 13π β 40 D. π2 β 3π β 40
Algebra 1 Semester 2 Instructional Materials 2015-2016
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15. What is the simplified form of (π + 7)2 ?
A. π2 + 14π + 49 C. π2 + 49π + 49
B. π2 + 49 D. π + 49
16. The polynomial π₯2 + 11π₯ + 30 is factorable. One factor is (π₯ + 6), what is the other
factor?
A. (π₯ + 1) C. (π₯ β 5)
B. (π₯ + 3) D. (π₯ + 5)
17. Which of the following is a factor of 3π₯2 β 12 ?
A. (π₯ + 12) C. (π₯ β 2)
B. (π₯ β 4) D. (π₯ + 4)
18. Which of the following is a factor of 2π₯2 + 7π₯ β 30 ?
A. (π₯ β 5) C. (π₯ β 12)
B. (π₯ + 6) D. (π₯ β 6)
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19. Select all of the expressions that are equivalent to βπ₯2 + 3π₯ + 10.
I. (π₯ + 5)(π₯ β 2)
II. β(π₯ + 2)(π₯ β 5)
III. (βπ₯ β 2)(π₯ β 5)
IV. (π₯ + 2)(5 β π₯)
A. I only C. II and III
B. II only D. II, III, and IV
20. What is the simplified form of (β3π + 7)2?
A. 9π2 β 42π + 49 C. β9π2 β 42π + 49
B. 9π2 + 49 D. β9π2 + 49
21. Find an equivalent form of 2(π + 7)2?
A. 2π + 14 C. 2π2 + 98
B. 2π2 + 28π + 98 D. 4π2 + 56π + 196
22. The expression π₯2 + ππ₯ + π factors to the expression (π₯ + π)(π₯ + π) where π, π, π, and π
represent non-zero rational numbers. If π < 0 and π < 0, then which of the following statements
is true?
A. both π and π are positive
B. π is positive and π is negative where |π| > |π|
C. π is positive and π is negative where |π| < |π|
D. both π and π are negative
Algebra 1 Semester 2 Instructional Materials 2015-2016
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23. What is the sum of the solutions of π₯2 + 8π₯ = 84 ?
A. β8 C. 8
B. β5 D. 0
24. Solve for x in 16π₯2 β 49 = 0 .
A. π₯ = Β±
49
16 C. π₯ =
16
49
B. π₯ = Β±7
4 D. π₯ =
7
4
25. The height (β), in feet, of a person jumping off a diving platform can be modeled by the equation
β = β16π‘2 + 4π‘ + 6 where π‘ represents the time in seconds the person is in the air. After how
many seconds does the person jumping off the platform enter the water?
A. β
1
2 π πππππ C.
4
3 π ππππππ
B. 3
4 π πππππ D. 2 π ππππππ
26. Given the equation and graph of π¦ = βπ₯2 β 1, what is the domain and range?
A. Domain: πππ ππππ ππ’πππππ
Range: π¦ β₯ 1
B. Domain: πππ ππππ ππ’πππππ
Range: π¦ β€ 1
C. Domain: πππ ππππ ππ’πππππ
Range: π¦ β€ β1
D. Domain: β1 β€ π₯ β€ 1
Range: π¦ β€ β1
Algebra 1 Semester 2 Instructional Materials 2015-2016
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27. Which of the following quadratic functions represents the function graphed below?
A. π¦ =
1
2π₯2 β 5
B. π¦ = 2π₯2 β 5
C. π¦ =1
2(π₯ + 5)2
D. π¦ = 2(π₯ β 5)2
28. Which of the following graphs represents π(π₯) = (π₯ β 4)2 + 3 ?
A.
C.
B.
D.
Algebra 1 Semester 2 Instructional Materials 2015-2016
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29. Translate the graph of π(π₯) = π₯2 four units to the left, three units up and compress the graph by a
factor of 1
2. Which of the following is the function after the transformations?
A. π(π₯) =
1
2(π₯ + 4)2 + 3 C. π(π₯) = 2(π₯ + 4)2 + 3
B. π(π₯) =1
2(π₯ β 4)2 + 3 D. π(π₯) = 2(π₯ β 4)2 + 3
30. Which of the following is the vertex for π(π₯) = β4(π₯ β 5)2 + 2 ?
A. (25, 2) C. (β5, 2)
B. (β20, 2) D. (5, 2)
31. What is the y-intercept of the graph of π¦ = 2(π₯ β 1)2 + 3 ?
A. (1, 3) C. (0, 3)
B. (0, 5) D. (0, 1)
32. Given the graph of π¦ = π₯2, what is the solution for x after the transformation down four units and
left three units?
