ExamView - Algebra 2 Final Exam Review 2015

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 Final Exam Review

All work necessary to solve the problem must be shown for credit.

The completed review packet is to be handed in on the day of the final exam.

Multiple Choice

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

____ 1. Consider the quadratic function f x( ) = −2x2

+ 2x + 2. Find the y-intercept and the equation of the axis of

symmetry.

a. The y-intercept is –2.

The equation of the axis of symmetry is x = −1

2.

b. The y-intercept is 1

2.

The equation of the axis of symmetry is x = 2.

c. The y-intercept is + 2.

The equation of the axis of symmetry is x = 1

2.

d. The y-intercept is −1

2.

The equation of the axis of symmetry is x = –2.

Name: ________________________ ID: A

2

____ 2. Graph the quadratic function f(x) = −2x2

+ 2x + 2.

a. c.

b. d.

Determine whether the given function has a maximum or a minimum value. Then, find the maximum or

minimum value of the function.

____ 3. f(x) = x2

− 2x + 2

a. The function has a maximum value. The maximum value of the function is 1.

b. The function has a maximum value. The maximum value of the function is 5.

c. The function has a minimum value. The minimum value of the function is 1.

d. The function has a minimum value. The minimum value of the function is 5.

Name: ________________________ ID: A

3

____ 4. f(x) = −x2

+ 2x + 7

a. The function has a minimum value. The minimum value of the function is 8.

b. The function has a minimum value. The minimum value of the function is 4.

c. The function has a maximum value. The maximum value of the function is 4.

d. The function has a maximum value. The maximum value of the function is 8.

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which

the roots are located.

____ 5. x2

+ 5x + 4 = 0

a.

The solution set is 1, 4{ }.

c.

The solution set is −2.5, − 2.25{ }.

b.

The solution set is −4, − 1{ }.

d.

The solution set is 1, 4{ }.

Name: ________________________ ID: A

4

____ 6. x2

+ 4x + 2 = 0

a.

One solution is between 3 and 4, while

the other solution is between 0 and 1.

c.

One solution is between –3 and 0, while

the other solution is between –4 and –1.

b.

One solution is between –3 and –1, while

the other solution is between 0 and –4.

d.

One solution is between –3 and –4, while

the other solution is between 0 and –1.

Solve the equation by factoring.

____ 7. x2

+ 3x − 28 = 0

a. −4, 7{ } c. 4, 7{ }

b. −7, 4{ } d. −4, − 7{ }

Name: ________________________ ID: A

5

____ 8. 2x2

+ 3x − 14 = 0

a. {–4, −7

2} c. {–4, 7}

b. {−7

2, 2} d. {2, 7}

Simplify.

____ 9. 196

a. 14 c. 196

b. 14 d. 3 14

____ 10. 245

64

a.7 5

8c.

5

8

b.49

8d.

7 7

8

____ 11. (2i)(−3i)(4i)

a. −24 c. 24i

b. −24i d. 24

____ 12. i7

a. −i c. i

b. 1 d. −1

____ 13. 11 + i( ) + 3 − 15i( )a. 14 − 14i c. 12 − 12i

b. − 4 + 4i d. 14 + 16i

____ 14. 11 − 12i( ) + 21 − 8i( )a. 9 + 19i c. 32 − 4i

b. 32 − 20i d. 29i − i

____ 15. 8 + 10i( )(5 − 8i)

a. 40 − 14i + 80 c. 40 − 14i − 80i2

b. 120 − 14i d. 88 + 50i

____ 16. −4 + 4i( )(−3 − 3i)

a. 16 + 12i c. 24 + 0i

b. 12 + 0i − 12i2

d. 12 + 0i + 12

____ 17. 3

6 + 7i

a.18

85+

21

85i c.

18

13+

21

13i

b.6

85−

7

85i d.

18

85−

21

85i

Name: ________________________ ID: A

6

____ 18. 6 − 3i

8 − 11i

a.81

185+

42

185i c.

6

185−

3

185i

b.15

57+

42

57i d.

81

185−

42

185i

Solve the equation by using the Square Root Property.

____ 19. 16x2

− 48x + 36 = 49

a. {3

2} c. {−

13

4,

1

4}

b. {3

2, 7} d. {−

1

4,

13

4}

____ 20. 100x2

− 80x + 16 = 9

a. {1

10,

7

10} c. {

2

5}

b. {−7

10, −

1

10} d. {

2

5, 3}

Solve the equation by completing the square.

____ 21. x2

+ 2x − 3 = 0

a. −3, 1{ } c. −6, 1{ }

b. −6, 2{ } d. −1, 3{ }

____ 22. 2x2

+ 2x = 0

a. −2, 0{ } c. 0{ }

b. 0, 1{ } d. −1, 0{ }

Find the exact solution of the following quadratic equation by using the Quadratic Formula.

____ 23. x2

− 8x = 20

a. −10, 2{ } c. −4, 20{ }

b. 20, 28{ } d. −2, 10{ }

____ 24. −x2

+ 3x + 7 = 0

a.3 − 37

−2,

3 + 37

−2

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔ

¸

˝

˛


c.−3 − −19

−2,

−3 + −19

−2

Ï

Ì

Ó


¸

˝

˛


b.−3 − 12

−2,

−3 + 12

−2

Ï

Ì

Ó


¸

˝

˛


d.−3 − 37

−2,

−3 + 37

−2

Ï

Ì

Ó


¸

˝

˛


Name: ________________________ ID: A

7

Find the value of the discriminant. Then describe the number and type of roots for the equation.

____ 25. −x2

− 14x + 2 = 0

a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect

square, the two roots are real and rational.

b. The discriminant is –204. Because the discriminant is less than 0, the two roots are

complex.

c. The discriminant is 204. Because the discriminant is greater than 0 and is not a perfect

square, the two roots are real and irrational.

d. The discriminant is –188. Because the discriminant is less than 0, the two roots are

complex.

____ 26. x2

+ x + 7 = 0

a. The discriminant is –29.

Because the discriminant is less than 0, the two roots are complex.

b. The discriminant is 1.

Because the discriminant is greater than 0 and is a perfect square, the two roots are real

and rational.

c. The discriminant is –27.

Because the discriminant is less than 0, the two roots are complex.

d. The discriminant is 27.

Because the discriminant is greater than 0 and is a perfect square, the two roots are real

and rational.

Write the following quadratic function in vertex form. Then, identify the axis of symmetry.

____ 27. y = x2

+ 4x − 6

a. The vertex form of the function is y = x + 2( )2

− 10.

The equation of the axis of symmetry is x = −2.

b. The vertex form of the function is y = x − 2( )2

− 10.


c. The vertex form of the function is y = x + 2( )2

− 10.


d. The vertex form of the function is y = x + 2( )2

+ 10.


____ 28. y = −3x2

+ 48x

a. The vertex form of the function is y = 3 x + 8( )2

+ 192.


b. The vertex form of the function is y = x + 192( )2

+ 8.


c. The vertex form of the function is y = −3 x − 8( )2

+ 192.


d. The vertex form of the function is y = −3 x + 8( )2

+ 192.


Name: ________________________ ID: A

8

Graph the quadratic inequality.

____ 29. y > x2

− 3x + 5

a. c.

b. d.

Name: ________________________ ID: A

9

____ 30. y < 2x2

− 6x + 10

a. c.

b. d.

Solve the inequality algebraically.

____ 31. 2x2

+ 14x < −12

a. {x |−1 < x −6 } c. {x |−6 < x < −1 }

b. {x |−12 < x < −2 } d. {x |−2 < x < −12 }

____ 32. x2

+ 4x > 45

a. {x x| < 9 or x > −5 } c. {x x| < 9 or x > 5 }

b. {x x| < −9 or x > 5 } d. {x x| < −9 or x > −5 }

Name: ________________________ ID: A

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Simplify the given expression. Assume that no variable equals 0.

