20
4th Quarter Test Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Graph the exponential function. ____ 1. a. 2 4 6 –2 –4 –6 x 4 8 12 16 20 –4 y c. 2 4 6 –2 –4 –6 x 4 8 12 16 20 –4 y b. 2 4 6 –2 –4 –6 x 4 8 12 16 20 –4 y d. 2 4 6 –2 –4 –6 x 4 –4 –8 –12 –16 –20 y ____ 2. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model the quail population. a. c. b. d. ____ 3. Write an exponential function for a graph that includes (1, 15) and (0, 6). a. c. b. d. ____ 4. Write an exponential function for the graph.

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Page 1: 16 4th Quarter Test Review y 12 Multiple Choice y Graph the ...bhsccmath.weebly.com/uploads/1/5/0/6/15062410/4th...4th Quarter Test Review Multiple Choice Identify the letter of the

4th Quarter Test Review

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

Graph the exponential function.

____ 1.

a.

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

c.

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

b.

2 4 6–2–4–6 x

4

8

12

16

20

–4

y

d.

2 4 6–2–4–6 x

4

–4

–8

–12

–16

–20

y

____ 2. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model

the quail population.

a. c.

b. d.

____ 3. Write an exponential function for a graph that includes (1, 15) and (0, 6).

a. c.

b. d.

____ 4. Write an exponential function for the graph.

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2 4 6–2–4–6 x

4

8

12

16

20

–4

y

a. b. c. d.

____ 5. Find the annual percent increase or decrease that models.

a. 230% increase c. 30% decrease

b. 130% increase d. 65% decrease

____ 6. For an annual rate of change of –31%, find the corresponding growth or decay factor.

a. 0.31 b. 0.69 c. 1.31 d. 1.69

____ 7. The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801

kg. Write an exponential function that models the decay of this material. Find how much radioactive material

remains after 10 days. Round your answer to the nearest thousandth.

a.

; 0.228 kg

c.

; 738.273 kg

b. ; 0 kg

d.

; 0.911 kg

____ 8. Use a graphing calculator. Use the graph of to evaluate to four decimal places.

a. 5.4739 b. 4.6211 c. 2.7183 d. 0.1827

____ 9. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you

have in the account after 4 years?

a. $800.26 b. $6,701.28 c. $10,138.07 d. $1,923.23

____ 10. How much money invested at 5% compounded continuously for 3 years will yield $820?

a. $952.70 b. $818.84 c. $780.01 d. $705.78

Evaluate the logarithm.

____ 11.

a. –3 b. 5 c. –4 d. 4

____ 12.

a. 5 b. –5 c. 4 d. 3

____ 13. log 0.01

a. –10 b. –2 c. 2 d. 10

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The pH of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a

liquid is labeled . Use the formula to answer questions about pH.

____ 14. Find the pH level, to the nearest tenth, of a liquid with [H+] about .

a. –3.8 b. 3.8 c. 2.2 d. 3.0

____ 15. The pH of a juice drink is 2.6. Find the concentration of hydrogen ions in the drink.

a. 2.6 b. 2.5 103

c. d. 2.5 103

____ 16. Write the equation in exponential form.

a.

b.

c.

d.

____ 17. A construction explosion has an intensity I of W/m2. Find the loudness of the sound in decibels if

and W/m2. Round to the nearest tenth.

a. 146.9 decibels c. 106.9 decibels

b. 115.8 decibels d. 48.5 decibels

____ 18. A company with loud machinery needs to cut its sound intensity to 37% of its original level. By how many

decibels would the loudness be reduced? Use the formula . Round to the nearest hundredth.

a. 2.01 decibels c. 1.37 decibels

b. 2.12 decibels d. 4.32 decibels

____ 19. Solve .

a.

b.

c.

d.

____ 20. Solve .

a. –1.8847 b. –0.1069 c. 0.3375 d. 1.0378

____ 21. Use a graphing calculator. Solve by graphing. Round to the nearest hundredth.

a. 1.19 b. 0.83 c. 4.76 d. 3.33

____ 22. Simplify .

a. 3 b.

c. 3e d.