A. π₯ = β2, π₯ = 2
B. π₯ = 3
C. π₯ = β5, π₯ = β1
D. π₯ = β4, π₯ = 3
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33. Which of the following are the x-intercepts for π¦ = (π₯ + 2)2 β 16
A. (β6, 0), (2, 0) C. (β6, 0), (β2, 0)
B. (β2, 0), (16, 0) D. (2, 0), (β16, 0)
34. Which of the following is a solution to 2π₯2 + 14π₯ = 18 ?
A. π₯ =7 Β± β85
2 C. π₯ =
β7 Β± β85
2
B. π₯ =β7 Β± β13
2 D. π₯ =
14 Β± β340
4
35. Which of the following is the vertex form for π(π₯) = π₯2 + 4π₯ + 7 ?
A. π(π₯) = (π₯ + 2)2 + 3 C. π(π₯) = (π₯ + 2)2 + 7
B. π(π₯) = (π₯ β 2)2 + 4 D. π(π₯) = (π₯ β 2)2 + 3
36. What is the vertex of the function π(π₯) = β2π₯2 + 8π₯ β 9 ?
A. (β4, β73) C. (β2, β33)
B. (4, β9) D. (2, β1)
Algebra 1 Semester 2 Instructional Materials 2015-2016
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37. Before a truck can drive through a tunnel, it must be determined if the load can fit safely
through the tunnel. The parabola π(π₯) = β1
4(π₯ β 8)2 + 16 models the curve of the tunnel.
If a truckload is 12 ππππ‘ high what is the maximum width it could be?
A. 4 ππππ‘
B. 8 ππππ‘
C. 12 ππππ‘
D. 16 ππππ‘
38. Describe how the graph of the function π(π₯) = π₯2 changes after the transformation
π(π₯ + 7) is applied.
A. The graph is translated 7 units up. C. The graph is translated 7 units left.
B. The graph is translated 7 units down. D. The graph is translated 7 units right.
39. Which of the following properly describes the graph of the function π(π₯) =1
2(π₯ β 6)2 β 10 ?
A. The graph of the function is compressed vertically by a factor of 1
2 and translated to the
right 6 units and down 10 units from the parent function.
B. The graph of the function is compressed vertically by a factor of 1
2 and translated to the
left 6 units and down 10 units from the parent function.
C. The graph of the function is stretched vertically by a factor of 2 and translated to the
left 6 units and down 10 units from the parent function.
D. The graph of the function is stretched vertically by a factor of 2 and translated to the
right 6 units and down 10 units from the parent function.
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40. If π(π₯) = π(π₯) and π(π₯) = 2(π₯ β 5)2 + 3, then which of the following functions can
represent π(π₯)?
A. π(π₯) = π₯2 β 10π₯ + 28 C. π(π₯) = 2π₯2 β 20π₯ + 53
B. π(π₯) = 2π₯2 β 10π₯ + 3 D. π(π₯) = 2π₯2 β 20π₯ + 50
41. Sarah is standing on the top of a diving board with a height of 50 feet. When she dives off,
she reaches a height of 30 feet in 2 seconds. Determine the quadratic function, π(π‘), that
would model Sarahβs height π‘ seconds after she jumps off the diving board.
A. π(π‘) = β5(π‘ β 0)2 + 30 C. π(π‘) = β5(π‘ β 0)2 + 50
B. π(π‘) = 5(π‘ β 0)2 + 30 D. π(π‘) = (π‘ β 0)2 + 50
42. A rocket was shot up into the air. The graph shows the height of its flight π‘ seconds after it
was shot. At about what height was the rocket after 3 seconds? How long did it take the
rocket to come back down to the ground?
A. The height of the rocket was 12 yards after 3 seconds. It took the rocket 12 seconds to
return to the ground.
B. The height of the rocket was 3 yards after 3 seconds. It took the rocket 12 seconds to
return to the ground.
C. The height of the rocket was 30 yards after 3 seconds. It took the rocket 0 seconds to
return to the ground.
D. The height of the rocket was 30 yards after 3 seconds. It took the rocket 12 seconds to
return to the ground.
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43. Which of the following best describes the data in the table?
