Algebra 2 Semester 1 Practice Final

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

To which set of numbers does the number belong?

____ 1. − 215

a integers b rational numbers c irrational numbers d natural numbers

Graph the number on a number line.

____ 2.

a

0 1 2 3 4 50–1–2–3–4–5

c

0 1 2 3 4 50–1–2–3–4–5

b

0 1 2 3 4 50–1–2–3–4–5

d

0 1 2 3 4 50–1–2–3–4–5

Evaluate the expression for the given value of the variable(s).

____ 3.

a 32 b 48 c −48 d 30

____ 4. ; b = 2

a 19 b 17 c –11 d 21

Use an algebraic equation to solve the problem.

____ 5. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster

than the other car. The cars are 300 mi apart in 3 h. How fast is each car traveling? a 35 mi/h and 45 mi/h c 45 mi/h and 55 mi/h b 55 mi/h and 35 mi/h d 55 mi/h and 65 mi/h

Solve the equation or formula for the indicated variable.

____ 6. , for t

a

b

c d

____ 7. , for U

a

b

c d

Solve the inequality. Graph the solution set.

____ 8. 26 + 6b ≥ 2(3b + 4)

a all real numbers

0 2 4 6 80–2–4–6–8

c b ≥ 11

2

0 2 4 6 80–2–4–6–8

b b ≤ 11

2

0 2 4 6 80–2–4–6–8

d no solutions

0 2 4 6 80–2–4–6–8

Solve the compound inequality. Graph the solution.

____ 9. 5x + 10 ≥ 10 and 7x – 7 ≤ 14

a x ≥ 4 or x ≤ 1

0 2 4 6 80–2–4–6–8

c x ≥ 4 or x ≤ 3

0 2 4 6 80–2–4–6–8

b x ≥ 0 and x ≤ 1

0 2 4 6 80–2–4–6–8

d x ≥ 0 and x ≤ 3

0 2 4 6 80–2–4–6–8

____ 10. 4x – 5 < –17 or 5x + 6 > 31

a x < –3 or x > 5

0 2 4 6 80–2–4–6–8

c x < –3 or x > 72

5

0 2 4 6 80–2–4–6–8

b x < −51

2 or x > 725

0 2 4 6 80–2–4–6–8

d x < −51

2 or x > 5

0 2 4 6 80–2–4–6–8

____ 11.

a 0 2 4 6 80–2–4–6–8

c

0 2 4 6 80–2–4–6–8

b

0 2 4 6 80–2–4–6–8

d

0 2 4 6 80–2–4–6–8

Solve the absolute value equation. Graph the solution.

____ 12.

a x = 4 or x = 2

0 2 40–2–4

c x = −2 or x =

13

0 1 2 3 4 50–1–2–3–4–5

b x = −2 or x = 2

0 1 2 3 4 50–1–2–3–4–5

d x = −2 or x = 4

0 1 2 3 4 50–1–2–3–4–5

____ 13.

a x =

38 or x = 1

0 1 2 3 4 50–1–2–3–4–5

c x =

38 or x = 11

2

0 1 2 3 4 50–1–2–3–4–5

b x = 1 or x = 11

2

0 1 2 3 4 50–1–2–3–4–5

d x =

38 or x = 13

8

0 1 2 3 4 50–1–2–3–4–5

____ 14.

a x = −

12 or x =

12

0 1 2 3 4 50–1–2–3–4–5

c x = −1 or x =

12

0 1 2 3 4 50–1–2–3–4–5

b x = −

12 or x = −1

0 1 2 3 4 50–1–2–3–4–5

d x = −

12 or x = −4

0 1 2 3 4 50–1–2–3–4–5

Solve the equation. Check for extraneous solutions.

____ 15.

a x =

107

c x =

107 or x =

613

b x =

107 or x =

67

d x =

613

Solve the inequality. Graph the solution.

____ 16.

a

0 10 20 30 400–10–20–30–40

c

0 5 10 15 200–5–10–15–20

b

0 5 10 15 200–5–10–15–20

d

0 5 10 15 200–5–10–15–20

____ 17.

a –18 x 8

0 5 10 15 200–5–10–15–20

c –36 x 16

0 10 20 30 400–10–20–30–40

b –18 x 8

0 5 10 15 200–5–10–15–20

d

0 5 10 15 200–5–10–15–20

____ 18. Make a mapping diagram for the relation.

{(–1, –5), (1, 4), (2, –4), (6, 1)} a

–1

1

2

6

–5

4

–4

1

c

–1

1

2

6

1

–4

4

–5

b

–1

1

2

6

1

–5

–4

4

d

–1

–5

2

–4

1

4

6

1

____ 19. Write the ordered pairs for the relation.

a {(–5, 5), (–1, 4), (0, –0.5), (1, 4), (5, 5)} b {(5, –5), (4, –1), (–0.5, 0), (4, 1), (5, 5)} c {(–5, 5), (4, –1), (0, –0.5), (1, 4), (5, 5)} d {(5, –5), (–1, 4), (–0.5, 0), (4, 1), (5, 5)}

For each function, what is the output of the given input?