____ 23. The sales of lawn mowers t years after a particular model is introduced is given by the function y =

, where y is the number of mowers sold. How many mowers will be sold 2 years after a model

is introduced? Round the answer to the nearest whole number.

a. 37,897 mowers c. 15,901 mowers

b. 7,383 mowers d. 17,000 mowers

____ 24. The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria

increase in population is shown by the formula , where t is the time period of the population

increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the

end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these

bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour.

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a. 177 hours b. 76 hours c. 4 hours d. 85 hours

Use natural logarithms to solve the equation. Round to the nearest thousandth.

____ 25.

a. –0.448 b. 0.327 c. 0.067 d. –0.046

____ 26.

a. –0.288 b. –0.275 c. 0.275 d. 0.288

____ 27.

a. –1.664 b. 0.073 c. 0.168 d. 0.190

____ 28. The amount of money in an account with continuously compounded interest is given by the formula

, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the

nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded

continuously at 6.2%. Round to the nearest tenth.

a. 1.1 yr b. 6.9 yr c. 11.2 yr d. 0.6 yr

Describe the pattern in the sequence. Find the next three terms.

____ 29. 13, 15, 17, 19, ...

a. Add 2; 23, 25, 27.

b. Multiply by 2; 38, 76, 152.

c. Add –2; 17, 15, 13.

d. Add 2; 21, 23, 25.

____ 30. 4, 8, 16, 32, ...

a. Multiply by 2; 64, 128, 256.

b. Multiply by –2; –64, 128, –256.

c. Multiply by 2; 128, 256, 512.

d. Add 2; 34, 36, 38.

____ 31. 625, 250, 100, 40,...

a. Divide by 3; 15, 5, 1. c. Add 7.5; 25, 32.5, 51.25.

b. Divide by 2.5; 16, 6.4, 2.56. d. Subtract 15; 10, –5, –20.

____ 32. Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its

previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

a. 9.2 feet b. 10.8 feet c. 7.8 feet d. 1.9 feet

____ 33. Orlando is making a design for a logo. He begins with a square measuring 24 inches on a side. The second

square has a side length of 19.2 inches, and the third square has a side length of 15.36 inches. Which square

will be the first square with a side length of less than 12 inches?

a. fourth square c. sixth square

b. fifth square d. seventh square

____ 34. Write a recursive formula for the sequence 8, 10, 12, 14, 16, .... Then find the next term.

a. ; 18

b. ; 8

c. ; 18

d. ; –2

____ 35. Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.

a. ; 356

b. ; 356

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c. ; 356

d. ; 356

____ 36. Write an explicit formula for the sequence 7, 2, –3, –8, –13, ... Then find .

a. ; –53 c. ; –58

b. ; –58 d. ; –63

____ 37. Write an explicit formula for the sequence , , , , , .... Then find .

a.

c.

b.

d.

____ 38. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit

formula for the sequence of the number of bacteria.

Hours (n) 1 2 3 4 5

Number of

Bacteria 19 38 57 76 95

a. c.

b. d.

____ 39. Is the formula is explicit or recursive? Find the first five terms of the sequence.

a. recursive; 1, –4, 16, –64, 256 c. explicit; 1, –4, 16, –64, 256

b. recursive; 0, –16, –24, –48, –80 d. explicit; 0, –8, –24, –48, –80

Is the sequence arithmetic? If so, identify the common difference.

____ 40. 13, 20, 27, 34, ...

a. yes, 7 b. yes, –7 c. yes, 13 d. no

____ 41. 14, 21, 42, 77, ...

a. yes, 7 b. yes, –7 c. yes, 14 d. no

____ 42. –2.4, 9.8, 22, 34.2, ...

a. yes, 12 b. yes, 12.2 c. yes, 12.3 d. no

____ 43. Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to

make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many

baskets will she have to sell?

a. 193 baskets c. 205 baskets

b. 156 baskets d. 181 baskets

____ 44. Find the 50th term of the sequence 5, –2, –9, –16, ...

a. –352 b. –343 c. –338 d. –331

____ 45. Find the missing term of the arithmetic sequence 22, , 34,...

a. 46 b. 16 c. 28 d. 40

____ 46. Find the arithmetic mean of .

a. 11 b. 5.5 c. 3.7 d. 1.6

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____ 47. Find the arithmetic mean of , .

a.

b.

c.

d.