π₯ 1 2 3 4
π¦ 3 9 27 81
A. Exponential with a growth factor of 3
B. Linear with a rate of change of 6
C. Quadratic with a second difference of 12
D. none of the above
44. Since the year 2001 the population of community A grows exponentially as illustrated in
the table. The exponential rate of growth is 1.3. What are the units for the rate of growth in
the table?
π¦πππ 2001 2002 2003 2004 2005 2006 ππππππ 1200 1560 2028 2636.4 3427.32 4455.52
A. people per year
B. years per people
C. years
D. people
45. Determine which of the following equations represent exponential growth or decay.
Equation 1 Equation 2 Equation 3 Equation 4
π¦ = 1.5βπ₯
π¦ = 0.8π₯
π¦ = 0.5βπ₯
π¦ = 2.7π₯
A. Equation 1: Growth
Equation 2: Growth
Equation 3: Decay
Equation 4: Decay
C. Equation 1: Decay
Equation 2: Growth
Equation 3: Growth
Equation 4: Decay
B. Equation 1: Decay
Equation 2: Decay
Equation 3: Growth
Equation 4: Growth
D. Equation 1: Growth
Equation 2: Decay
Equation 3: Decay
Equation 4: Growth
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46. If π(π₯) = 3 β 4π₯ and π(π₯) = 3 β 2π₯, compare the functions and determine which of the
following statements is correct.
A. The x-intercept of π(π₯) is greater than the x-intercept of π(π₯).
B. The y-intercept of π(π₯) is greater than the y-intercept of π(π₯).
C. The functions increase at the same rate.
D. The functions have the same y-intercept.
47. What is the solution for x in 4π₯ = 64 ?
A. π₯ = 16 C. π₯ = 3
B. π₯ = 4 D. π₯ = 2
48. What is the solution for x in 52π₯β9 = 125 ?
A. π₯ = 6 C. π₯ = 5
B. π₯ = 4 D. π₯ = 3
49. What is the solution to the system graphed?
A. (2, 4)
B. (4, 2)
C. (1, 2)
D. ππ π πππ’π‘πππ
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50.
What is the solution for x in the system?
{π¦ = 8
π¦ = 2π₯
A. π₯ =
1
3 C. π₯ = 1
B. π₯ =1
2 D. π₯ = 3
51. Which of the following represents the function π(π₯) = 2π₯ β 5 ?
A.
C.
B.
D.
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52. Write a recursive formula for the sequence below, assuming π(1) is the first term in the sequence:
3, β6, 12, β24, 48 β¦
A. π(1) = β6 and π(π) = π(π β 1) β (β2), for π β₯ 2
B. π(1) = β2 and π(π) = π(π β 1) β 3, for π β₯ 2
C. π(1) = 3 and π(π) = π(π β 1) β (β2), for π β₯ 2
D. π(1) = 3 and π(π) = π(π β 1) β 9, for π β₯ 2
53. Write an explicit formula for the geometric sequence given π3 = 1 and π5 = 0.25. Assume the
common ratio is positive.
A. ππ = 8(0.25)πβ1 C. ππ = 0.5(4)πβ1
B. ππ = 4(0.5)πβ1 D. ππ = 0.25(8)πβ1
54. Which of the following functions is equivalent to the function π(π₯) = (1
3)
2
?
I. π(π₯) = 3β2
II. π(π₯) =1
9
III. π(π₯) = (2
3)
β1
IV. π(π₯) = 2(β3)
V. π(π₯) =1
6
VI. π(π₯) = 9β1
A. I, III, V
B. II, IV, VI
C. I, II, VI
D. III, V, VI
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55. A supervisor at a factory is testing the companyβs packaging machines for accuracy. The machines
are labeled X, Y, and Z. The company standard for packaging a product is that each bag should
contain 6 to 10 ππ’ππππ . The supervisor randomly chose 10 bags from each machine and recorded
the results in the table below. Based on the dot plots below, which statement is correct?
A. Machine X is both the most consistent and the most accurate.
B. Machine X and Y are equally consistent, but Machine Y is the most accurate.
C. Machine Z is both the most consistent and the most accurate.
D. Machine Z is the most consistent, but Machine Y is the most accurate.
56. A fast food chain took a random survey of some of their stores to find the average number of sodas
they sell per day. The data collected is given below. Which measure of central tendency best
represents the data? Justify your answer.