____ 33. 19x−6

y11Ê

ËÁÁÁ

ˆ¯˜̃̃ −6xy

5ÊËÁÁÁ

ˆ¯˜̃̃

a. −114x−5

y16

c.−114y

16

x5

b.13y

16

x5

d. −114x−7

y−24

____ 34. 14x 4xy14Ê

ËÁÁÁ

ˆ¯˜̃̃ −4x

−10y

7ÊËÁÁÁ

ˆ¯˜̃̃

a. −224x−11

y−110

c.14y

21

x9

b.−224y

21

x9

d. −224x−9

y21

____ 35. 32x

18y

10

16x9y

20

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃̃

2

a. 2x9y

20c.

4x9

y10

b.4x

18

y20

d. 4x18

y−20

____ 36. 20x

20y

9

40x7y

13

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃̃

4

a.x

52

2y16

c.x

13

16y4

b.x

52y

−16

16d.

x52

16y16

Evaluate the expression. Express the result in scientific notation.

____ 37. 7.02 × 10−8Ê

ËÁÁÁ

ˆ¯˜̃̃ 6.9 × 10

−3ÊËÁÁÁ

ˆ¯˜̃̃

a. 0.48438 × 10−11

c. 4.8438 × 10−10

b. 4.8438 × 1011

d. 48.438 × 10−11

____ 38. 31.02 × 10

26

2 × 105

a. 0.1551 × 1023

c. 15.51 × 1021

b. 1.551 × 1031

d. 1.551 × 1022

Name: ________________________ ID: A

11

Simplify the given expression.

____ 39. 11x2

+ 3x + 19ÊËÁÁÁ

ˆ¯˜̃̃ + 6x

2− 18x − 8

ÊËÁÁÁ

ˆ¯˜̃̃

a. 17x2

− 15x + 11 c. 17x2

+ 9x + 11

b. 17x2

+ 21x + 27 d. 29x2

− 15x + 11

____ 40. 13x2

+ 6xy − 12y2Ê

ËÁÁÁ

ˆ¯˜̃̃ − 9x

2− 4xy

ÊËÁÁÁ

ˆ¯˜̃̃

a. 4x2

+ 2xy − 12y2

c. 4x2

− 10xy

b. 4x2

+ 10xy − 12y2

d. 4x2

− 6xy − 8y2

____ 41. −2xy(3xy3

− 5xy + 7y2)

a. −6x2y

4+ 10x

2y

2− 14xy

3c. −6x

2y

4− 5x

2y

2+ 7x

2y

3

b. −6x2y

4− 5xy + 7y

2d. −6x

2y

4+ 10xy + 14y

2

Simplify the expression using long division.

____ 42. (2x2

− 33x + 16) ÷ (x − 16)

a. quotient 2x − 33 and remainder 16 c. quotient 2x − 1 and remainder –32

b. quotient 2x − 1 and remainder 0 d. quotient 2x + 1 and remainder 32

____ 43. (9x2

− 41x − 6) ÷ (x − 4)

a. quotient 9x − 5 and remainder –26 c. quotient 9x − 5 and remainder –14

b. quotient 9x − 41 and remainder 4 d. quotient 9x + 5 and remainder 14

Simplify the expression using synthetic division.

____ 44. (3x3

− 35x2

+ 128x − 140) ÷ (x − 5)

a. quotient 3x2

− 50x − 122 and remainder 470

b. quotient 15x2

+ 40x + 328 and remainder 1,500

c. quotient 3x2

− 20x + 28 and remainder 0

d. quotient 18x2

+ 55x − 403 and remainder 1,875

____ 45. (6x3

− 48x2

+ 120x − 96) ÷ (x − 4)

a. quotient 24x2

+ 48x + 312ÊËÁÁÁ

ˆ¯˜̃̃ and remainder 1,152

b. quotient 6x2

− 24x + 24ÊËÁÁÁ

ˆ¯˜̃̃ and remainder 0

c. quotient 30x2

+ 72x − 408ÊËÁÁÁ

ˆ¯˜̃̃ and remainder 1,536

d. quotient 6x2

− 72x − 168ÊËÁÁÁ

ˆ¯˜̃̃ and remainder 576

____ 46. Find p −3( ) and p(5) for the function p x( ) = 4x4

+ 8x3

− 2x2

+ 13x + 10.

a. 51; 3,515 c. –371; 1,525

b. 61; 3,525 d. 113; 3,473

Name: ________________________ ID: A

12

For the given graph,

a. describe the end behavior,

b. determine whether it represents an odd-degree or even-degree polynomial function, and

c. state the number of real zeros.

____ 47.

a. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → +∞ as x → −∞.

It is an odd-degree polynomial function.

The function has five real zeros.

b. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → −∞ as x → −∞.



c. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → −∞ as x → −∞.


The function has four real zeros.

d. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → −∞ as x → −∞.

It is an even-degree polynomial function.


Name: ________________________ ID: A

13

____ 48.

a. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → +∞ as x → −∞.



b. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → +∞ as x → −∞.



c. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → +∞ as x → −∞.



d. The end behavior of the graph is f x( ) → +∞ as x → +∞ and f x( ) → −∞ as x → −∞.



Name: ________________________ ID: A

14

____ 49. Graph the function f x( ) = 3x5

+ 8x4

− 3x3

− 10x2

+ 12 by making a table of values.

a. c.

b. d.

For the given function, determine consecutive values of x between which each real zero is located.

____ 50. f x( ) = −2x4

− 4x3

− 2x2

+ 3x + 8

a. There is a zero between x = 1 and x = 2.

b. There are zeros between x = 2 and x = 3, x = 1 and x = 0, x = –2 and x = –3.

c. There are zeros between x = 1 and x = 2, x = –1 and x = –2.

d. There is a zero between x = –1 and x = –2.

Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.

____ 51. f x( ) = 8x3

+ 2x2

− 8

a. The relative maximum is at x = −0.17, and the relative minimum is at x = 1.

b. The relative maximum is at x = 0.17, and the relative minimum is at x = 0.

c. The relative maximum is at x = 0.17, and the relative minimum is at x = 1.

d. The relative maximum is at x = −0.17, and the relative minimum is at x = 0.

Name: ________________________ ID: A

15

Factor the polynomial completely.

____ 52. 5x4y − 10x

2y

2

a. 5x2y x

2− 2y

ÊËÁÁÁ

ˆ¯˜̃̃ c. x

2y 5x

2− 10y

ÊËÁÁÁ

ˆ¯˜̃̃

b. 5x2

x2y − 2y

2ÊËÁÁÁ

ˆ¯˜̃̃ d. 5 x

4y − 2x

2y

2ÊËÁÁÁ

ˆ¯˜̃̃

____ 53. 2xy − 3y − 32x + 48

a. (y − 16)(2x − 3) c. (2xy − 3y) − (32x − 48)

b. y(2x − 3) − 32x + 48 d. y(2x − 3) − 16(2x − 3)

____ 54. 4x2

− 13x + 9

a. 4x2

− 4x − 9x + 9 c. 4x(x − 1) − 9(x − 1)

b. 4x2

− 3x − 10x + 9 d. (4x − 9)(x − 1)

____ 55. 7x2

+ 5x − 18

a. (7x − 9)(x + 2) c. (7x + 9)(x + 2)

b. (7x + 9)(x − 2) d. (7x − 9)(x − 2)

____ 56. Use synthetic substitution to find g 2( ) and g (–7) for the function g x( ) = 5x4

− 3x2

+ 6x − 4.

a. 100, 2,216 c. 84, 11,896

b. 76, 11,812 d. 36, –536

Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors

may not be binomials.

____ 57. 16x3

− 144x2

− 81x + 729; x − 9

a. (4x −9)(4x + 9) c. (4x − 9)

b. (16x2

− 81) d. (4x −9)(4x − 9)

____ 58. 36x3

+ 60x2

− 143x − 242; x − 2

a. (6x − 11)2

c. (6x + 11)(6x + 11)

b. 2(6x + 11) d. (6x + 11)(6x − 11)

Solve the given equation. State the number and type of roots.

