Algebra 2, Spring Semester Review 2013starkmath.weebly.com/uploads/1/3/2/3/13234781/alg_2_spring_revie… · Viola makes gift baskets for Valentine’s Day. She has 13 baskets left

Name: ______________________ Class: _________________ Date: _________ ID: A

1

Algebra 2, Spring Semester Review 2013

____ 1. (1 point)Find the annual percent increase or decrease that y = 0.35(2.3) x models.a. 230% increase c. 30% decreaseb. 130% increase d. 65% decrease

____ 2. (1 point)An initial population of 820 quail increases at an annual rate of 23%. Write an exponential function to model the quail population. What will the approximate population be after 3 years?a. f(x) = 820(1.23) x; 1526 c. f(x) = 820 ⋅ 0.23( ) x; 6,708,494b. f(x) = 820(23) x; 9,976,940 d. f(x) = 820(0.23) x; 1526

____ 3. (1 point)The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

a. y = 361 12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃

32 x

; 0 kg c. y = 2 1361

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃

132

x

; 0.797 kg

b. y = 361 12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃

132

x

; 323.945 kg d. y = 12

1361

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃

132

x

; 0.199 kg

____ 4. (1 point)Use the graph of y = ex to evaluate e 1.7 to four decimal places.a. 5.4739 b. 4.6211 c. 2.7183 d. 0.1827

____ 5. (1 point)Use the table feature on a graphing calculator to evaluate e 1.8 to four decimal places.a. 6.0496 b. 0.1653 c. 2.7183 d. 4.8929

____ 6. (1 point)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

____ 7. (1 point)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

Write the equation in logarithmic form.

____ 8. (1 point)2 5 = 32a. log 32 = 5 ⋅ 2 c. log 32 = 5b. log2 32 = 5 d. log5 32 = 2

Name: ______________________ ID: A

2

Evaluate the logarithm.

____ 9. (1 point)

log51

625a. –3 b. 5 c. –4 d. 4

____ 10. (1 point)log3 243a. 5 b. –5 c. 4 d. 3

____ 11. (1 point)log 0.01a. –10 b. –2 c. 2 d. 10

____ 12. (1 point)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 H+

È

ÎÍÍÍÍÍÍ

˘

˚˙̇̇˙̇̇. Use the formula pH = −log H+

È

ÎÍÍÍÍÍÍ

˘

˚˙̇̇˙̇̇ to find the pH level, to the nearest tenth, of a

liquid with [H+] about 6.5 × 10 −3 .a. –3.8 b. 3.8 c. 2.2 d. 3.0

____ 13. (1 point)Use the Change of Base Formula to evaluate log4 20. a. 2.161 c. 1.301b. 2.996 d. 2.161

____ 14. (1 point)Use the Change of Base Formula to evaluate log7 28. a. 1.712 c. 1.712b. 3.332 d. 1.447

____ 15. (1 point)A construction explosion has an intensity I of 4.85 × 10 −2 W/m2. Find the loudness of the sound in

decibels if L = 10 log II 0

and I o = 10 −12 W/m2. Round to the nearest tenth.

a. 146.9 decibels c. 106.9 decibelsb. 115.8 decibels d. 48.5 decibels

____ 16. (1 point)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 L = 10 log II o

. Round to the nearest

hundredth.

a. 2.01 decibels c. 1.37 decibelsb. 2.12 decibels d. 4.32 decibels

Name: ______________________ ID: A

3

Solve the exponential equation.

____ 17. (1 point)1

16= 64 4x − 3

a. 112

b. 14

c. 712

d. 1112

____ 18. (1 point)

4 4x = 8

a. 34

b. 83

c. 38

d. 2

____ 19. (1 point)125 9x − 2 = 150a. –1.8847 b. –0.1069 c. 0.3375 d. 1.0378

____ 20. (1 point)

Solve 15 2x = 36. Round to the nearest ten-thousandth.a. 0.6616 b. 2.6466 c. 1.7509 d. 1.9091

