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t , , , • • • t • • t t t t " " It It , II II II , It , II , :l\.p ClIJculus- MaximumlMinimum Problems - 60 P!S Name _-+'--;-_+---------- Directions: Sh.ow work for partial credit. Be sure to show your primary and s condary equations. • . ' . 1- 1. Two positive numbers x, yhave a sUm of What are their values ifone n: mbet plus the square root of the other is a} as large as possible, b) as small as possible? (10 points) 2. A rectangular plot of land is to be fenced in using two kinds of fencing. Tw ' . opposite sides will use heavy duty fencing selling for $3 a foot while the remaining two sides will uSe s dard fencing costing $2 a foot If the area to be fel1ced in is 150,000 square fe.et, nod the dimensions ufth rectangle thatcould be built with the cheilpest cost. What is that cost? (nearest ceilt) (10 points) , Wlllw.MasterMathMentor.com SlirSchwaf"ll "- •
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:l\.p ClIJculus- MaximumlMinimum Problems - 60 P!S Name _-+'--;-_+----------Directions: Sh.ow work for partial credit. Be sure to show your primary and s condary equations.
• . ' . 1-
1. Two positive numbers x, yhave a sUm of 20~ What are their values ifone n: mbet plus the square root of the other is a} as large as possible, b) as small as possible? (10 points)
2. A rectangular plot of land is to be fenced in using two kinds of fencing. Tw ' . opposite sides will use heavy duty fencing selling for $3 a foot while the remaining two sides will uSe s dard fencing costing $2 a foot If the area to be fel1ced in is 150,000 square fe.et, nod the dimensions ufth rectangle thatcould be built with the cheilpest cost. What is that cost? (nearest ceilt) (10 points)
, Wlllw.MasterMathMentor.com SlirSchwaf"ll
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3. The number of flies around a dropped piece of bread is modeled by the .to ula p(t) ~ lOOO~ 10+ t
where t is meas.ured in hour.s. How long will it take for the number offli s to be at a maximum? What is
the maximum size of the population of flies (to the nearest fly)? (10 poin )
4. A pro golf operator has found that he can sell 50.0. sets a year of his top gt e clubs at $30.0. per set, For each $5.0.0. he drops the price, he will sell 10. more sets of clubs. What priCle wo d give him the largest in!:ome and what would that income be? Make a chart if it will help. (10 pointi)
5. Find the radiUS and height oftb\! right-circular cylinder oflargest volume. at can. b~ inscribed in· a right circular .cone with radius 6 inches and .b,eight 10. inches. Answer accurate t 3 decimal place. (Volume of a
I cylinder = nr2h), volume of a cone = -nr2h (lOpoints) .... 3
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6. A man is on thf; b<tIlk of a river that is 1 mile wide. He wants to travel to a to on the opposite panIc but I mile upstream. He intelJds to row on a straight line to some point P on the op asite bank and then walk the remaining dist!l.\Jte along the bank How far ftom the town should he row in rder to -reach his destination in the shortest time ifhe can walk 5 at mph and row at 3 mph. (10 points)
1 mile Town
p
1 mile River
Man
l S ; redit: A rectangle is to be inscribed under the arch of the curve Y= 4 os(O.5x) from x= -It to x = It. • ~-_~[ are the dimensions of the rectangle. with the largest area, and wbat is the largest area? You must use ;::'::c:lus in your :answer, but calculators are allowed. (3 decimal places) ( points)
Shl Schwartz
NAME _________________________________ D TE _____ _ PEAIOD __
Chapter 4 Test, Form 2D
L Use a protractor and ruler to classify the triangle by its angles and sides.
2. Find x, AB, BC, AC if MBC is isosceles.
SCORE __
1. ______ _
2. _ _____ _
3. Find the measure of the sides of the triangle if the vertice of 3. _________ _ MFG are E(l, 4), F(5, 1), and G(2, - 3). Then classify the triangle by its sides.
Find the measure of each angle.
4. mLl
5. mL2
6.mL3
7. Identify the congruent triangles and name their corresponding congruent angles.
8. In the figure, AC == FD, AB " DE, andAC " FD. Name the postulate that could be used to prove Mi3C == J:JJEC. Choose from SSS SAS, ASA, and AAS. '
9. In quadrilateral JKLM, JK == LK and MK bisects LLKJ. Name the postulate that could be used to prove /l,MKL '" /l,MKJ. Choose from SSS, SAS, ASA, and AAS.
!!J a.. •• Use the figure to fmd mLl.