____ 48. A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle

and one at the top. How many cartons of cola are needed for the complete display? This is only a partial

picture of the finished display.

a. 180 cartons c. 120 cartons

b. 30 cartons d. 15 cartons

Is the sequence geometric? If so, identify the common ratio.

____ 49. 6, 12, 24, 48, ...

a. yes, 2 b. yes, –2 c. yes, 4 d. no

____ 50. 2, –4, –16, –36, ...

a. yes, –2 b. yes, 2 c. yes, –3 d. no

____ 51. , , , , ,...

a. yes,

c. yes,

b. yes,

d. not geometric

Write the explicit formula for the sequence. Then find the fifth term in the sequence.

____ 52.

a. ; 243 c. ; 243

b. ; –243 d. ; –729

____ 53.

a. ; 0.2916 c. ; 0.972

b. ; 0.2916 d. ; 0.972

Find the missing term of the geometric sequence.

____ 54. 45, , 1620, ...

a. 9720 b. 51 c. 6 d. 270

____ 55. 1250, , 50, ...

a. 1200 b. 650 c. 250 d. 125

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____ 56. Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by

painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2

inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues

painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length

of less than 29 inches?

a. Triangle 4 c. Triangle 5

b. Triangle 3 d. Triangle 6

____ 57. A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18

feet long and the third arc is 8 feet long, what is the length of the second arc?

a. 12 feet b. 10 feet c. 5 feet d. 72 feet

Use the finite sequence. Write the related series. Then evaluate the series.

____ 58. 26, 29, 32, 35, 38, 41, 44

a. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 219

b. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 245

c. 26 – 29 – 32 – 35 – 38 – 41 – 44 = –193

d. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 201

____ 59. 7.6, 6.3, 5, 3.7, 2.4, 1.1, –0.2, –1.5

a. 7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (–0.2) + (–1.5) = 17.4

b. 7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (–0.2) + (–1.5) = 24.4

c. 7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (–0.2) + (–1.5) = 27.8

d. 7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (–0.2) + (–1.5) = 36.4

____ 60. The sequence 15, 21, 27, 33, 39, ..., 75 has 11 terms. Evaluate the related series.

a. 420 c. 210

b. 495 d. 480

____ 61. The sequence –5, 0, 5, 10, ..., 65 has 15 terms. Evaluate the related series.

a. 900 b. 455 c. 450 d. 445

____ 62. The sequence 2, 4, 6, 8, ..., 24 has 12 terms. Evaluate the related series.

a. 288 b. 156 c. 144 d. 132

____ 63. A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into

space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance

(in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic

sequence 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds.

a. 534 feet b. 560 feet c. 212 feet d. 426 feet

____ 64. Evaluate the series 1 + 4 + 16 + 64 + 256 + 1024.

a. 1365 b. 1364 c. 341 d. 5461

____ 65. Evaluate the series 6 – 24 + 96 – 384 + ... to .

a. 19,662 b. –78,642 c. –4914 d. 1230

____ 66. Evaluate the series 1000 + 500 + 250 + ... to .

a. 968.75 b. 1062.5 c. 1937.5 d. 12,500

____ 67. Justine earned $17,000 during the first year of her job at city hall. After each year she received a 4% raise.

Find her total earnings during the first five years on the job.

a. $3,541.44 b. $72,189.89 c. $517,077.48 d. $92,077.48

____ 68. A rubber ball dropped on a hard surface takes a sequence of bounces, each one as high as the preceding

one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it

hits the surface the 5th time?