____ 21. (1 point)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 G = t3.3 loga P

, 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

Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

____ 22. (1 point)3 log 2x = 4a. 10.7722 b. 5 c. 2.7826 d. 0.6309

____ 23. (1 point)Solve log(4x + 10) = 3.

a. − 74

b. 4952

c. 250 d. 990

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

____ 24. (1 point)6e 4x − 2 = 3a. –0.448 b. 0.327 c. 0.067 d. –0.046

____ 25. (1 point)2e 2x + 12 = 22a. –4.801 b. 1.417 c. –4.801 d. 0.576

Name: ______________________ ID: A

4

____ 26. (1 point)

ex = 34

a. –0.288 b. –0.275 c. 0.275 d. 0.288____ 27. (1 point)

e 2x = 1.4a. –1.664 b. 0.073 c. 0.168 d. 0.190

____ 28. (1 point)The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 4 years after a model is introduced? Round the answer to the nearest whole number.a. 20,289 mowers c. 8,811 mowersb. 41,709 mowers d. 19,713 mowers

Generate the first five terms in the sequence using the explicit formula.

____ 29. (1 point)yn = −5n − 5

a. –30, –25, –20, –15, –10b. 30, 25, 20, 15, 10c. –10, –15, –20, –25, –30d. 10, 15, 20, 25, 30

____ 30. (1 point)cn = 12n − 11

a. 49, 37, 25, 13, 1b. –1, –13, –25, –37, –49c. 1, 13, 25, 37, 49d. –49, –37, –25, –13, –1

____ 31. (1 point)

What is the 15 th term in the sequence using the given formula?

cn = 3n − 1

a. 14b. 57c. 44d. –44

____ 32. (1 point)Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term.a. a n = a n − 1 + 6, where a 1 = 7; 37b. a n = a n − 1 + 6, where a 1 = 37; 7c. a n = a n − 1 − 6, where a 1 = 6; –23d. a n = a n − 1 − 6, where a 1 = 7; 37

Name: ______________________ ID: A

5

____ 33. (1 point)Write a recursive formula for the sequence 7, 4, 1, –2, –5, .... Then find the next term.a. a n = a n − 1 − 3, where a 1 = −8; 7b. a n = a n − 1 − 3, where a 1 = 7; –8c. a n = a n − 1 + 3, where a 1 = −3; 22d. a n = a n − 1 + 3, where a 1 = 7; –8

____ 34. (1 point)Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a 14 .a. a n = −2n + 10; –16 c. a n = −2n + 8; –20b. a n = −2n + 8; –18 d. a n = −2n + 10; –18

____ 35. (1 point)Suppose you drop a tennis ball from a height of 8 feet. After the ball hits the floor, it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.a. 3.3 feet b. 4.1 feet c. 5.1 feet d. 1 feet

____ 36. (1 point)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 5Number of Bacteria 21 42 63 84 105

a. a n = 21n c. a n = n + 21

b. a n = 121

n d. a n = 21n + 21

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

____ 37. (1 point)13, 20, 27, 34, ...a. yes; 7 b. yes; –7 c. yes; 13 d. no


____ 39. (1 point)–2.4, 9.8, 22, 34.2, ...a. yes; 12 b. yes; 12.2 c. yes; 12.3 d. no

____ 40. (1 point)Find the 110 term of the sequence −7, 3, 13, 23, ... a. 1083 b. –1097 c. 1093 d. 40

____ 41. (1 point)

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

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

Name: ______________________ ID: A

6

____ 42. (1 point)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 basketsb. 156 baskets d. 181 baskets

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


____ 44. (1 point)2, –4, –16, –36, ...a. yes; –2 b. yes; 2 c. yes; –3 d. no

____ 45. (1 point)13

, 29

, 427

, 881

, 16243

, ...

a. yes; 23

c. yes; 16

b. yes; 19

d. not geometric

What is the fifth term of the geometric sequence?

____ 46. (1 point)5, 15, 45, ...

a. 1215 c. 405b. 1875 d. 3645

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

____ 47. (1 point)a 1 = −4, a 2 = 8, a 3 = −16a. a n = −4 ⋅ (2) n ; –64 c. a n = −4 ⋅ (−2) n ; 128b. a n = −4 ⋅ (−2) n − 1 ; –64 d. a n = −2 ⋅ (−4) n − 1 ; –512

____ 48. (1 point)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

Name: ______________________ ID: A

7

What is a possible value for the missing term of the geometric sequence?

____ 49. (1 point)

39, , 975, ...

a. −44 b. −195 c. −5 d. −4875

What is the sum of the finite arithmetic series?

