algebra 2 with trigonometry final exam...

Algebra 2 with Trigonometry Final Exam Review

Find the value of the given expression.

1. [32 + (40( 42))]

2. Evaluate the given expression if x = 25, y = 10, w = 11, and z = 18.

(x y) + 10wz

Solve the given equation. Check your solution.

3. 57p 13p + 61p p = 128

4. 49(46x + 3) – 6(13x + 7) = 149

5. | m 1 | = 23

6. 20| 2s + 5 | = 24

Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the

solution set on a number line.

7.

8. 1 1

Solve the given inequality. Graph the solution set on a number line.

9. 4m 2 < 2 or 6m + 2 6

10. m 1< 7 and m + 2 8

11. | m | 10

12. | p 5 | 9

13. Graph the function f(x) = | x | + 4. Identify its domain and range.

14. Graph the function f(x) = [[x + 4]]. Identify its domain and range.

15. Graph the function f(x) = x + 3. Identify its domain and range.

16. Graph the function f(x) = –5 . Identify the domain and range.

17. Graph the given relation or equation and find the domain and range. Then determine whether the relation or

equation is a function.

(3.2, 5.2), (–1.8, 5.2), (–4.8, 3.2), (–4.8, –2.8)

18. Graph the given relation or equation and find the domain and range. Then determine whether the relation or

equation is a function.

y = 4x 3

19. Find the value of f(–10) and g(3) if f(x) = –10x 9 and g(x) = 3x + 27x–2

.

20. Find the slope of the line that passes through the pair of points (6, 7) and (9, 2).

21. Graph the line that passes through (3, 1), parallel to a line whose slope is –0.5.

22. Write an equation in slope-intercept form for the line that satisfies the following condition.

slope 4, and passes through (2, 20)


passes through (1, –20) and (18, 3)


passes through (9, –9), parallel to the graph of y = x + 10

Identify the function below as S for step, C for constant, A for absolute value, I for identity, or P for

piecewise.

25.

26.

27.

20

3

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

28.

29. Graph the given inequality.

Solve the given system of equations.

30. –8a = 12

4a + 8c = 0

7b + 1c = 18

Solve each system of equations by using substitution.

31. 6x + 5y = 10

7x – 3y = 24

32.

Solve each system of equations by using elimination.

33.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

34.

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

35.

36.

37.

38.

Simplify the given expression.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

Factor the polynomial completely.

50.

51.

52.

53.

54.

Simplify.

55.

56.

57.

58.

59.

60. Use a calculator to approximate the value of to three decimal places.

61. Use a calculator to approximate the value of to three decimal places.

62. Simplify .

Write the given radical using rational exponents.

63.

Solve the given inequality.

64.

Solve the given equation.

65.

66.

67.

68. y 5y + 4 = 0

69.

70.

71. .

72.

73. Consider the quadratic function –2 + 5 + 2. Find the y-intercept and the equation of the axis of

symmetry.

74. Graph the quadratic function –2 – – 2.

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

minimum value of the function.

75. 2 – 6 6

Solve the equation by factoring.

76. + 8 – 48

Write a quadratic equation with the given roots. Write the equation in the form , where a, b,

and c are integers.

77. –10 and –2

Solve the equation by using the Square Root Property.

78. 16 + 32 + 16 81

Solve the equation by completing the square.

79. + 8 + 15

80. –2 +

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

81. – 7 60

82. – + 7 + 11

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

83. –4 – 14 + 3 0

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

84. + 4 – 6

Find the coordinates of the vertex of the quadratic function.

85.

86. Write an equation for the parabola whose vertex is at and which passes through .

87. Find and for the function .

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.

88.

89.

90. Write the expression in quadratic form.

91. List all of the possible rational zeros of the following function.

1 2 3 4 5–1–2–3–4–5 x

2

4

6

8

10

–2

–4

–6

–8

–10

f(x)

1 2 3 4 5 6–1–2–3–4–5–6 x

5

10

15

20

25

30

–5

–10

–15

–20

–25

–30

f(x)

92. Find for the following functions.



95. Find and .

96. Find the values of the six trigonometric functions for angle , when AC = 10 and BC = 8.

97. Solve ABC by using the measurements , , and . Round measures of sides to

the nearest tenth and measures of angles to the nearest degree.

98. Solve ABC by using the measurements , , and . Round measures of sides to

the nearest tenth and measures of angles to the nearest degree.

99. A 15-m long ladder rests against a wall at an angle of with the ground. How far is the foot of the ladder

from the wall?

100. In a tourist bus near the base of Eiffel Tower at Paris, a passenger estimates the angle of elevation to the top

of the tower to be 60°. If the height of Eiffel Tower is about 984 feet, what is the distance from the bus to the

base of the tower?

Rewrite the radian measure in degrees.

101.

102.

Rewrite the degree measure in radians.

103. –1080°

104. 9°

105. Find one angle with positive measure and one angle with negative measure coterminal with an angle of 172°.

Find the value of the given trigonometric function.

106. sin –585

107. cos 780

108. sec –1020

Find the exact values of the remaining five trigonometric functions of .

109. Suppose is an angle in the standard position whose terminal side is in Quadrant III and .

110. Suppose is an angle in the standard position whose terminal side is in Quadrant IV and .

111. Suppose is an angle in the standard position whose terminal side is in Quadrant II and .



114. Suppose is an angle in the standard position whose terminal side is in Quadrant II and .

Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the

nearest degree.