____ 20. For , .

a –19 b 1 c –21 d 21

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

____ 21.

x y

6 24

18 72

54 216

162 648 a yes; k = 4; y =4x c yes; k = 6; y =6x b yes; k = 3; y =3x d no

What is an equation of the line in slope intercept form?

____ 22. m = 12 and the y-intercept is (0, –2)

a +

12

c 12

b 12

d 12

Write the equation in slope-intercept form. What are the slope and y-intercept?

____ 23.

a 58

18 ;

slope: 18 ; y-intercept:

58

c 58

18 ;

slope: 58 ; y-intercept:

18

b 58

18 ;

slope: 58 ; y-intercept:

18

d 58

18

slope: 58 ; y-intercept:

18

What is the graph of the equation?

____ 24.

a

c

b d

What are the intercepts of the equation? Graph the equation.

____ 25.

a x-intercept: (–4, 0) y-intercept: (0, –6)

c x-intercept: (–6, 0) y-intercept: (0, –4)

b x-intercept: (–4, 0)

y-intercept: (0, –6) d x-intercept: (–6, 0)

y-intercept: (0, –4)

What is the equation of the line in slope-intercept form?

____ 26. the line parallel to through (–4, 6)

a 17

c

b d

____ 27. the line perpendicular to

12 through (3, 3)

a 2 c 12

b 2 d 12

What is the graph of the absolute value equation?

____ 28.

a c

b d

____ 29.

a c

b d

What is the graph of each absolute value inequality?

____ 30. y < |x + 2| – 2

a c

b d

____ 31. –|x – 1| > y – 5

a c

b d

Solve the system by substitution.

____ 32.

a (–4, –5) c (–5, –4) b (5, 4) d (4, 5)

Solve the system using elimination.

____ 33.

a (3, 5) c (–3, –5) b (5, 3) d (–5, –3)

____ 34.

a (–7, –8) c (7, 8) b (–8, –7) d (8, 7)

What are the solutions of the following systems?

____ 35.

a infinitely many solutions c (5, –2) b (–5, 2) d no solutions

____ 36.

a (5, –6) c (–5, 6)

b no solutions d infinitely many solutions

____ 37. A group of 52 people attended a ball game. There were three times as many children as adults in the group.

Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.

a

; 39 adults; 25 children c

; 25 adults; 39 children

b ; 39 adults, 13 children

d ; 13 adults, 39 children

Solve the system of inequalities by graphing.

____ 38.

a c

b d

Solve the system of inequalities by graphing.

____ 39.

a c

b d

What point in the feasible region maximizes the objective function?

____ 40. Constraints

Objective function: a c b d

Solve the system by elimination.

____ 41.

a (5, –1, 0) c (–5, –1, 0) b (–5, 1, 0) d (–5, –1, –2)

Solve the system by substitution.

____ 42.

a (–8, 7, 5) c (8, –7, 5) b (–8, –7, 5) d (–8, –7, –5)

____ 43.

a (1, –1, 3) c (1, –1, –3) b (1, 1, –3) d (–1, –1, –3)

What is the graph of the function?

____ 44.

a

c

b

d

4

Graph each function. How is each graph a translation of ?

____ 45.

a

translated up 3 unit(s)

c

translated to the right 3 unit(s)

b d

translated down 3 unit(s)

translated to the left 3 unit(s)

____ 46. Identify the vertex and the axis of symmetry of the graph of the function .

a vertex: (–2, 4); axis of symmetry:

b vertex: (2, –4); axis of symmetry:

c vertex: (–2, –4); axis of symmetry:

d vertex: (2, 4); axis of symmetry:

____ 47. Identify the maximum or minimum value and the domain and range of the graph of the function

. a minimum value: 3

domain: all real numbers range: all real numbers

b maximum value: –3 domain: all real numbers range: all real numbers

c maximum value: 3 domain: all real numbers range: all real numbers

d minimum value: –3 domain: all real numbers range: all real numbers

____ 48. Which is the graph of ?

a c

b d

____ 49. Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of

the parabola in vertex form. a c b d

____ 50. Suppose a parabola has an axis of symmetry at , a maximum height of 1 and also passes through the

point (9, –1). Write the equation of the parabola in vertex form. a c b d

What are the vertex and the axis of symmetry of the equation?