____ 50. (1 point)26 + 29 + 32 + 35 + 38 + 41 + 44a. 219b. 245c. –193d. 201

____ 51. (1 point)7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (−0.2) + (–1.5)a. 17.4b. 24.4c. 27.8d. 36.4

____ 52. (1 point)29 + 32 + 35 + 38 + 41 +…+ 59a. 234 c. 484b. 425 d. 455

____ 53. (1 point)(−5) + 0 + 5 + 10 +…+ 65a. 900 b. 455 c. 450 d. 445

____ 54. (1 point)Justine earned $26,000 during the first year of her job at city hall. After each year she received a 3% raise. Find her total earnings during the first five years on the job.a. $138,037.53 b. $1,004,704.20 c. $4,020.51 d. $108,774.30

____ 55. (1 point)

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 35

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 7125

feet b. 36 14125

feet c. 43 111125

feet d. 46 14125

feet

____ 56. (1 point)Find the sine of 180º. Round your answers to the nearest hundredth if necessary.a. –0.5 b. –1.1 c. 0 d. 0.5

____ 57. (1 point)Find the cosine 315º. Round your answers to the nearest hundredth if necessary.a. 0 b. 0.71 c. 1 d. –0.78

Name: ______________________ ID: A

8

____ 58. (1 point)Find the exact value of sin 120º.

a. sin =3

2c. sin = 1

2

b. sin = −3

2d. sin = − 1

2____ 59. (1 point)

Find the exact value of cos 300º.

a. cos = − 12

c. cos = −3

2

b. cos = 12

d. cos =3

2____ 60. (1 point)

Find the exact values of cos 150º and sin 150º.

a. cos = − 12

, sin =3

2c. cos = −

32

, sin = 12

b. cos = 12

, sin = −3

2d. cos =

32

, sin = − 12

____ 61. (1 point)Find the radian measure of an angle of –280º.

a. 9−14π

b. −14π9

c. 9π−14

d. −149π

____ 62. (1 point)

Find the degree measure of an angle of 3π5

radians.

a. 1.88º b. 108πº c. 108º d. π300

º

____ 63. (1 point)Find the radian measure of an angle of 110º.

a. 1118π

b. 11π18

c. 1811π

d. 18π11

____ 64. (1 point)

Find the degree measure of an angle of – 4π3

radians.

a. –4.19º b. −240πº c. –240º d. − π135

º

____ 65. (1 point)

Find the exact values of cos 3π4

radiansÊ

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃ and sin 3π

4radians

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃.

a. 22

, − 22

b. − 12

, 32

c. −2

2, 2

2d. −

32

, 12

Name: ______________________ ID: A

9

____ 66. (1 point)

Find the exact value of sin − π

6radians

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃.

a. −3

2b. − 1

2c. −

22

d. −1

____ 67. (1 point)

Find the exact value of cos − 7π4

radiansÊ

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃.

a. 22

b. 12

c. 32

d. − 12

Use the graph of y = sin θ to find the value of sin θ for each value of θ.

____ 68. (1 point)270º

a. –0.4 b. –0.8 c. –0.6 d. –1

Name: ______________________ ID: A

10

____ 69. (1 point)Find the period of the graph shown below.

a. 2π b. 23π c. 1

2π d. 4π

____ 70. (1 point)A particular sound wave can be graphed using the function y = −3 sin x. Find the period of the function.a. period = 2π c. period = 3

b. period = –3 d. period = 12

____ 71. (1 point)Find the amplitude of the sine curve shown below.

a. 2π b. 8 c. 2 d. 4____ 72. (1 point)

A particular sound wave can be graphed using the function y = 3 sin 5x. Find the amplitude of the function.

a. amplitude = 52π c. amplitude = 3

b. amplitude = 25π d. amplitude = –3

Name: ______________________ ID: A

11

What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin bθ, what is an equation for the sine curve?

____ 73. (1 point)amplitude = 3, period = 2π, and a > 0

a.

y = 3 sin 2θ

c.

y = 3 sin θb.

y = −3 sin 2θ

d.

y = 3 sin θ

Name: ______________________ ID: A

12

____ 74. (1 point)

amplitude = 4, period = 12π, and a < 0

a.

y = –4 sin 8θ

c.

y = –4 sin 4θb.

y = −–4 sin 8θ

d.

y = –4 sin 14θ

Name: ______________________ ID: A

13

____ 75. (1 point)y = 2 sin θa. c.

b. d.