____ 59. x2

+ 2x − 8 = 0

a. The equation has two real roots, 2 and 4.

b. The equation has two real roots, 2 and –4.

c. The equation has two real roots, –2 and –4.

d. The equation has two real roots, –2 and 4.

____ 60. x2

+ 9x − 10 = 0

a. The equation has two real roots, 1 and –10.

b. The equation has two real roots, –1 and –10.

c. The equation has two real roots, –1 and 10.

d. The equation has two real roots, 1 and 10.

Name: ________________________ ID: A

16

____ 61. Find all of the zeros of the function f(x) = x3

− 15x2

+ 73x − 111.

a. 3, 6 – i, 6 + i c. 3, 6 – i

b. 6 – i, 6 + i d. –3, 6 – i, 6 + i

____ 62. List all of the possible rational zeros of the following function.

f x( ) = 2x6

− 10x5

− 23x4

+ 80x3

+ 28x2

− 20x + 9

a. ±1, ±3, ±9, ±1

2, ±

3

2, ±

9

2c. 1, 3, 9,

1

2,

3

2,

9

2

b. 1, 3, 9, ±1

2, ±

3

2, ±

9

2d. –1, –3, –9, −

1

2, −

3

2, −

9

2

____ 63. Find all the rational zeros of the function f x( ) = 12x4

− 36x3

− 636x2

− 108x.

a. 1, –9 c. 1, 9

b. 0, 9 d. 0, –9

Name: ________________________ ID: A

17

Sketch the graph of the given function. Then state the function’s domain and range.

____ 64. y = –1.2(3)x

a.

The domain is all real numbers and the

range is all negative numbers.

c.


range is all positive numbers.

b.


range is all negative numbers.

d.



Name: ________________________ ID: A

18

____ 65. y = 2(4)x

a.


range is all real numbers.

c.



b.



d.



Solve the given equation.

____ 66. 65n + 6

= 1,296

a. n = −3

5c. n = −

2

5

b. n = –2 d. n = 2

Solve the given inequality.

____ 67. 4,0962n

< 512n+ 9

a. n < 3 c. n < 9

b. n < 9

5d. n <

27

5

Name: ________________________ ID: A

19

Evaluate the logarithmic expression.

____ 68. log8 32,768

a. 58

c. 832,768

b. 32,768 d. 5

____ 69. log9

1

729

a. 3 c. 9

1

729

b. 93

d. –3

____ 70. Solve log8 n =4

3.

a.4

3c. 8

b.32

3d. 16

____ 71. Solve log3x = 6.

a. 18 c. 6

b. 216 d. 729

____ 72. Solve log3 b > 4.

a. b > 4−3

c. b > 12

b. b > 3 d. b > 81

____ 73. Solve log27 b >1

3.

a. b > 23

c. b >1

27

b. b >1

3d. b > 3

____ 74. Use log43 ≈ 0.7925 and log44 = 1 to approximate the value of the expression log4 384.

a. 1.2528 c. 384

b. 3.5 d. 4.2925

Solve the given equation. If necessary, round to four decimal places.

____ 75. log2 9 + log2 a = log2 13

a. 26 c. 0.69

b. 1.4444 d. 4

____ 76. 13y

= 21

a. 18.8519 c. 1.1870

b. 0.2083 d. 3.0445

____ 77. 92x

= 21

a. 11.0035 c. 2.1972

b. 3.0445 d. 0.6928

Name: ________________________ ID: A

20

Solve the given inequality. If necessary, round to four decimal places.

____ 78. 3y

≥ 12

a. y ≥ 1.0986 c. y ≥ 25.1508

b. y ≥ 2.2619 d. y ≥ 0.6021

____ 79. 96a

< 17

a. a < 2.1972 c. a < 0.2149

b. a < 1.7918 d. a < 2.9692

Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal

places.

____ 80. log6 5.6

a. log5.6

6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; –0.0300 c.

log 6

log 5.6; 1.0400

b. log6

5.6

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; 0.0300 d.

log 5.6

log 6; 0.9615

____ 81. log12 14

a. log12

14

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; –0.0669 c.

log 12

log 14; 0.9416

b. log14

12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ; 0.0669 d.

log 14

log 12; 1.0620

____ 82. Evaluate the expression lne2.

a. e2

c. ln2e

b. 2e

d. 2

____ 83. Evaluate the expression e ln 14.

a. ln14e

c. lne14

b. 14 d. e14

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

____ 84. 4ex

− 4 = 2

a. 1.7918 c. 1.5

b. 0.4055 d. 0

____ 85. 10 + 5e2x

= 17

a. 1.4 c. 0.5666

b. 0.6592 d. 0.1682

Name: ________________________ ID: A

21

Solve the given inequality. Round to the nearest ten-thousandth, if necessary.

____ 86. ex

> 7

a. x > −7 c. x > 0.8451

b. x > 1.9459 d. x > 7

____ 87. e7x

≤ 20

a. x < 20 c. x < −20

b. x ≤ 1.301 d. x ≤ 0.428

____ 88. Radioactive iodine is used to determine the health of thyroid gland. It decays according to the equation

y = ae−0.0856t

, where t is in days. Find the one-third life of this substance. Round to the nearest integer.

a. 6 c. 16

b. 13 d. 67

Short Answer

89. A rocket is launched with an initial velocity of 107 feet per second from the top of a cliff 63 feet high. Its

height is described by h(t) = −16t2

+ 107t + 63. How long will the rocket take to hit the ground?

90. The standard equation of a circle with center (h, k) and radius r is given by (x − h)2

+ (y − k)2

= r2. Write the

equation of a circle with center (0, 0) and radius 3.

91. A rectangular frame has length (x + 2) units and width (x − 4) units. If the area is 7 square units, what is the

value of x?

92. Describe the end behavior of the graph.

Name: ________________________ ID: A

22

93. Describe the end behavior of the graph and determine whether it represents an odd-degree or an even-degree

polynomial function.

The production of a new car model in the year 1995 was 1.25 million units. In the year 2005, it rose to 3.5

million units.

94. Write an exponential function to model the cars y produced after x years.

95. Assuming that production continued at the same rate of increase, estimate production in 2010.

Solve each equation.

96. log10 5 + log 10x = log 10 25

97. log5 x + log5 (x + 23) = log5 50

98. 2 log3 x − log3 4 = log3 16

99. log2 0.5 + 2log2 x = log2 5 + log2 40

100. log10 49 − log10

7

5+ log10 4 = log10 5x

In a survey in 2000, the population of two plant species were found to be growing exponentially. Their

growth is given by these equations: species A, P = 2000e0.05t

and species B, P = 5000e0.02t

, where t = 0 in the

year 2000.

101. Based on this information, find the population of species A in 2010.

102. It is estimated that the conditions necessary for the survival of species A in the forest will disappear when the

species reaches a population of 20,000. Based on this information, for how many more years will the forest

support species A?

103. After how many years will the population of species A be equal to the population of species B in the forest?

ID: A

1

Algebra 2 Final Exam Review

Answer Section

MULTIPLE CHOICE

1. ANS: C

For the quadratic equation ax2

+ bx + c, the y-intercept is c and the equation of axis of

symmetry is x =−b

2a.

Feedback

A Did you check the signs?

B Did you interchange the y-intercept and the x-coordinate of the vertex?

C Correct!

D Did you use the correct formulas for the y-intercept and the x-coordinate of the vertex?

PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

2. ANS: B

First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate

pairs and connect the points with a smooth curve.

Feedback

A Graph ordered pairs that satisfy the function.

B Correct!

C Did you plot the graph correctly?

D When the coefficient of x2 is less than 0, the graphs opens down.

PTS: 1 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 TOP: Graph quadratic functions.