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a. 23 feet

b. 36 feet

c. 43 feet

d. 46 feet

____ 69. Evaluate the series 1 + 2 + 4 + 8 to .

a. 256.5 b. 511 c. 1023 d. 2047

____ 70. In June, Cory begins to save money for a video game and a TV he wants to buy in December. He starts with

$20. Each month he plans to save 10% more than the previous month. How much money will he have at the

end of December?

a. $154.31 b. $251.59 c. $228.72 d. $189.74

____ 71. The screen below shows the graph of a sound recorded on an oscilloscope. What is the period and the

amplitude? (Each unit on the t-axis equals 0.01 seconds.)

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 t

2

4

–2

–4

f(t)

a. 0.05 seconds, 4.5 c. 0.025 seconds, 9

b. 0.05 seconds, 9 d. 0.025 seconds, 4.5

____ 72. Find the cosine and sine of 240º. Round your answers to the nearest hundredth if necessary.

240

x

y

a. –0.5, –0.87 b. –0.87, –0.5 c. 0, –1 d. –0.95, –0.55

____ 73. Find the exact value of cos 300º and sin 300º.

a.

c.

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b.

d.

____ 74. For an angle in standard position measuring –163º, find the values of cos and sin . Round your answers

to the nearest hundredth.

a. 0.96, –0.29 c. –0.96, –0.29

b. 0.96, 0.29 d. –0.96, 0.29

____ 75. For an angle in standard position measuring 92º, find the values of cos and sin . Round your answers to the

nearest hundredth.

a. 0.03, –1.00 c. –0.03, –1.00

b. 0.03, 1.00 d. –0.03, 1.00

Write the measure in radians. Express the answer in terms of .

____ 76. 320º

a.

b.

c.

d.

____ 77. 45º

a.

b.

c.

d.

Write the measure in degrees.

____ 78. radians

a. º b. º

c. 108º d. 1.88º

____ 79. – radians

a. º b. º

c. –315º d. –5.5º

____ 80. Find the degree measure of an angle of 4.23 radians.

a. 62º b. 242º c. 118º d. 28º

____ 81. Find the exact value of sin .

a.

b. c. 1 d.

____ 82. Use the circle below. Find the length s to the nearest tenth.

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7_

5

s

5 ft

a. 7.0 ft b. 3.1 ft c. 22.0 ft d. 44.0 ft

____ 83. A weather satellite in circular orbit around Earth completes one orbit every 5 hours. The radius of Earth is

about 6,400 km and the satellite is positioned 4,700 km above the Earth. How far does the satellite travel in 1

hour? Round your answer to the nearest kilometer.

a. 5,906 km b. 69,743 km c. 13,949 km d. 8,042 km

____ 84. A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between

them is 165º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the

Ferris wheel?

a. 27.8 feet b. 13,200.0 feet c. 502.7 feet d. 230.4 feet

____ 85. Find the period of the graph shown below.

2

O

3

1

2

–1

–2

y

a. 2 b. 2

3

c. 1

2

d. 4

____ 86. Find the amplitude of the sine curve shown below.

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2O

3

2

4

–2

–4

y

a. 2 b. 8 c. 2 d. 4

____ 87. Use a graphing calculator to solve the equation in the interval from 0 to 2. Round to the

nearest hundredth.

a. 2.41, 4.17 c. 2.30, 3.98

b. 2.20, 3.80 d. –3.80, –2.20, 2.20, 3.80

____ 88. Write an equation of the cosine function with amplitude 2 and period 4.

a.

c.

b.

d.

____ 89. Write an equation for the translation 3 units down of y = sin x.

a. c.

b. d.

____ 90. cos 420°

a.

b.

c.

d.

____ 91. Find the period, range, and amplitude of the cosine function .

a.

b.

c.

d.

Write a cosine function for the graph.

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____ 92.

2

O

2

4

–2

–4

y

a.

c.

b. d.

____ 93. Write an equation of a circle with center (–5, –8) and radius 2.

a.

c.

b.

d.

____ 94. Write an equation for the translation of , 2 units right and 4 units down.

a.

c.

b.

d.

____ 95. A satellite is launched in a circular orbit around Earth at an altitude of 120 miles above the surface. The

diameter of Earth is 7920 miles. Write an equation for the orbit of the satellite if the center of the orbit is the

center of the Earth labeled (0, 0).

a. c.

b. d.