Name: ______________________ ID: A

14

Sketch one cycle of the cosine function.

____ 76. (1 point)y = – cos 3θa. c.

b. d.

Name: ______________________ ID: A

15

____ 77. (1 point)y = 2 cos 2θa. c.

b. d.

Name: ______________________ ID: A

16

____ 78. (1 point)What is the graph of one cycle of a cosine curve with amplitude 2, period 2π, and a < 0?

a. c.

b. d.

Use the unit circle to find the inverse function value in degrees.

____ 79. (1 point)

sin −1 32

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃˜̃̃˜

a. 30° c. 240° b. 60° d. 150°

Name: ______________________ ID: A

17

____ 80. (1 point)

cos−1 32

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃˜̃̃˜

a. 60° c. 240°b. 30° d. 150°

Find the height of the triangle.

____ 81. (1 point)

a. 83.1 b. 46.1 c. 171.4 d. 108.6____ 82. (1 point)

a. 3.4 b. 9.4 c. 3.6 d. 6.6

Name: ______________________ ID: A

18

____ 83. (1 point)The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 25° angle with the water. To the nearest foot, how far is the boat from the cliff?

a. 141 feet b. 128 feet c. 27 feet d. 75 feet

In ΔABC, ∠C is a right angle, what is the measure of x?

____ 84. (1 point)

a. 42.1 b. 64.8 c. 23.1 d. 25.2____ 85. (1 point)

a. 22.4° b. 67.6° c. 20.9° d. 69.1°

Name: ______________________ ID: A

19

____ 86. (1 point)

What are the focus and directrix of the parabola with equation y = 112

x 2 ?

a. focus: 3,0ÊËÁÁ

ˆ̃̃; directrix: y = −3 c. focus: 0,3Ê

ËÁÁˆ̃̃; directrix: y = −3

b. focus: −3,0ÊËÁÁ

ˆ̃̃; directrix: y = 3 d. focus: 0,−3Ê

ËÁÁˆ̃̃; directrix: y = 3

____ 87. (1 point)

Identify the focus and the directrix of the graph of x = − 120

y 2 .

a. focus (0, –5), directrix x = 5 c. focus (0, –5), directrix x = –5b. focus (–5, 0), directrix x = –5 d. focus (–5, 0), directrix x = 5

____ 88. (1 point)A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 2 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.

a. y = − 14

x 2 c. y = 18

x 2

b. y = − 18

x 2 d. y = 14

x 2

Write an equation of a circle with the given center and radius.

____ 89. (1 point)center (2, –4) and radius 5a. x − 2( ) 2 + y + 4Ê

ËÁÁˆ̃̃

2= 5 c. x + 2( ) 2 + y − 4Ê

ËÁÁˆ̃̃

2= 25

b. x + 2( ) 2 + y − 4ÊËÁÁ

ˆ̃̃

2= 5 d. x − 2( ) 2 + y + 4Ê

ËÁÁˆ̃̃

2= 25

____ 90. (1 point)center (–7, –6) and radius 2a. x + 7( ) 2 + y + 6Ê

ËÁÁˆ̃̃

2= 4 c. x + 7( ) 2 + y + 6Ê

ËÁÁˆ̃̃

2= 2

b. x − 7( ) 2 + y − 6ÊËÁÁ

ˆ̃̃

2= 2 d. x − 7( ) 2 + y − 6Ê

ËÁÁˆ̃̃

2= 4

____ 91. (1 point)Write an equation for the translation of x 2 + y 2 = 49 by 3 units left and 4 units up.

a. x + 3( ) 2 + y + 4ÊËÁÁ

ˆ̃̃

2= 49 c. x − 3( ) 2 + y − 4Ê

ËÁÁˆ̃̃

2= 49

b. x + 3( ) 2 + y − 4ÊËÁÁ

ˆ̃̃

2= 49 d. x − 3( ) 2 + y + 4Ê

ËÁÁˆ̃̃

2= 49

What is the center and radius of the circle with the given equation?