KEY: Quadratic Functions | Graph Quadratic Functions

ID: A

2

3. ANS: C

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The coefficient of x2 is greater than zero.

B The graph of this function opens up.

C Correct!

D What is the value of the y-coordinate of the vertex?

PTS: 1 DIF: Average REF: Lesson 5-1

OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

4. ANS: D

The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the

function.

Feedback

A The graph of the function opens down.

B The coefficient of x2 is less than zero.

C What is the value of the y-coordinate of the vertex?

D Correct!


OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.

NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3

TOP: Find and interpret the maximum and minimum values of a quadratic function.

KEY: Maximum Values | Minimum Values | Quadratic Functions

5. ANS: B

The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic

equation because f(x) = 0 at those points.

Feedback

A What are the x-intercepts of the graph?

B Correct!

C Find the zeros of the function, not the vertex.

D The zeros of the function are the solutions of the related equation.

PTS: 1 DIF: Advanced REF: Lesson 5-2

OBJ: 5-2.1 Solve quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.3 TOP: Solve quadratic equations by graphing.

KEY: Quadratic Equations | Solve Quadratic Equations

ID: A

3

6. ANS: D

When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers

between which the roots are located.

Feedback

A Is the coefficient of x2 less than zero?

B Did you graph the function correctly?

C When the coefficient of x2 is greater than 0, the graph opens up.

D Correct!


OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.

NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 STA: 4.3.12 B.2

TOP: Estimate solutions of quadratic equations by graphing.

KEY: Quadratic Equations | Solve Quadratic Equations

7. ANS: B

For any real numbers a and b, if ab = 0, then either a = 0, b − 0, or both a and b are equal to zero.

Feedback

A Did you use the Zero Product Property correctly?

B Correct!

C Did you verify the answer by substituting the values?

D Did you factor the binomial correctly?


OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

STA: 4.3.12 D.2 TOP: Solve quadratic equations by factoring.

KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

8. ANS: B

For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b are equal to zero.

Feedback

A Did you use the Zero Product Property correctly?

B Correct!

C Did you factor the binomial correctly?

D Did you verify the answer by substituting the values?


OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2

STA: 4.3.12 D.2 TOP: Solve quadratic equations by factoring.

KEY: Quadratic Equations | Solve Quadratic Equations | Factoring

ID: A

4

9. ANS: A

For any numbers a, b, and c, abc = a ⋅ b ⋅ c . Also, −1 = i2

= i.

Feedback

A Correct!

B Check for the radical sign.

C Take the square root of the number.

D Check your calculation.

PTS: 1 DIF: Basic REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 TOP: Find square roots.

KEY: Square Roots

10. ANS: A

a

b=

a

b

Feedback

A Correct!

B Check the numerator.

C Check the square root of the numerator.

D Check your calculation.

PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.1 Find square roots.

NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2 TOP: Find square roots.

KEY: Square Roots

11. ANS: C

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Multiply the imaginary numbers again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers

ID: A

5

12. ANS: A

Multiply the real numbers and imaginary numbers separately.

Feedback

A Check your calculation.

B Check the sign.

C Correct!

D Compute again.


OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers

13. ANS: A

Combine the real and imaginary parts of the complex numbers to add them.

Feedback

A Correct!

B Combine the real parts and then combine the imaginary parts.

C Add the real and imaginary parts of the two numbers separately.

D Did you combine the similar terms correctly?


OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform addition and subtraction operations with complex numbers.

KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers

14. ANS: B

Combine the real and imaginary parts of the complex numbers to add them.

Feedback

A Combine the real parts and then combine the imaginary parts.

B Correct!

C Combine the similar terms correctly.

D Add the real and imaginary parts of the two numbers separately.


OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform addition and subtraction operations with complex numbers.

KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers

ID: A

6

15. ANS: B

Use the FOIL method to multiply the complex numbers and use the formula i2

= −1. Combine the real parts

and then the imaginary parts of the two numbers.

Feedback

A Did you combine the real parts?

B Correct!

C Use the value of i2.

D Did you use the FOIL method to find the product?


OBJ: 5-4.4 Perform multiplication operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform multiplication operations with complex numbers.

KEY: Complex Numbers | Multiply Complex Numbers

16. ANS: C

Use the FOIL method to multiply the complex numbers and use the formula i2

= −1. Combine the real parts

and then the imaginary parts of the two numbers.

Feedback

A Use the FOIL method to find the product.

B Use the value of i2.

C Correct!

D Combine the real parts.


OBJ: 5-4.4 Perform multiplication operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform multiplication operations with complex numbers.

KEY: Complex Numbers | Multiply Complex Numbers

17. ANS: D

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL

method and the difference of squares to simplify the given expression.

Feedback

A Multiply the numerator with the conjugate of the denominator.

B Have you multiplied the constant in the numerator with its conjugate of the

denominator?

C Did you multiply the conjugates correctly in the denominator?

D Correct!


OBJ: 5-4.5 Perform division operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform division operations with complex numbers.

KEY: Complex Numbers | Divide Complex Numbers

ID: A

7

18. ANS: A

Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL

method and the difference of squares to simplify the given expression.

Feedback

A Correct!

B Did you multiply the conjugates correctly in the denominator?

C Multiply the numerator also with the conjugate of the denominator.

D Did you combine the similar terms correctly?


OBJ: 5-4.5 Perform division operations with complex numbers.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2

TOP: Perform division operations with complex numbers.

KEY: Complex Numbers | Divide Complex Numbers

19. ANS: D

For any real number n, if x2

= n, then x = ± n .

Feedback

A Did you use the Square Root Property correctly?

B Did you verify the answer by substituting the values?

C Did you factor the perfect square trinomial correctly?

D Correct!


OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.

NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: 4.3.12 D.2

TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

20. ANS: A

For any real number n, if x2

= n, then x = ± n .

Feedback

A Correct!

B Did you factor the perfect square trinomial correctly?

C Did you use the Square Root Property correctly?

D Did you verify the answer by substituting the values?


OBJ: 5-5.1 Solve quadratic equations by using the Square Root Property.


TOP: Solve quadratic equations by using the Square Root Property.

KEY: Quadratic Equations | Solve Quadratic Equations | Square Root Property

ID: A

8

21. ANS: A

To complete the square for any quadratic expression of the form x2

+ bx, find half of b, and square the result.

Then, add the result to x2

+ bx.

Feedback

A Correct!

B Did you make the quadratic expression a perfect square?

C Did you verify the answer by substituting the values?

D Did you check the signs of the roots?


OBJ: 5-5.2 Solve quadratic equations by completing the square.


TOP: Solve quadratic equations by completing the square.

KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

22. ANS: D

To complete the square for any quadratic expression of the form x2

+ bx, find half of b, and square the result.

Then, add the result to x2

+ bx.

Feedback

A Did you make the quadratic expression a perfect square?

B Did you check the signs of the roots?

C Find both the solutions.

D Correct!


OBJ: 5-5.2 Solve quadratic equations by completing the square.


TOP: Solve quadratic equations by completing the square.

KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square

23. ANS: D

The solution of a quadratic equation of the form ax2

+ bx + c = 0, where a ≠ 0, is obtained by using the

formula x =−b ± b

2− 4ac

2a.

Feedback

A Did you check the signs of the solution?

B Did you use the correct formula?

C Did you substitute the values of a, b, and c correctly in the formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.


TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

ID: A

9

24. ANS: D

The solution of a quadratic equation of the form ax2

+ bx + c = 0, where a ≠ 0, is obtained by using the

formula x =−b ± b

2− 4ac

2a.

Feedback

A Did you substitute the values of a, b, and c correctly in the formula?

B Did you evaluate the discriminant correctly?

C Did you use the correct formula?

D Correct!


OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.


TOP: Solve quadratic equations by using the Quadratic Formula.

KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula

25. ANS: C

If b2

− 4ac > 0 and b2

− 4ac is a perfect square, then the roots are rational.