115.

c = 9.0, B = 40°, C = 65°

116.

Q = 35°, p = 8, q = 5

The given point P is located on the unit circle. Find sin and cos .

117. P(0.8, 0.6)

118. P

119. Solve x = Sin by finding the value of x to the nearest degree.

Find the amplitude, if it exists, and period of the function. Then, graph the function.

5

6

120. y = sin

121. y = 5 cos

State the amplitude, period, and phase shift for the function. Then, graph the function.

122. y = 3 cos ( 90 )

123. Find the value of cos , if sec = ; 0 90 .

124. Find the value of csc , if cos = ; 180 < < 270 .

125. Simplify .

Algebra 2 with Trigonometry Final Exam Review

Answer Section

SHORT ANSWER

1. –824

2. 2205

3. 1.23

4. 0.02

5. {24, –22}

6. {–1.9, –3.1}

7. The solution set is {6, }.

8. The solution set is {m –8}.

9. {m | m < 1 or m 0.67}

10. {m | m < 8 and m 6}

11. The solution set is {m | m 10 or m 10}.

12. The solution set is {p | p > –4 and p < 14}.

0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10

0 10 20 30 40 50 60 70 80 90 1000–10–20–30–40–50–60–70–80–90–100

0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10

0 1 2 3 4 5 6 7 8 9 10 11 120–1–2–3–4–5–6–7–8–9–10–11–12

0 1 2 3 4 5 6 7 8 9 10 11 120–1–2–3–4–5–6–7–8–9–10–11–12

0 2 4 6 8 10 12 14 16 18 20 22 240–2–4–6–8–10–12–14–16–18–20–22–24

13.

The domain of the function is all real numbers. The range of the function is

.

14.

The domain of the function is all real numbers. The range of the function is all integers.

15.

The domain of the function is the set of all real numbers. The range of the function is the set of all real

numbers.

4 8 12 16 20–4–8–12–16–20 x

4

8

12

16

20

–4

–8

–12

–16

–20

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

16.

The domain of the function is all real numbers. The range of the function is , y is a real number}.

17.

Domain: {–4.8, –1.8, 3.2}

Range: {–2.8, 3.2, 5.2}

The equation is not a function.

1 2 3 4 5–1–2–3–4–5 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

(3.2, 5.2)(–1.8, 5.2)

(–4.8, 3.2)

(–4.8, –2.8)

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

18. The domain and the range are all real numbers.

The equation represents a function.

19. f(–10) = 109

g(3) = 12

20.

21.

22. y =

23. y =

24. y =

25. I

26. S

27. A

28. P

(–1, –1)

(0, 3)

(1, 7)

(2, 11)

4 8 12 16 20–4–8–12–16–20 x

4

8

12

16

20

24

–4

–8

–12

–16

–20

–24

y

(3, 1)

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

29.

30. a = –1.50, b = 2.46, c = 0.75

31. 2.83, –1.4

32. 6.34, 1.22

33. 2.71, –1.2

34. 2, –2.5

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49. quotient and remainder –26

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60. 28.478

61. 90.945

62.

63.

64.

65.

66. 1.93, , 1,

67. 1.77, , 1,

68. 1, 64

69.

70.

71.

72.

73. The y-intercept is + 2.

The equation of axis of symmetry is .

19

5

5

4

74.

75. The function has a minimum value. The minimum value of the function is 1.5.

76. {–12, 4}

77. + 12 + 20

78. { , }

79. {–5, –3}

80. {0.5, 0}

81. {–5, 12}

82.

83. The discriminant is 244. Because the discriminant is greater than 0 and is not a perfect square, the roots are

real and irrational.

84. The vertex form of the function is ( ) .

The equation of the axis of symmetry is –2.

85.

86.

87. –35; 1,493

88. The end behavior of the graph is as and as .

It is an even-degree polynomial function.

The function has four real zeros.

89. The end behavior of the graph is as and as .

It is an odd-degree polynomial function.

The function has three real zeros.

90.

91. 2, 4, 5, 10, 20, 25, 50, 100

92.

1 2 3 4 5 6 7 8 9 10 11–1–2–3–4–5 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

f(x)

5

4

13

4

93.

94.

95.

96. sin = , cos = , csc = , sec = , tan = , and cot = .

97. , ,

98. , ,

99. 7.5 m

100. 568.13 feet

101. 10

102. 45

103.

104.

105. 532°, –188°

106.

107.

108. 2

109. sin , cos , csc , tan , and cot

110. sin , cos , csc , sec , tan

111. sin , cos , csc , sec , cot

112. sin , cos , csc , sec , tan

113. cos , csc , sec , tan , cot

114. cos , csc , sec , tan , cot

115. A = 75°, a = 9.6, b = 6.4

116. P = 90°, R = 55°, r = 6.6

117. sin = 0.6; cos = 0.8

118. sin = ; cos =

119. 56.4

4

5

3

5

5

4

5

3

4

3

3

4

120.

amplitude: ; period: 2

121.

amplitude: 5; period: 2

122.

amplitude = 3; period = 360 ; phase shift = 90

123.

90 180 270–90–180–270

0.1

0.2

0.3

0.4

0.5

–0.1

–0.2

–0.3

–0.4

–0.5

y

90 180 270–90–180–270

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

90 180 270–90–180–270

2

4

6

8

10

12

14

16

–2

–4

–6

–8

–10

–12

–14

–16

y

124.

125.

algebra 2 with trigonometry final exam...

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