____ 51.

a vertex: ( –1, – 6) axis of symmetry:

c vertex: ( 1, – 6) axis of symmetry:

b vertex: ( –1, – 6) axis of symmetry:

d vertex: ( –1, 6) axis of symmetry:

What is the graph of the equation?

____ 52.

a

c

b

d

What is the vertex form of the equation?

____ 53.

a c b d

____ 54.

a c b d

What is the equation, in standard form, of a parabola that contains the following points?

____ 55. (–2, 18), (0, 4), (4, 24)

a c b d

What is the expression in factored form?

____ 56.

a c b d

What is the expression in factored form?

____ 57.

a c b d

____ 58.

a c b d

____ 59.

a c b d

____ 60.

a c b d

____ 61.

a c b d

What are the solutions of the quadratic equation?

____ 62. = 0

a 2, 4 c 52 , 2

b –2, 2 d 2,

52

What is the solution of each equation?

____ 63.

a 7 c

b 7 , – 7 d

____ 64.

a −49

36 , 4936

c −6

7 , 67

b −7

6 , 76

d −36

49 , 3649

Solve the quadratic equation by completing the square.

____ 65.

a 6 c 6 b d

What is the number of real solutions?

____ 66.

a one solution c two solutions b no real solutions d cannot be determined

____ 67.

a one solution c two solutions b no real solutions d cannot be determined

____ 68. Identify the graph of .

a c

b

d

What is the absolute value of each number?

____ 69. .

a 2 c 10 b –8 d

Simplify the expression.

____ 70.

a c b d

____ 71.

a –30 c 30 b –30i d 30i

____ 72.

a c

b d

____ 73.

a

c

b

d

What are the solutions?

____ 74.

a −4

3 i, 43 i

c −3

4 i, 34 i

b −16

9 i, 169 i

d −4

3 , 43

Write the polynomial in factored form.

____ 75. 4x3 + 8x2 – 96x

a 6x(x + 4)(x – 4) c 4x(x + 6)(x + 4) b 4x(x – 4)(x + 6) d –4x(x + 6)(x + 4)

____ 76. What is a cubic polynomial function in standard form with zeros 5, 2, and –5?

a c b d

What are the zeros of the function? What are their multiplicities?

____ 77.

a the numbers –1 and –3 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1

b the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1 c the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1 d the number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeros of multiplicity

1

What are the real or imaginary solutions of each polynomial equation?

____ 78.

a 6, –6, 2, –2 c 6, –6 b 6, –2 d no solution

What are the real or imaginary solutions of the polynomial equation?

____ 79.

a c b d no solution

____ 80. Divide by x + 4.

a c , R –232 b , R 240 d

____ 81. Is a factor of ? If it is, write as a product of two factors.

a yes:

c yes:

b yes:

d is not a factor of

____ 82. Use synthetic division to find P(3) for .

a 12 b 216 c –54 d 3

____ 83. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation

. Do not find the actual roots. a –9, –1, 1, 9 c –9, –3, –1, 1, 3, 9 b 1, 3, 9 d no roots

____ 84. A polynomial equation with rational coefficients has the roots . Find two additional

roots. a c b d

____ 85. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 2 + i.

a c b d

Algebra 2 Semester 1 Final Answer Section

MULTIPLE CHOICE

1. B

2. D

3. B

4. D

5. C

6. D

7. D

8. A

9. D

10. A

11. B

12. A

13. B

14. C

15. A

16. C

17. B

18. B

19. A

20. A

21. A

22. C

23. C

24. A

25. D

26. D

27. B

28. D

29. C

30. A

31. D

32. B

33. B

34. A

35. D

36. D

37. D

38. C

39. A

40. D

41. C

42. B

43. C

44. C

45. C

46. C

47. D

48. A

49. C

50. A

51. A

52. A

53. C

54. B

55. B

56. D

57. C

58. D

59. C

60. C

61. C

62. D

63. B

64. B

65. D

66. C

67. A

68. B

69. C

70. C

71. C

72. B

73. D

74. A

75. B

76. C

77. B

78. A

79. C

80. C

81. B

82. C

83. C

84. C

85. A