If b2

− 4ac > 0 and b2

− 4ac is not a perfect square, then the roots are real and irrational.

Feedback

A Did you use the correct formula for the discriminant?

B Did you check the sign of the answer?

C Correct!

D Did you use the correct order of operations while evaluating the discriminant?

PTS: 1 DIF: Basic REF: Lesson 5-6

OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.


TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.

KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates

26. ANS: C

If b2

− 4ac < 0, then the roots are complex.

Feedback

A Did you use the correct order of operations while evaluating the discriminant?

B Did you use the correct formula for the discriminant?

C Correct!

D Did you check the sign of the answer?


OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.


TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.

KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates

ID: A

10

27. ANS: A

The vertex form of a quadratic function is y = a(x − h)2

+ k .

The equation of the axis of symmetry of a parabola is x = h.

Feedback

A Correct!

B Did you check the x-coordinate of the vertex?

C Did you identify the coordinates of the vertex correctly?

D Did you use the correct equation of the axis of symmetry of a parabola?


OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.


TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.

KEY: Quadratic Functions | Axis of Symmetry

28. ANS: C

The vertex form of a quadratic function is y = a(x − h)2

+ k .

The equation of the axis of symmetry of a parabola is x = h.

Feedback

A Did you use the correct equation of the axis of symmetry?

B Did you check the x-coordinate of the vertex?

C Correct!

D Did you identify the coordinates of the vertex correctly?


OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.


TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.

KEY: Quadratic Functions | Axis of Symmetry

29. ANS: A

Graph the related quadratic equation. Because the inequality symbol is >, the parabola should be dashed. Test

a point (x1 , y1) inside the parabola. If (x1 , y1) is the solution of the inequality, shade the region inside the

parabola. If (x1 , y1) is not a solution, shade the region outside the parabola.

Feedback

A Correct!

B What is the inequality symbol used in the equation?

C Did you test a point inside the parabola correctly?

D Did you shade correctly?


OBJ: 5-8.1 Graph quadratic inequalities in two variables. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

STA: 4.3.12 B.1 TOP: Graph quadratic inequalities in two variables.

KEY: Quadratic Inequalities | Graph Quadratic Inequalities

ID: A

11

30. ANS: A

Graph the related quadratic equation. Since the inequality symbol is <, the parabola should be dashed. Test a

point (x1 , y1) inside the parabola. If (x1 , y1) is the solution of the inequality, shade the region inside the

parabola. If (x1 , y1) is not a solution, shade the region outside the parabola.

Feedback

A Correct!

B Did you test a point inside the parabola correctly?

C Did you shade correctly?

D What is the inequality symbol used in the equation?


OBJ: 5-8.1 Graph quadratic inequalities in two variables. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

STA: 4.3.12 B.1 TOP: Graph quadratic inequalities in two variables.

KEY: Quadratic Inequalities | Graph Quadratic Inequalities

31. ANS: C

First, write the related quadratic equation and factor it. Then, use the Zero Product Property and solve each

equation. The solution is all real numbers when all test points satisfy the inequality. The solution is an empty

set when none of the test points satisfy the inequality.

Feedback

A Is it possible to have this solution?

B Did you write the related quadratic equation and factor it correctly?

C Correct!

D Did you test a value in the interval to see if it satisfies the original inequality?


OBJ: 5-8.2 Solve quadratic inequalities in one variable. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

TOP: Solve quadratic inequalities in one variable.

KEY: Quadratic Inequalities | Solve Quadratic Inequalities

32. ANS: B

First, write the related quadratic equation and factor it. Then, use the Zero Product Property and solve each

equation. The solution is all real numbers when all test points satisfy the inequality. The solution is an empty

set when none of the test points satisfy the inequality.

Feedback

A Did you write the related quadratic equation and factor it correctly?

B Correct!

C Did you test a value in each interval to see if it satisfies the original inequality?

D Test a value in each interval to see if it satisfies the original inequality.


OBJ: 5-8.2 Solve quadratic inequalities in one variable. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3

TOP: Solve quadratic inequalities in one variable.

KEY: Quadratic Inequalities | Solve Quadratic Inequalities

ID: A

12

33. ANS: C

Multiply the constants and then multiply the powers using the Power of a Product Property.

Feedback

A A simplified expression cannot contain negative exponents.

B Multiply the constants.

C Correct!

D Multiply the powers of the same variable using the Power of a Product Property.


OBJ: 6-1.1 Use properties of exponents to multiply monomials.


TOP: Use properties of exponents to multiply monomials. KEY: Monomials | Multiply Monomials

34. ANS: B

Multiply the constants and then multiply the powers using the Power of a Product Property.

Feedback

A Multiply the powers of the same variable using the Power of a Product Property.

B Correct!

C Multiply the constants.

D A simplified expression cannot contain negative exponents.


OBJ: 6-1.1 Use properties of exponents to multiply monomials.


TOP: Use properties of exponents to multiply monomials. KEY: Monomials | Multiply Monomials

35. ANS: B

Simplify each base using the properties of powers. Then, write all the fractions in the simplest terms and

ensure there are no negative exponents.

Feedback

A Use the Power of a Power Property to all the terms in the monomial.

B Correct!

C Raise the numerator and the denominator to the second power before simplifying.

D There should be no negative exponents.


OBJ: 6-1.2 Use properties of exponents to divide monomials. NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2

STA: 4.3.12 D.1 TOP: Use properties of exponents to divide monomials.

KEY: Monomials | Divide Monomials

ID: A

13

36. ANS: D

Simplify each base using the properties of powers. Then, write all the fractions in the simplest terms and

ensure there are no negative exponents.

Feedback

A Use the Power of a Power Property to all the terms in the monomial.

B There should be no negative exponents.

C Raise the numerator and the denominator to the fourth power before simplifying.

D Correct!


OBJ: 6-1.2 Use properties of exponents to divide monomials. NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2

STA: 4.3.12 D.1 TOP: Use properties of exponents to divide monomials.

KEY: Monomials | Divide Monomials

37. ANS: C

Use the Associative Property of Multiplication and then the Commutative Property of Multiplication and

Addition.

Feedback

A The number should be greater than or equal to 1.

B Did you check the power of 10?

C Correct!

D The number should be less than 10.


OBJ: 6-1.3 Use expressions written in scientific notation. NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2

TOP: Use expressions written in scientific notation. KEY: Scientific Notation

38. ANS: D

Use the Properties of Powers to divide numbers in scientific notation.

Feedback

A The number should be greater than or equal to 1.

B Use the Power of a Quotient Property to simplify the powers of 10.

C The number should be less than 10.

D Correct!


OBJ: 6-1.3 Use expressions written in scientific notation. NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2

TOP: Use expressions written in scientific notation. KEY: Scientific Notation

ID: A

14

39. ANS: A

Group similar terms and then combine them.

Feedback

A Correct!

B Did you combine the similar terms correctly?

C Did you group the similar terms and then combine them?

D Did you group the similar terms?

PTS: 1 DIF: Average REF: Lesson 6-2 OBJ: 6-2.1 Add polynomials.


TOP: Add polynomials. KEY: Polynomials | Add Polynomials

40. ANS: B

Group the similar terms and then combine them.

Feedback

A Did you combine the similar terms correctly?

B Correct!

C Did you consider all the terms of the expression?

D Did you group the similar terms?

PTS: 1 DIF: Average REF: Lesson 6-2 OBJ: 6-2.2 Subtract polynomials.


TOP: Subtract polynomials. KEY: Polynomials | Subtract Polynomials

41. ANS: A

Use the Distributive Property and then multiply the monomials using the Product of Powers Property.

Feedback

A Correct!

B Did you use the Distributive Property?

C Did you multiply the monomials correctly?

D Did you calculate the product of powers correctly?

PTS: 1 DIF: Average REF: Lesson 6-2 OBJ: 6-2.3 Multiply polynomials.