{165, 142, 153, 160, 135, 140, 155, 30, 162, 157}
A. The mean would be best because there is an outlier.
B. The mean would be best because there is not an outlier.
C. The median would be best because there is an outlier.
D. The median would be best because there is not an outlier.
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57. The two-way frequency table shows all of the grades for males and females in a science class. If
the females were to have the same percent of Bβs as the males, how many more females would
need to get a B in the class?
A. 2
A B C D F
Females 6 3 4 2 1
Males 3 6 1 0 2
B. 3
C. 4
D. 5
58. Use the table below to help determine which function has the greatest value as x gets larger and
larger.
π₯ π(π₯) = π₯ + 3 π(π₯) = 3π₯ β(π₯) = π₯3 π(π₯) = 3π₯
3
4
5
6
A. π(π₯) has the greatest value as x gets larger and larger.
B. π(π₯) has the greatest value as x gets larger and larger.
C. β(π₯) has the greatest value as x gets larger and larger.
D. π(π₯) has the greatest value as x gets larger and larger.
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59. The maximum height reached by a bouncing ball is given by β(π₯) = 10(0.75)π₯ where h is
measured in feet and x is the bounce number. Describe the domain of this function and what it
means when π₯ = 0.
A. The domain is all real numbers. When the bounce number π₯ = 0, the height h of the ball is
10 ππππ‘, which represents its original height of the ball before it is dropped and bounces.
B. The domain is all real numbers. When the bounce number π₯ = 0, the height h of the ball is
7.5 ππππ‘, which represents its original height of the ball before it is dropped and bounces.
C. The domain is all nonnegative integers, or 0, 1, 2, 3, β¦ . The domain represents the bounce
number x and does not have units. When π₯ = 0 the height h of the ball is 10 ππππ‘, which
represents its original height of the ball before it is dropped and bounces.
D. The domain is all nonnegative integers, or 0, 1, 2, 3, β¦ . The domain represents the bounce
number x and does not have units. When π₯ = 0 the height h of the ball is 7.5 ππππ‘, which
represents its original height of the ball before it is dropped and bounces.
60. In the box-and-whisker plots below, which class has the greater interquartile range of arm spans?
What is the interquartile range for that class?
A. Class A; 12 inches C. Class A; 4 inches
B. Class B; 5 inches D. Class B; 9 inches
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The Department of Transportation requires guardrails to be constructed at a height of 48 inches
with a tolerance of 3 inches. The boxplots below show the measurements for three different
companies on their last 100 projects. Using the formula |π β 48| β€ 3, where π is the actual
measurement.
61. Which company is most accurate in their guardrail construction?
A. L&M Construction C. Traffic Guards, Inc.
B. TJ Highway Co. D. L&M Construction and Traffic Guards, Inc.
62. Which company is most consistent in their guardrail construction?
A. L&M Construction C. Traffic Guards, Inc.
B. TJ Highway Co. D. L&M Construction and Traffic Guards, Inc.
63. What type of histogram is shown below?
A. skewed left
B. skewed right
C. symmetric
D. uniform
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64. Describe the relationship between the two variables based on the scatterplot below.
A. As the winning times (π₯) increase, the years (π¦) decrease.
B. As the years (π₯) increase, the winning times (π¦) increase.
C. As the years (π₯) decrease, the winning times (π¦) decrease.
D. As the years (π₯) increase, the winning times (π¦) decrease.
65. Which of the following is a reasonable trend line (line of best fit) for the scatterplot below?
A. π¦ =
1
3π₯ + 8
B. π¦ =
1
2π₯ β 3
C. π¦ =
2
3π₯ + 3
D. π¦ = 3π₯ + 3
Algebra 1 Semester 2 Instructional Materials 2015-2016
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Algebra 1 S2 Instructional Material Answers 2015-2016
Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 11
1. D 7. D 13. D 26. C 43. A 55. D
2. D 8. A 14. D 27. B 44. A 56. C
3. A 9. C 15. A 28. A 45. B 57. D
4. B 10. A 16. D 29. A 46. D 58. D
5. C 11. B 17. C 30. D 47. C 59. C
6. B 12. C 18. B 31. B 48. A 60. B
19. D 32. C 49. A 61. A
20. A 33. A 50. D 62. B
21. B 34. C 51. B 63. B
22. C 35. A 52. C 64. D
23. A 36. D 53. B 65. C
24. B 37. B 54. C
25. B 38. C
39. A
40. C
41. C
42. D