____ 96. Find the center and radius of the circle with equation .

a. (5, –6); 3 c. (5, –6); 9

b. (–5, 6); 9 d. (–5, 6); 3

____ 97. Find the center and radius of the circle with equation .

a. center (–1, 1); radius 4 c. center (–1, 1); radius 2

b. center (1, –1); radius 4 d. center (1, –1); radius 2

____ 98. Graph .

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a.

8–8 x

8

–8

y c.

8–8 x

8

–8

y

b.

8–8 x

8

–8

y d.

8–8 x

8

–8

y

Identify the center and intercepts of the conic section. Then find the domain and range.

____ 99.

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

a. The center of the circle is (6, 6). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts

are (0, 6) and (0, –6). The domain is {y | 6 y –6}. The range is {x | 6 x –6}.

b. The center of the circle is (6, 6). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts

are (0, 6) and (0, –6). The domain is {x | –6 x 6}. The range is {y | –6 y 6}.

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c. The center of the circle is (0, 0). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts

are (0, 6) and (0, –6). The domain is {x | –6 x 6}. The range is {y | –6 y 6}.

d. The center of the circle is (0, 0). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts

are (0, 6) and (0, –6). The domain is {y | 6 y –6}. The range is {x | 6 x –6}.

____ 100. Write an equation in standard form for the circle.

2 4–2–4 x

2

4

–2

–4

y

a.

c.

b.

d.

Essay

101. The table gives the diameters of some of the planets. Assume each planet is a sphere.

Planet Diameter (miles)

Venus 7519

Mercury 3032

Saturn 74,978

a. Write an equation of the cross section through the center of Venus.

b. Write an equation of the cross section through the center of Mercury.

c. Write an equation of the cross section through the center of Saturn.

d. An equation for the cross section through the center of Earth’s moon is . What is the

diameter of the moon?

102. The graph shows the pattern of the water from a sprinkler used for irrigating crops. Each unit on the graph

represents one yard.

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2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

a. What are the intercepts of the circle?

b. Write an equation for the circle of water from the sprinkler.

c. What is the diameter of the circle of land watered by the sprinkler? Explain how you found your answer.

d. What is the area of land covered by the sprinkler?

Other

103. Consider the equation of the circle .

a. Explain how to find the center and radius of the circle. Then find the center and radius.

b. Graph the circle. Explain how you drew the graph.

Short Answer

104. A radio station has a broadcast area in the shape of a circle with equation , where the

constant represents square miles.

a. Graph the equation and state the radius in miles.

b. What is the area of the region in which the broadcast from the station can be picked up?

105. The plans of a public park include a circular fountain. The outline of the fountain can be modeled with the

equation , where the units are meters and the graph is on a grid map of the park.

a. Find the coordinates of the center.

b. Find the circumference of the fountain.

106. Mariah is making a graphic design on a computer using a coordinate grid. She began with a circle with center

(0, 0). Then she drew a congruent circle with the equation .

a. What was the radius of the first circle?

b. What translation did Mariah make to draw the second circle?