TOP: Multiply polynomials. KEY: Polynomials | Multiply Polynomials

ID: A

15

42. ANS: B

Use the division algorithm. When dividing, you can add or subtract only similar terms.

Feedback

A Did you consider both the terms of the divisor?

B Correct!

C Change the signs of the product terms only.

D Did you use the correct signs of the terms?


OBJ: 6-3.1 Divide polynomials using long division. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2

STA: 4.3.12 D.1 TOP: Divide polynomials using long division.

KEY: Polynomials | Divide Polynomials | Long Division

43. ANS: A

Use the division algorithm. When dividing, you can add or subtract only similar terms.

Feedback

A Correct!

B Did you consider both the terms of the divisor?

C Change the signs of the product terms only.

D Did you multiply the divisor with the correct term?


OBJ: 6-3.1 Divide polynomials using long division. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2

STA: 4.3.12 D.1 TOP: Divide polynomials using long division.

KEY: Polynomials | Divide Polynomials | Long Division

44. ANS: C

To use synthetic division, the divisor must be of the form x − r.

Feedback

A Add the product of the constant in the divisor to the coefficient above it.

B Multiply the first coefficient with the constant in the divisor and bring it below the

second coefficient.

C Correct!

D Bring the first coefficient below itself in the third row.


OBJ: 6-3.2 Divide polynomials using synthetic division. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2

STA: 4.3.12 D.1 TOP: Divide polynomials using synthetic division.

KEY: Polynomials | Divide Polynomials | Synthetic Division

ID: A

16

45. ANS: B

To use synthetic division, the divisor must be of the form x − r.

Feedback

A Multiply the first coefficient with the constant in the divisor and bring it below the

second coefficient.

B Correct!

C Bring the first coefficient below itself in the third row.

D Add the product of the constant in the divisor to the coefficient above it.


OBJ: 6-3.2 Divide polynomials using synthetic division. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2

STA: 4.3.12 D.1 TOP: Divide polynomials using synthetic division.

KEY: Polynomials | Divide Polynomials | Synthetic Division

46. ANS: B

Replace the values of p(x) with p(–3) and simplify.

Feedback

A Add the value of the constant.

B Correct!

C The exponent value of the first term is 4, not 3.

D Did you substitute the correct values in the function?


OBJ: 6-4.1 Evaluate polynomial functions. NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2

STA: 4.3.12 D.1 TOP: Evaluate polynomial functions. KEY: Polynomial Functions

47. ANS: B

The end behavior is the behavior of the graph as x approaches positive infinity +∞( ) or negative infinity

−∞( ). The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function.

Feedback

A What is the end behavior of the graph?

B Correct!

C Did you verify the number of real zeros?

D Check the degree of the polynomial function.


OBJ: 6-4.2 Identify general shapes of graphs of polynomial functions.


TOP: Identify general shapes of graphs of polynomial functions.

KEY: Polynomial Functions | Graph Polynomial Functions

ID: A

17

48. ANS: A


−∞( ). The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function.

Feedback

A Correct!

B Did you verify the number of real zeros?

C Check the degree of the polynomial function.

D What is the end behavior of the graph?


OBJ: 6-4.2 Identify general shapes of graphs of polynomial functions.


TOP: Identify general shapes of graphs of polynomial functions.

KEY: Polynomial Functions | Graph Polynomial Functions

49. ANS: A

Make a table of values and plot the graph.

Feedback

A Correct!

B Did you use the correct equation to plot the graph?

C Did you plot the correct graph?

D The degree of the polynomial is 5, not 4.

PTS: 1 DIF: Average REF: Lesson 6-5 OBJ: 6-5.1 Graph polynomial functions.


TOP: Graph polynomial functions. KEY: Polynomial Functions | Graph Polynomial Functions

50. ANS: C

Make a table of values to obtain the required answer.

Feedback

A Did you locate all the real zeros?

B Does the sign of the polynomial change between these consecutive values?

C Correct!

D You have obtained only some of the real zeros.


OBJ: 6-5.2 Locate real zeros of polynomial functions. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2

STA: 4.3.12 B.2 TOP: Locate real zeros of polynomial functions.

KEY: Polynomial Functions | Zeroes of Polynomial Functions

ID: A

18

51. ANS: D

Make a table of values and graph the equation.

Feedback

A A relative minimum is a point that has no nearby points with a lesser y-coordinate.

B Did you obtain the correct value of the relative maximum?

C Did you find the correct coordinates of the function?

D Correct!


OBJ: 6-5.3 Find the maxima and minima of polynomial functions.


TOP: Find the maxima and minima of polynomial functions.

KEY: Maxima of Polynomial Functions | Minima of Polynomial Functions

52. ANS: A

Find the GCF (greatest common factor) of the monomials in the given polynomial, and use it in grouping the

polynomial.

Feedback

A Correct!

B Take the GCF of the monomials using all the terms given in it.

C Take the GCF of the whole numbers in the monomials.

D Take the GCF using the monomials in the given polynomial and not just the whole

numbers.


OBJ: 6-6.1 Factor polynomials with the GCF. NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2

STA: 4.3.12 D.2 TOP: Factor polynomials with the GCF.

KEY: Polynomials | Factor Polynomials | GCF

53. ANS: A

Group the monomials to find the GCF (greatest common factor), factor the GCF of each binomial, and then

use the Distributive Property to obtain the factors.

Feedback

A Correct!

B Group the polynomial into binomials to find the GCF.

C Factor the GCF of each binomial.

D Use the Distributive Property.


OBJ: 6-6.2 Factor polynomials by grouping. NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2

STA: 4.3.12 D.2 TOP: Factor polynomials by grouping. KEY: Polynomials | Factor Polynomials

ID: A

19

54. ANS: D

To find the coefficient of the x terms, find two numbers whose product is 4 ⋅ 9 or 36 and whose sum is 13.

Feedback

A Factor the GCF of each group.

B The product of the coefficient of the x terms should be equal to the product of the

coefficient of the x2 term and the constant term.

C Use the Distributive Property to obtain two binomial factors.

D Correct!


OBJ: 6-6.3 Factor polynomials with addition recognizing the FOIL method.


TOP: Factor polynomials with addition by recognizing the FOIL method.

KEY: Polynomials | Factor Polynomials | FOIL Method

55. ANS: A

To find the coefficient of the x terms, find two numbers such that their product is 7 ⋅ −18( ) or –126 and their

difference is + 5.

Feedback

A Correct!

B Rewrite the coefficients of the x term in two parts such that their difference is equal to

the x coefficient in the original expression.

C Use the Distributive Property to obtain two binomial factors.

D Rewrite the coefficients of the x term in two parts such that their product is equal to the

product of the coefficient of the x2 term and the constant.


OBJ: 6-6.4 Factor polynomials with subtraction recognizing the FOIL method.


TOP: Factor polynomials with subtraction recognizing the FOIL method.

KEY: Polynomials | Factor Polynomials | FOIL Method

56. ANS: B

Use synthetic substitution to obtain the required answer.

Feedback

A Did you calculate correctly?

B Correct!

C Did you substitute the correct values?

D The degree of the function is 4, not 3.


OBJ: 6-7.1 Evaluate functions using synthetic substitution. NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2

STA: 4.3.12 D.1 TOP: Evaluate functions using synthetic substitution.

KEY: Polynomial Functions | Synthetic Substitution

ID: A

20

57. ANS: A

Use the Factor Theorem.

Feedback

A Correct!

B You have to factor the depressed polynomial to its simplest form.

C Did you factor correctly?

D Did you verify the answer by multiplying the factors?


OBJ: 6-7.2 Determine whether a binomial is a factor of a polynomial by using synthetic substitution.

NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2

TOP: Determine whether a binomial is a factor of a polynomial by using synthetic substitution.


58. ANS: C

Use the Factor Theorem.

Feedback

A Is the square of the binomial equal to the depressed polynomial?