____ 92. (1 point)(x − 1) 2 + (y + 1) 2 = 4a. center (–1, 1); radius 4 c. center (–1, 1); radius 2b. center (1, –1); radius 4 d. center (1, –1); radius 2

Name: ______________________ ID: A

20

____ 93. (1 point)

x − 4( ) 2 + y − 8ÊËÁÁ

ˆ̃̃

2= 9

a. center at (–4, –8); radius 9 c. center at (4, 8); radius 3b. center at (4, 8); radius 9 d. center at (–4, –8); radius 3

____ 94. (1 point)

x 2 + y 2 + 14x − 12y = −69a. center at (–7, 6); radius 16 c. center at (7, –6); radius 16b. center at (7, –6); radius 4 d. center at (–7, 6); radius 4

Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.

____ 95. (1 point)vertex at (–3, 0) and co-vertex at (0, 2)

a. x 2

9+

y 2

4= 1 c. x 2

3+

y 2

2= 1

b. x 2

4+

y 2

9= 1 d. x 2

2+

y 2

3= 1

____ 96. (1 point)vertex at (3, 0) and co-vertex at (0, 5)

a. x 2

5+

y 2

3= 1 c. x 2

9+

y 2

25= 1

b. x 2

25+

y 2

9= 1 d. x 2

3+

y 2

5= 1

____ 97. (1 point)vertex at (–5, 0) and co-vertex at (0, 4)

a. x 2

25+

y 2

16= 1 c. x 2

5+

y 2

4= 1

b. x 2

16+

y 2

25= 1 d. x 2

4+

y 2

5= 1

Name: ______________________ ID: A

21

What are the foci of the ellipse? Graph the ellipse.

____ 98. (1 point)

x 2

49+

y 2

64= 1

a. foci (0, ± 15 ) c. foci (0, ± 113 )

b. foci (0, ± 15 ) d. foci (0, ± 113 )

Name: ______________________ ID: A

22

Use matrices A, B, and C. Find the sum or difference if you can.

A = −5 4

−8 2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

B = −2 7 −3

1 −6 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

C= 5 3 −1

−3 0 6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

____ 99. (1 point)B – A

a. −7 −4 2

−4 6 6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. −7 11

−7 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. not possible d. 3 10 −4

−2 −6 6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

____100. (1 point)

−3 0

5 −7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

+ −4 2

−1 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. −1 2

−4 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. −7 2

4 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. −7 −2

4 −15

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. −7 2

4 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

____101. (1 point)

−9 −1 7

0 9 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

+ −2 0 7

−3 5 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. −11 1 14

−3 14 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. −11 1 14

−3 14 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. −11 −1 14

−3 14 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. −11 −1 14

3 −14 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

Name: ______________________ ID: A

23

____102. (1 point)

−5 2 0

−5 9 9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

− −1 3 3

7 4 7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. −4 −1 −3

12 −5 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. −4 −1 −3

−12 5 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. −4 −1 3

−12 5 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. −4 1 −3

−12 5 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

____103. (1 point)The first table shows the teams with the four best records halfway through their season. The second table shows the full season records for the same four teams. Which team had the best record during the second half of the season?

Record for the First half of the Season

Team Wins LossesTeam 1 26 14Team 2 27 13Team 3 25 15Team 4 24 16

Record for the SeasonTeam Wins Losses

Team 1 59 21Team 2 56 24Team 3 56 24Team 4 52 28

a. Team 2 c. Team 3b. Team 1 d. Team 4

Find the values of the variables.

____104. (1 point)

−8 + t 0

8 −12

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

= −5 0

8 −2y − 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. t = 5, y = 3 c. t = 3, y = 7b. t = –13, y = 5 d. t = 3, y = 5

Name: ______________________ ID: A

24

____105. (1 point)

−12 −w2

2f 3

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇

= 2k −81

−14 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. f = –7, k = 6, w = 9 or –9 c. f = –7, k = –6, w = 81 or –81b. f = –7, k = –6, w = 9 or –9 d. f = –7, k = –6, w = 9

____106. (1 point)

15 8

4x 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

− 2 5

x 3y + 6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

= 13 3

12 4y + 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. x = −4 and y = 2 c. x = 4 and y = −2b. x = 5 and y = −1 d. x = −5 and y = 1

Find the product.

