Post on 28-Feb-2021
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.
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
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.
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
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
____ 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
____ 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?
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.
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.
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.
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.
____ 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 .
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}.
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.
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?
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
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
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.
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
106. ANS:
a. 35
b. 6 units to the left and 2 units down
DIF: L2 OBJ: 10-6.2 Identifying Translated Conic Sections