B Did you factor correctly?

C Correct!

D Did you verify the answer by multiplying the factors?


OBJ: 6-7.2 Determine whether a binomial is a factor of a polynomial by using synthetic substitution.

NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2

TOP: Determine whether a binomial is a factor of a polynomial by using synthetic substitution.


59. ANS: B

Factor the equation and find the roots.

Feedback

A Did you factor correctly?

B Correct!

C You have calculated the incorrect roots.

D Did you calculate correctly?


OBJ: 6-8.1 Determine the number and types of roots for a polynomial equation.

NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

TOP: Determine the number and types of roots for a polynomial equation.

KEY: Polynomial Equations | Roots | Real Roots

ID: A

21

60. ANS: A

Factor the equation and find the roots.

Feedback

A Correct!

B You have obtained the incorrect roots.

C Did you calculate correctly?

D Did you factor correctly?


OBJ: 6-8.1 Determine the number and types of roots for a polynomial equation.

NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

TOP: Determine the number and types of roots for a polynomial equation.

KEY: Polynomial Equations | Roots | Real Roots

61. ANS: A

Use synthetic substitution to obtain the required answer.

Feedback

A Correct!

B The function also has a positive real zero.

C Find all the possible imaginary zeros.

D There is no change in sign for the coefficients of f(–x).


OBJ: 6-8.2 Find the zeros of a polynomial function. NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

STA: 4.3.12 B.2 TOP: Find the zeros of a polynomial function.


62. ANS: A

Use the Rational Zero Theorem.

Feedback

A Correct!

B You have missed some of the negative real zeros.

C Did you consider the negative rational zeros?

D You must also include the positive rational zeros in the answer.


OBJ: 6-9.1 Identify the possible rational zeros of a polynomial function.


TOP: Identify the possible rational zeros of a polynomial function.


ID: A

22

63. ANS: B

Use the Rational Zero Theorem.

Feedback

A Did you apply the Rational Zero Theorem correctly?

B Correct!

C Did you verify the answer by substituting the values of the rational zeros?

D Did you correctly?


OBJ: 6-9.2 Find all the rational zeros of a polynomial function.


TOP: Find all the rational zeros of a polynomial function.


64. ANS: A

Make a table of values. Connect the points to sketch a smooth curve.

Feedback

A Correct!

B Multiply the constant with the value of the exponential function.

C Did you check the sign of the constant in the function?

D What is the effect of multiplying a function by a constant?

PTS: 1 DIF: Average REF: Lesson 9-1 OBJ: 9-1.1 Graph exponential functions.


TOP: Graph exponential functions.

KEY: Exponential Functions | Graphs | Graph Exponential Functions

65. ANS: B

Make a table of values. Connect the points to sketch a smooth curve.

Feedback

A Did you use a linear function instead of an exponential function?

B Correct!

C Multiply the constant with the value of the exponential function.

D What is the effect of multiplying a function by a constant?

PTS: 1 DIF: Average REF: Lesson 9-1 OBJ: 9-1.1 Graph exponential functions.


TOP: Graph exponential functions.

KEY: Exponential Functions | Graphs | Graph Exponential Functions

ID: A

23

66. ANS: C

Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation.

Feedback

A Did you check the exponent of the base on the right side of the equation?

B Check the exponent of the base on the left side of the equation.

C Correct!

D Did you solve the equation correctly?

PTS: 1 DIF: Average REF: Lesson 9-1 OBJ: 9-1.2 Solve exponential equations.


TOP: Solve exponential equations. KEY: Solve Equations | Exponential Equations

67. ANS: D

Eliminate the bases. Then, use the Property of Inequality for Exponential Functions and the Distributive

Property.

Feedback

A Did you check the exponential form of the right side of the inequality?

B Use the Distributive Property while simplifying exponents.

C Rewrite each side of the inequality with the same base.

D Correct!


OBJ: 9-1.3 Solve exponential inequalities. NAT: NA 1 | NA 3 | NA 4 | NA 10 | NA 2

STA: 4.3.12 D.2 TOP: Solve exponential inequalities.

KEY: Solve Inequalities | Exponential Inequalities

68. ANS: D

Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression.

Feedback

A Use the Property of Equality for Exponential Functions.

B Write the correct exponential form of the given expression.

C The exponential and logarithmic functions are inverses.

D Correct!


OBJ: 9-2.1 Evaluate logarithmic expressions. NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

STA: 4.3.12 D.1 TOP: Evaluate logarithmic expressions.

KEY: Logarithms | Evaluate Expressions | Logarithmic Expressions

ID: A

24

69. ANS: D

Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression.

Feedback

A Did you check the exponential form?

B Use the Property of Equality for Exponential Functions.


D Correct!


OBJ: 9-2.1 Evaluate logarithmic expressions. NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

STA: 4.3.12 D.1 TOP: Evaluate logarithmic expressions.

KEY: Logarithms | Evaluate Expressions | Logarithmic Expressions

70. ANS: D

Use the definition of logarithms with base b to solve the logarithmic equation.

Feedback

A Did you apply the definition of logarithm?

B Did you simplify correctly?

C What is the value on the right side of the equation?

D Correct!

PTS: 1 DIF: Basic REF: Lesson 9-2 OBJ: 9-2.2 Solve logarithmic equations.

NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: 4.3.12 D.2 TOP: Solve logarithmic equations.

KEY: Solve Equations | Logarithmic Equations

71. ANS: D

Use the definition of logarithms with base b.

Feedback

A Did you use the definition of logarithm correctly?

B Did you calculate correctly?

C Did you consider the base of the logarithm on the left side of the equation?

D Correct!

PTS: 1 DIF: Basic REF: Lesson 9-2 OBJ: 9-2.2 Solve logarithmic equations.



ID: A

25

72. ANS: D

Use the Logarithmic to Exponential Inequality Property.

Feedback

A Did you substitute the correct exponent and base values?

B Did you convert the inequality to an exponential inequality correctly?

C Did you use the definition of logarithm?

D Correct!


OBJ: 9-2.3 Solve logarithmic inequalities. NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

STA: 4.3.12 D.2 TOP: Solve logarithmic inequalities.

KEY: Solve Inequalities | Logarithmic Inequalities

73. ANS: D

Use the Logarithmic to Exponential Inequality Property.

Feedback

A Did you convert the inequality to an exponential inequality correctly?

B Did you substitute the correct exponent and base values?

C Use the definition of logarithm.

D Correct!


OBJ: 9-2.3 Solve logarithmic inequalities. NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2

STA: 4.3.12 D.2 TOP: Solve logarithmic inequalities.

KEY: Solve Inequalities | Logarithmic Inequalities

74. ANS: D

Use the Product Property and the Inverse Property of Exponents and Logarithms.

Feedback

A Did you calculate the logarithm correctly?

B Did you use the Inverse Property of Logarithms?

C Did you substitute the given logarithmic values for solving the expression?

D Correct!


OBJ: 9-3.1 Simplify and evaluate expressions using the properties of logarithms.


TOP: Simplify and evaluate expressions using the properties of logarithms.

KEY: Simplify Expressions | Evaluate Expressions | Logarithmic Properties

ID: A

26

75. ANS: B

Use the Product Property and the definition of logarithm.

Feedback

A Did you substitute the values correctly?

B Correct!

C Have you used the Quotient Property of Logarithms?

D Did you use the properties of logarithms?


OBJ: 9-3.2 Solve logarithmic equations using the properties of logarithms.



76. ANS: C

Use the Property of Inequality for Logarithmic Functions and the Power Property of Logarithms to solve the

equation.

Feedback

A Take the logarithms of both the sides of the equation.

B Did you use the Quotient Property of Logarithms?

C Correct!

D Did you substitute the values of the equation according to the Power Property of

Logarithms?


OBJ: 9-4.1 Solve exponential equations using common logarithms.


TOP: Solve exponential equations using common logarithms.