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4th Quarter Test Review

Answer Section

MULTIPLE CHOICE

1. ANS: A DIF: L2 OBJ: 8-1.1 Exponential Growth

2. ANS: D DIF: L1 OBJ: 8-1.1 Exponential Growth

3. ANS: A DIF: L1 OBJ: 8-1.1 Exponential Growth

4. ANS: A DIF: L2 OBJ: 8-1.1 Exponential Growth

5. ANS: B DIF: L3 OBJ: 8-1.2 Exponential Decay

6. ANS: B DIF: L2 OBJ: 8-1.2 Exponential Decay

7. ANS: C DIF: L1 OBJ: 8-2.1 Comparing Graphs

8. ANS: A DIF: L1 OBJ: 8-2.2 The Number e

9. ANS: D DIF: L1 OBJ: 8-2.2 The Number e

10. ANS: D DIF: L2 OBJ: 8-2.2 The Number e

11. ANS: C DIF: L2 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

12. ANS: A DIF: L1 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

13. ANS: B DIF: L2 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

14. ANS: C DIF: L2 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

15. ANS: B DIF: L1 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

16. ANS: A DIF: L2 OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions

17. ANS: C DIF: L1 OBJ: 8-4.1 Using the Properties of Logarithms

18. ANS: D DIF: L1 OBJ: 8-4.1 Using the Properties of Logarithms

19. ANS: C DIF: L2 OBJ: 8-5.1 Solving Exponential Equations

20. ANS: C DIF: L2 OBJ: 8-5.1 Solving Exponential Equations

21. ANS: A DIF: L1 OBJ: 8-5.1 Solving Exponential Equations

22. ANS: A DIF: L2 OBJ: 8-6.1 Natural Logarithms

23. ANS: D DIF: L1 OBJ: 8-6.1 Natural Logarithms

24. ANS: D DIF: L2 OBJ: 8-5.1 Solving Logarithmic Equations

25. ANS: D DIF: L2 OBJ: 8-6.2 Natural Logarithmic and Exponential Equations

26. ANS: A DIF: L1 OBJ: 8-6.2 Natural Logarithmic and Exponential Equations

27. ANS: C DIF: L1 OBJ: 8-6.2 Natural Logarithmic and Exponential Equations

28. ANS: C DIF: L2 OBJ: 8-6.2 Natural Logarithmic and Exponential Equations

29. ANS: D DIF: L1 OBJ: 11-1.1 Identifying Mathematical Patterns

30. ANS: A DIF: L1 OBJ: 11-1.1 Identifying Mathematical Patterns

31. ANS: B DIF: L2 OBJ: 11-1.1 Identifying Mathematical Patterns

32. ANS: A DIF: L1 OBJ: 11-1.1 Identifying Mathematical Patterns

33. ANS: B DIF: L2 OBJ: 11-1.1 Identifying Mathematical Patterns

34. ANS: A DIF: L1 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

35. ANS: A DIF: L2 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

36. ANS: C DIF: L1 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

37. ANS: C DIF: L3 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

38. ANS: D DIF: L1 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

39. ANS: D DIF: L2 OBJ: 11-1.2 Using Formulas to Generate Mathematical Patterns

40. ANS: A DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

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41. ANS: D DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