____107. (1 point)

5 5

−2 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

−4 9

8 7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. 20 80

32 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. −20 40

45 35

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 20 80

3 32

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. 8 24

−18 21

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

____108. (1 point)

−5 −2

−8 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

−5 7

−9 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. 25 18

−35 10

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 40 45

−56 25

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 43 −25

85 −31

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. 43 −25

−31 85

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

Name: ______________________ ID: A

25

____109. (1 point)The table summarizes the scoring of a football game between Team A and Team B. A touchdown (TD) is worth 6 points, a field goal (FG) is worth 3 points, a safety (S) is worth 2 points, and a point after touchdown (PAT) is worth 1 point. Use matrix multiplication to find the final score.

TD FG S PATTeam A 3 2 1 0Team B 4 4 1 2

a. Team A: 35Team B: 36

c. Team A: 26Team B: 40

b. Team A: 36Team B: 39

d. Team A: 17Team B: 38

Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix.

____110. (1 point)

1 1 −4

5 6 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

9

1

−7

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a. defined; 3 × 3 c. defined; 2 × 3b. defined; 2 × 1 d. undefined

____111. (1 point)

4 5

9 −2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

1 7È

Î

ÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇

a. defined; 2 × 2 c. defined; 1 × 2b. defined; 2 × 1 d. undefined

Are matrices A and B inverses?

____112. (1 point)

A = −5 −18

2 7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

and B = 7 18

−2 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. yes b. no____113. (1 point)

A = −9 −23

2 5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

and B = 5 23

−2 9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. no b. yes

Name: ______________________ ID: A

26

Evaluate the determinant of the matrix.

____114. (1 point)

−4 5 6

0 4 4

−2 −5 4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a. –104 b. –72 c. –136 d. 136____115. (1 point)

−9 −9

−6 6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. –108 b. 108 c. 0 d. 0

Does the given matrix, A, have an inverse? If it does, what is A−1 ?

____116. (1 point)

A = −7 −25

2 7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. −7 −25

−2 −7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 7 25

−2 7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 7 25

−2 −7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. does not exist

____117. (1 point)

A = 0 19

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

a. 0 19

0 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 0 0

0 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 0 19

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. does not exist

Name: ______________________ ID: A

27

____118. (1 point)

Write the system

6a + 5b − 5c = 6

−7a + 7b + 4c = 6

−7a − 4b − 9c = −1

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

as a matrix equation. Then identify the coefficient matrix,

the variable matrix, and the constant matrix.

Name: ______________________ ID: A

28

a.

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

=

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

variable matrix:

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

constant matrix:

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

coefficient matrix:

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

c.

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

=

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

coefficient matrix:

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

variable matrix:

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

constant matrix:

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

b.

6 −7 −7

5 7 −4

−5 4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

=

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

coefficient matrix:

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

constant matrix:

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

variable matrix:

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

d.

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

=

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

variable matrix:

6 5 −5

−7 7 4

−7 −4 −9

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

coefficient matrix:

a

b

c

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

constant matrix:

6

6

−1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

Name: ______________________ ID: A

29

What is the solution of the system? Solve using matrices.

____119. (1 point)

x + 2y = 9

x + y = 1

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

.

a. −7

8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 8

−7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 7

−8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. no solution

____120. (1 point)

−3x + 2y = 10

−4x + 3y = 2

Ï

Ì

Ó


.

a. −26

−34

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. −34

−26

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 26

34

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. no solution

____121. (1 point)

x + 2y = −1

−x − 3y = −2

Ï

Ì

Ó


a. −7

3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. 3

−7

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 7

−3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. no solution

____122. (1 point)

−7x + 2y = −2

11x − 3y = −5

Ï

Ì

Ó


a. −57

−16

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

b. −16

−57

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

c. 16

57

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙

d. no solution

Solve the system.

____123. (1 point)

3x + y − 4z = −30

3x + 2y + 2z = −8

5x + 5y + z = −26

Ï

Ì

Ó


a. (–30, –8, –26) c. (–4, –2, 4)b. (4, –2, 4) d. (–4, 2, –4)

Name: ______________________ ID: A

30

____124. (1 point)

− 5x − y = 21

3x − 4y + 5z = −8

−3x − z = 12

Ï

Ì

Ó


a. (–4, 1, –1) c. (4, –1, 0)b. (21, –8, 12) d. (–4, –1, 0)