KEY: Solve Equations | Exponential Equations | Common Logarithms

77. ANS: D


equation.

Feedback

A Take the logarithm of both sides of the equation.

B Did you use the Power Property of Logarithms?

C How do you solve an exponential equation?

D Correct!


OBJ: 9-4.1 Solve exponential equations using common logarithms.


TOP: Solve exponential equations using common logarithms.

KEY: Solve Equations | Exponential Equations | Common Logarithms

ID: A

27

78. ANS: B


inequality.

Feedback

A How do you solve an exponential inequality?

B Correct!

C Take the logarithm of both sides of the inequality.

D Did you use the Quotient Property of Logarithms?


OBJ: 9-4.2 Solve exponential inequalities using common logarithms.


TOP: Solve exponential inequalities using common logarithms.

KEY: Solve Inequalities | Exponential Inequalities | Common Logarithms

79. ANS: C


inequality.

Feedback

A Did you use the Power Property to calculate the logarithmic expression?

B How do you solve an exponential inequality?

C Correct!

D Take the logarithm of both sides of the inequality.


OBJ: 9-4.2 Solve exponential inequalities using common logarithms.


TOP: Solve exponential inequalities using common logarithms.

KEY: Solve Inequalities | Exponential Inequalities | Common Logarithms

80. ANS: D

Use the Change of Base Formula to express the logarithm in terms of common logarithms.

Feedback

A Did you use the Change of Base Formula correctly?

B What is the Change of Base Formula?

C Did you interchange the original base and exponent?

D Correct!


OBJ: 9-4.3 Evaluate logarithmic expressions using the Change of Base Formula.


TOP: Evaluate logarithmic expressions using the Change of Base Formula.

KEY: Evaluate Expressions | Logarithmic Expressions | Change of Base Formula

ID: A

28

81. ANS: D

Use the Change of Base Formula to express the logarithm in terms of common logarithms.

Feedback

A Did you use the Change of Base Formula correctly?

B What is the Change of Base Formula?

C Did you interchange the original base and exponent values?

D Correct!


OBJ: 9-4.3 Evaluate logarithmic expressions using the Change of Base Formula.


TOP: Evaluate logarithmic expressions using the Change of Base Formula.

KEY: Evaluate Expressions | Logarithmic Expressions | Change of Base Formula

82. ANS: D

Use the Inverse Property of Base e and Natural Logarithms to evaluate the expression.

Feedback

A You have used an incorrect base value.

B Did you apply the Inverse Property of Base e and Natural Logarithms correctly?


D Correct!


OBJ: 9-5.1 Evaluate expressions involving the natural base and natural logarithms.


TOP: Evaluate expressions involving the natural base and natural logarithms.

KEY: Evaluate Expressions | Natural Logarithms

83. ANS: B

Use the Inverse Property of Base e and Natural Logarithms to evaluate the expression.

Feedback

A The exponential and logarithmic functions are inverses.

B Correct!

C Did you apply the Inverse Property of Base e and Natural Logarithms correctly?

D You have used an incorrect base value.


OBJ: 9-5.1 Evaluate expressions involving the natural base and natural logarithms.


TOP: Evaluate expressions involving the natural base and natural logarithms.

KEY: Evaluate Expressions | Natural Logarithms

ID: A

29

84. ANS: B

Use natural logarithms to solve the equation.

Feedback

A Did you verify the solution in the original equation?

B Correct!

C Apply the Inverse Property of Exponents and Logarithms.

D Did you substitute all the logarithm values correctly?


OBJ: 9-5.2 Solve exponential equations using natural logarithms.


TOP: Solve exponential equations using natural logarithms.

KEY: Solve Equations | Exponential Equations | Natural Logarithms

85. ANS: D


Feedback

A Apply the Inverse Property of Exponents and Logarithms.

B Did you verify the solution in the original equation?

C Did you check the constant in the original equation?

D Correct!


OBJ: 9-5.2 Solve exponential equations using natural logarithms.


TOP: Solve exponential equations using natural logarithms.

KEY: Solve Equations | Exponential Equations | Natural Logarithms

86. ANS: B


Feedback

A Did you calculate the logarithm for the given base value?

B Correct!

C Calculate the natural logarithm for the value in the expression.

D Did you calculate according to the Inverse Property of Exponents and the Property of

Equality for Logarithms?


OBJ: 9-5.3 Solve exponential inequalities using natural logarithms.


TOP: Solve exponential inequalities using natural logarithms.

KEY: Solve Inequalities | Exponential Inequalities | Natural Logarithms

ID: A

30

87. ANS: D


Feedback

A Did you calculate the logarithm for the base value?

B Did you calculate the natural logarithm for the value in the expression?

C Did you calculate according to the Inverse Property of Exponents and the Property of

Equality for Logarithms?

D Correct!


OBJ: 9-5.3 Solve exponential inequalities using natural logarithms.


TOP: Solve exponential inequalities using natural logarithms.

KEY: Solve Inequalities | Exponential Inequalities | Natural Logarithms

88. ANS: B

Apply the formula y = ae−kt

to calculate the exponential decay.

Feedback

A Use natural logarithm for calculation, not common logarithm.

B Correct!

C Did you substitute the correct values in the formula?

D Is the rate of decay given in percent?


OBJ: 9-6.1 Use logarithms to solve problems involving exponential decay.

NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: 4.3.12 C.1

TOP: Use logarithms to solve problems involving exponential decay.

KEY: Solve Problems | Logarithms | Exponential Decay

SHORT ANSWER

89. ANS:

7.2 s

When the rocket hits the ground, it’s height will be 0. Replace h(t) by 0 in the given quadratic function and

solve for t.

PTS: 1 DIF: Advanced REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems.

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

90. ANS:

x2

+ y2

= 9

Replace h with 0, k with 0, and r with 3 in the given equation.

PTS: 1 DIF: Basic REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems.


ID: A

31

91. ANS:

x = 5

Solve the quadratic equation (x + 2) ⋅ (x − 4) = 7.

PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems.


92. ANS:

f(x) → −∞ as x → +∞ and

f(x) → +∞ as x → −∞


−∞( ).



93. ANS:

f(x) → −∞ as x → +∞ and

f(x) → +∞ as x → −∞;

odd-degree


−∞( ). If the function behaves the same way as x approaches positive and negative infinity, then the degree of

the function is even. If the function exhibits opposite behavior as x approaches positive and negative infinity,

then the degree of the function is odd.



94. ANS:

y = 1.25(1.108)x

The exponential function is y = abx, where y is the final production, a is the initial production, b is the rate of

increase in the production, and x is the number of years.



95. ANS:

about 5.82 million

Use the formula y = abx, where y is the final production, a is the initial production, b is the rate of increase in

the production, and x is the number of years. Replace the variables in the formula with the given values and

solve.



ID: A

32

96. ANS:

x = 5




97. ANS:

x = 2




98. ANS:

x = 8




99. ANS:

x = 20

Use the Product Property and the Property of Equality for Logarithmic Functions.



100. ANS:

x = 28

Use the Quotient Property, the Product Property, and the Property of Equality for Logarithmic Functions.



101. ANS:

approximately 3297

Subtract the year 2000 from the year 2010 to get the number of years or time t.

Replace the variables in the formula with the given values and solve.

PTS: 1 DIF: Basic REF: Lesson 9-5 OBJ: 9.5.4 Solve multi-step problems.


ID: A

33

102. ANS:

about 46 years

Replace the variables in the formula with the given values. Use natural logarithms to solve the equation.

PTS: 1 DIF: Average REF: Lesson 9-5 OBJ: 9.5.4 Solve multi-step problems.


103. ANS:

about 31 years

Replace the variables in the formula with the given values. Use natural logarithms to solve the equation.

PTS: 1 DIF: Average REF: Lesson 9-5 OBJ: 9.5.4 Solve multi-step problems.


ExamView - Algebra 2 Final Exam Review 2015

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