4. ______ _
5. ______ _
6. ______ _
B D 7. ______ _
F
8. _____ __
A D
9. ______ _
L """'---+---"'J
11 ______ _
10. l:JABC is an isosceles triangle - -with BD J.AC. Name the theorem that could be used to determine LA "= Le. Then name the postulate that could be used to prove !:-J3DA == !:-J3DC. Choose from SSS, SAS, ABA, and AAS.
c
B-?----... D
A
For Questions 9 and 10, complete this two-column proof.
Giv<>n, L'ABC is an isosceles triangle with base AC.
B
1 2 D is the midpoint of AG.
Prove: BD bisects LARG.
Statements
1. l:JABG is isosceles with baseAG.
2.AB == CB
3. LA ~ LG
4. D is the midpoint of AG.
5.AD == GD
6. l:JABD ~ f:,.GBD
7. L1 ~ L2
8. BD bisects LARG.
AL---D!:-----' c
Reasons
1. Given
2. Def. of isosceles triangle.
3. (Question 9)
4. Given
5. Midpoint Theorem
6. (Question 10)
7. CPCTC
8. De£ of angle bisector
11. Find x. ~17X+9)"
(21x-3)~15X+ 15)"
12. Find x.
/3(18X-8)"
(6x + 4)" ---.....>:>'
1(. _____ _
H
11 ___________ __
1. _______ .
Bonus In the figure, l:JABC is isosceles, /:,.ADG is equilateral, B: _______ _ MEC is isosceles, and the measures of L9, Ll, and L3 are all equal. Find the measures of the nine numbered angles.
9 8
© Glencoe/McGraw·Hili 236 Glencoe Geometry
NAME ________________ D :rE ____ _ PERIOD __
Chapter 5 Test, Form 2D
Simplify. Assume that no variable equals O.
1. (2c2d O)3(5c-7d 2)
For Questions 3-12, simplify.
3. (3(2 + 5f- 9) + (4f2 - 7f+ 12)
4. (6g3 - 2g + 1) - (3g2 + 5g - 7)
5. (5m - 6)(2m + 1)
6. Hi
9. 2\150 + V45 - vI8
10. (2 + \1'3)(4 - \1'3)
11. (7 + 6i) + (-3 + 2i)
12. (4 + i)(1 - 7i)
13. Evaluate(6 x 10- 4)(2.5 X 106). Express the result in scientific notation.
14. Use long division to find (8x3 - 10x2 + 9x - 10) + (2x - 1
15. Use synthetic division to find (x3 + 4x2 - 9x + 10) ~ (x - ).
16. FaClor 20x2 - 8x + 5xy - 2y completely. If the polynomial
is n t factorable, write prime.
© G,enC01 MCGraW-H111 301
SCORE __
1. _____ _
2. _____ _
3. ______ _
4. ______ _
5. ______ _
6. ______ _
7. ______ _
8. ______ _
9. _____ _
10. ______ _
11. ______ _
12 ______ _
13. _ _____ _
14. _ _____ _
15. ______ _
16. ___ ___ _
Glencoe Algebra 2
NAME DATE
Chapter 5 Test, Form 2D (con
17. SimplifY ",2 x2:: ;520 . Assume that the denominator is
not equal to O.
18. TREES The diameter of a tree d (in inches) is related to its
basal area BA (in square feet) by the fonnula d = J576~BA) . If the basal area of a tree is 8.9 square feet, what is the diameter of the tree? Use a calculator to approximate your answer to three decimal places.
19. Write the radical 1/ -125x2 using rational exponents.
~
20. SimplifY the expression ",5 1 •
x ·x2
21. Solve ~ lOs + 1 = 3.
22. Solve 2 + V3t + 6 > 5.
23. POPULATION In 2000, the population of Hong Kong was approximately 6.8 million. Its total area is about 1000 square kilometers. What was the population density (number of people per square kilometer) of Hong Kong in 2000? Express your answer in scientific notation.
24. ELECTRICITY The total impedance of a series circuit is the sum of the impedances of all parts of the circuit. Suppose that the first part of a circuit has an impedance of 7 + 4j ohms and that the total impedance of the circuit is 16 - 2j ohms. What is the impedance of the remainder of the circuit?
25. ELECTRICITY In an AC circuit, the voltage E (in volts), current I (in amps), and impedance Z (in ohms) are related by the fonnula E = I . Z. Find the impedance in a circuit with voltage 12 + 2j volts and current 3 + 5j amps.
B S· l'f 4i 4i onus ImpIY -s . --s .. + I -1
© Glencoe/McGraw-Hili 302
PERIOD __
tim ed)
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B
Glencoe Algebra 2