42. ANS: B DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

43. ANS: A DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

44. ANS: C DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

45. ANS: C DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

46. ANS: B DIF: L1 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

47. ANS: A DIF: L2 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

48. ANS: C DIF: L2 OBJ: 11-2.1 Identifying and Generating Arithmetic Sequences

49. ANS: A DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

50. ANS: D DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

51. ANS: A DIF: L2 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

52. ANS: A DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

53. ANS: D DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

54. ANS: D DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

55. ANS: C DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

56. ANS: A DIF: L2 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

57. ANS: A DIF: L1 OBJ: 11-3.1 Identifying and Generating Geometric Sequences

58. ANS: B DIF: L1 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

59. ANS: B DIF: L1 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

60. ANS: B DIF: L1 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

61. ANS: C DIF: L1 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

62. ANS: B DIF: L1 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

63. ANS: B DIF: L2 OBJ: 11-4.1 Writing and Evaluating Arithmetic Series

64. ANS: A DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

65. ANS: A DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

66. ANS: C DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

67. ANS: D DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

68. ANS: B DIF: L2 OBJ: 11-5.1 Evaluating a Finite Geometric Series

69. ANS: C DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

70. ANS: D DIF: L1 OBJ: 11-5.1 Evaluating a Finite Geometric Series

71. ANS: A DIF: L1 OBJ: 13-1.2 Finding the Amplitude of a Periodic Function

72. ANS: A DIF: L1 OBJ: 13-2.2 Using the Unit Circle

73. ANS: B DIF: L1 OBJ: 13-2.2 Using the Unit Circle

74. ANS: C DIF: L2 OBJ: 13-2.2 Using the Unit Circle

75. ANS: D DIF: L2 OBJ: 13-2.2 Using the Unit Circle

76. ANS: A DIF: L1 OBJ: 13-3.1 Using Radian Measure

77. ANS: A DIF: L1 OBJ: 13-3.1 Using Radian Measure

78. ANS: C DIF: L1 OBJ: 13-3.1 Using Radian Measure

79. ANS: C DIF: L1 OBJ: 13-3.1 Using Radian Measure

80. ANS: B DIF: L2 OBJ: 13-3.1 Using Radian Measure

81. ANS: D DIF: L2 OBJ: 13-3.1 Using Radian Measure

82. ANS: C DIF: L1 OBJ: 13-3.2 Finding the Length of an Arc

83. ANS: C DIF: L1 OBJ: 13-3.2 Finding the Length of an Arc

84. ANS: D DIF: L2 OBJ: 13-3.2 Finding the Length of an Arc

85. ANS: B DIF: L1 OBJ: 13-4.1 Interpreting Sine Functions

86. ANS: D DIF: L1 OBJ: 13-4.1 Interpreting Sine Functions

87. ANS: B DIF: L1 OBJ: 13-5.2 Solving Trigonometric Equations

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88. ANS: C DIF: L1 OBJ: 13-5.2 Solving Trigonometric Equations

89. ANS: D DIF: L1 OBJ: 13-7.2 Writing Equations of Translations

90. ANS: B DIF: L2 OBJ: 14-7.1 Double-Angle Identities

91. ANS: A DIF: L2 OBJ: 13-5.1 Graphing and Writing Cosine Functions

92. ANS: D DIF: L1 OBJ: 13-5.2 Solving Trigonometric Equations

93. ANS: B DIF: L1 OBJ: 10-3.1 Writing the Equation of a Circle

94. ANS: B DIF: L1 OBJ: 10-3.1 Writing the Equation of a Circle

95. ANS: D DIF: L2 OBJ: 10-3.1 Writing the Equation of a Circle

96. ANS: A DIF: L1 OBJ: 10-3.2 Using the Center and Radius of a Circle

97. ANS: D DIF: L1 OBJ: 10-3.2 Using the Center and Radius of a Circle

98. ANS: D DIF: L1 OBJ: 10-3.2 Using the Center and Radius of a Circle

99. ANS: C DIF: L1 OBJ: 10-1.2 Identifying Conic Sections

100. ANS: B DIF: L1 OBJ: 10-3.1 Writing the Equation of a Circle

ESSAY

101. ANS:

[4] a.

b.

c.

d. 2160 miles

[3] only three parts correct

[2] only two parts correct

[1] only one part correct

DIF: L2 OBJ: 10-3.1 Writing the Equation of a Circle

102. ANS:

[4] a. (–6, 0), (6, 0), (0, –6), (0, 6)

b.

c. 12 yards; the radius is 6 yards and twice the radius equals the diameter.

d. about 113 square yards

[3] only three parts correct

[2] only two parts correct

[1] only one part correct

DIF: L3 OBJ: 10-1.2 Identifying Conic Sections

OTHER

103. ANS:

a. To find the center and radius of the circle, you must complete the square for the x and y terms. Then you

can write the equation in standard form to find the center and radius.

Group like terms.

Complete the square and add the

same to the right hand side of the

equation.

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Factor.

Rewrite in standard form.

The center is (–2, –2) and the radius is 3.

b.

2 4–2–4 x

2

4

–2

–4

y

To make the graph, locate the center (–2, –2). Then draw a circle with this center and radius 3.

DIF: L2 OBJ: 10-3.2 Using the Center and Radius of a Circle

SHORT ANSWER

104. ANS:

a.

30 60 90 120–30–60–90–120 x

30

60

90

120

–30

–60

–90

–120

y

The radius of the circle is 80 miles.

b. about 20,100 square miles

DIF: L2 OBJ: 10-1.1 Graphing Equations of Conic Sections

105. ANS:

a. (4, –5)

b. about 44.4 meters

DIF: L2 OBJ: 10-3.2 Using the Center and Radius of a Circle

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106. ANS:

a. 35

b. 6 units to the left and 2 units down

DIF: L2 OBJ: 10-6.2 Identifying Translated Conic Sections