ID: A

1

Algebra 2, Spring Semester Review 2013Answer Section

1. ANS: B PTS: 1 2. ANS: A PTS: 1 3. ANS: B PTS: 1 4. ANS: A PTS: 1 5. ANS: A PTS: 1 6. ANS: D PTS: 1 7. ANS: D PTS: 1 8. ANS: B PTS: 1 9. ANS: C PTS: 1 10. ANS: A PTS: 1 11. ANS: B PTS: 1 12. ANS: C PTS: 1 13. ANS: D PTS: 1 14. ANS: A PTS: 1 15. ANS: C PTS: 1 16. ANS: D PTS: 1 17. ANS: C PTS: 1 18. ANS: C PTS: 1 19. ANS: C PTS: 1 20. ANS: A PTS: 1 21. ANS: D PTS: 1 22. ANS: A PTS: 1 23. ANS: B PTS: 1 24. ANS: D PTS: 1 25. ANS: A PTS: 1 26. ANS: A PTS: 1 27. ANS: C PTS: 1 28. ANS: A PTS: 1 29. ANS: C PTS: 1 30. ANS: C PTS: 1 31. ANS: C PTS: 1 32. ANS: A PTS: 1 33. ANS: B PTS: 1 34. ANS: D PTS: 1 35. ANS: B PTS: 1 36. ANS: A PTS: 1 37. ANS: A PTS: 1 38. ANS: D PTS: 1 39. ANS: B PTS: 1 40. ANS: A PTS: 1 41. ANS: C PTS: 1 42. ANS: A PTS: 1

ID: A

2

43. ANS: A PTS: 1 44. ANS: D PTS: 1 45. ANS: A PTS: 1 46. ANS: C PTS: 1 47. ANS: B PTS: 1 48. ANS: A PTS: 1 49. ANS: B PTS: 1 50. ANS: B PTS: 1 51. ANS: B PTS: 1 52. ANS: C PTS: 1 53. ANS: C PTS: 1 54. ANS: A PTS: 1 55. ANS: B PTS: 1 56. ANS: C PTS: 1 57. ANS: B PTS: 1 58. ANS: B PTS: 1 59. ANS: B PTS: 1 60. ANS: C PTS: 1 61. ANS: B PTS: 1 62. ANS: C PTS: 1 63. ANS: B PTS: 1 64. ANS: C PTS: 1 65. ANS: C PTS: 1 66. ANS: B PTS: 1 67. ANS: A PTS: 1 68. ANS: D PTS: 1 69. ANS: B PTS: 1 70. ANS: A PTS: 1 71. ANS: D PTS: 1 72. ANS: C PTS: 1 73. ANS: C PTS: 1 74. ANS: C PTS: 1 75. ANS: D PTS: 1 76. ANS: D PTS: 1 77. ANS: C PTS: 1 78. ANS: C PTS: 1 79. ANS: B PTS: 1 80. ANS: B PTS: 1 81. ANS: A PTS: 1 82. ANS: A PTS: 1 83. ANS: B PTS: 1 84. ANS: B PTS: 1 85. ANS: B PTS: 1 86. ANS: C PTS: 1 87. ANS: D PTS: 1 88. ANS: C PTS: 1

ID: A

3

89. ANS: D PTS: 1 90. ANS: A PTS: 1 91. ANS: B PTS: 1 92. ANS: D PTS: 1 93. ANS: C PTS: 1 94. ANS: D PTS: 1 95. ANS: A PTS: 1 96. ANS: C PTS: 1 97. ANS: A PTS: 1 98. ANS: A PTS: 1 99. ANS: B PTS: 1 100. ANS: C PTS: 1 101. ANS: B PTS: 1 102. ANS: C PTS: 1 103. ANS: B PTS: 1 104. ANS: D PTS: 1 105. ANS: B PTS: 1 106. ANS: C PTS: 1 107. ANS: A PTS: 1 108. ANS: B PTS: 1 109. ANS: C PTS: 1 110. ANS: B PTS: 1 111. ANS: D PTS: 1 112. ANS: A PTS: 1 113. ANS: A PTS: 1 114. ANS: C PTS: 1 115. ANS: A PTS: 1 116. ANS: B PTS: 1 117. ANS: D PTS: 1 118. ANS: C PTS: 1 119. ANS: A PTS: 1 120. ANS: A PTS: 1 121. ANS: A PTS: 1 122. ANS: B PTS: 1 123. ANS: C PTS: 1 124. ANS: D PTS: 1

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