Free Printable Final Exam Review

1.

Evaluate f(-3)

a)

f(-3) = -3

b)

f(-3) = 0

c)

f(-3) = 2

d)

not enough information to give an answer

2.

f(x) = -x + 2; Evaluate g(-5)

a)

g(-5) = 7

b)

g(-5) = -3

c)

g(-5) = 0

d)

g(-5) = 3

3.

Evaluate f(8)

a)

f(8) = -3

b)

f(8) = 1

c)

f(8) = 0

d)

f(8) = -1

4.

Evaluate $f\left(0\right)$ .

a)

-3

b)

0

c)

1

d)

3

5.

Based on the image, what is f(3)?

a)

1

b)

2

c)

-3

d)

-4

6.

Find h(5) using the equation.

a)

-25

b)

25

c)

3

d)

7

e)

undefined

7.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

8.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

9.

Given the graph of f(x), evaluate f(4).

(a)

10.

Given the graph of f(x), evaluate f(-10).

a)

-10

b)

10

c)

undefined

d)

it cannot be determined from the information given

11.

Given the graph of g(x), find g(-2).

(a)

12.

Given the graph of g(x), find g(-6).

(a)

13.

Find f(2).

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

14.

Using the graph, find f(-3).

a)

-3

b)

-1

c)

1

d)

3

15.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

16.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

17.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D: {-4, 0, 1, 2}
R:{-4, -3, 1}

c)

D: {0, 1, 2, 3, 4}
R:{1, -3, -4}

d)

D: {0, 1, 2, -4}
R: {1, -3, -4, 1}

18.

a)

Function

b)

Not a Function

19.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

20.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

21.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

22.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

23.

Is this table a function or not a function?

a)

Function

b)

Not a Function

24.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

25.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

26.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

27.

a)

{-2, 3, 7}

b)

[-2, 7]

c)

{1, 2, 3, 4}

d)

[1, 4]

28.

In the given relation, what domain value corresponds to the range value -2?

{(-1, 2), (-2, 4), (2, 5), (0, -2), (2, 0)}

a)

-2

b)

2

c)

4

d)

0

29.

What is the range?

a)

The set of all x-values

b)

The set of all y-values

c)

The set of all x- and y-values

30.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

31.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

32.

Rewrite the following in the form $\log\left(c\right)$ :

$\log\left(5\right)+\log\left(6\right)$

(a)

33.

Match the following:

Rewrite the following in the form $\log\left(c\right)$

a)

$2\log\left(5\right)$

1.

log(25)

b)

$\log\left(5\right)+\log\left(4\right)$

2.

log(20)

c)

$\log\left(35\right)-\log\left(7\right)$

3.

log(5)

d)

$3\log\left(4\right)$

4.

log(64)

e)

$\log\left(4\right)-\log\left(16\right)$

5.

log(.25)

34.

Condense: $\log_25+\log_2x$

a)

$\log_2x^5$

b)

$\log_2\ \frac{5}{x}$

c)

$\log_2\ \frac{x}{5}$

d)

$\log_25x$

35.

Condense: $\log_bm-\log_bn$

a)

$\log_bmn$

b)

$\log_b\ \frac{n}{m}$

c)

$\log_b\ \frac{m}{n}$

d)

$\log_bm^n$

36.

Condense: $\log_65-\log_62$

a)

$\log_610$

b)

$\log_6\ \frac{5}{2}$

c)

$\log_6\ 5^2$

d)

$\log_6\ \frac{2}{5}$

37.

Condense: $4\log_5k-\log_5d$

a)

$\log_5k^4d$

b)

$\log_5\ 4kd$

c)

$\log_5\ \frac{k^4}{d}$

d)

$\log_5\ \frac{k}{d^4}$

38.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

39.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

40.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

41.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

42.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

43.

Solve:

ln (3x + 2) = ln (5x - 6)

a)

x = 1

b)

x = 4

c)

x = 2

d)

x = 7

44.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

45.

p(x) = 4x - 5
q(x) = 2x²
Find p(q(x))

a)

8x² + 5

b)

8x² - 10x

c)

8x² - 5

d)

None of these.

46.

f(x) = 2x - 5

g(x) = -4x - 2

Find f(g(-2))

a)

25

b)

-25

c)

-7

d)

7

47.

h(x) = -4x + 3

g(x) = 4x - 2

Find h(g(6))

a)

-107

b)

107

c)

-85

d)

85

48.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

49.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

50.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

51.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

52.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

53.

cos(300°)

a)

0

b)

1/2

c)

√3/2

d)

1

54.

cos 150^o

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

55.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

56.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

57.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

58.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

59.

Solve equation for $0\le\theta<2\pi$ .
$4+4\tan\theta=0$

a)

$\theta=\pi$

b)

$\theta=\frac{7\pi}{4}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\frac{3\pi}{4}$

60.

Solve equation for $0\le\theta<2\pi$ .
$-2=-5+3\sec\theta$

a)

$\theta=0,\frac{\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

d)

$No\ Solution$

61.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

62.

Solve equation for $0\le\theta<2\pi$ .
$1+\tan^2\theta=4\tan^2\theta$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6}$

63.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta+4=5+\sin^2\theta$

a)

$\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4}$

d)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

64.

Solve for x

Hint: Solve using Elimination Method:

a)

1/2

b)

1

c)

-1

d)

-1/2

65.

Solve using Elimination Method:

x - y = 11

2x + y = 19

a)

(10,-1)

b)

(-1,10)

c)

(3,-4)

d)

(6,7)

66.

Solve the system:

x + 6y = 17

-x + 3y = -8

a)

(5, 2)

b)

(11, 1)

c)

(1, 11)

d)

no solution

67.

Solve the following system of equations: 5x - 4y = 3 and 2x + 3y = 8

a)

x = 4, y = 3

b)

x = 2, y = 1

c)

x = 3, y = 2

d)

x = 1, y = 5

68.

7. Solve the system of linear equations: 2x + 5y = 13 and 3x - 2y = 4

a)

x = 4, y = 4

b)

x = 3, y = 1

c)

x = 2, y = 3

d)

x = 5, y = 2

69.

Solve the system using any method:

3x + 2y = 16

7x + y = 19

Answer is ( (a) , (b) )

Choose from the below words

2

5

1

3

4

7

16

19

0

No solution

70.

What is the equation of the circle.

a)

(x - 3)²+ (y + 4)² = 9

b)

(x - 3)²+ (y + 4)² = 3

c)

(x)²+ (y)² = 9

d)

(x - 1)²+ (y + 1)² = 7

71.

Which of the following equations would generate the ellipse pictured?

a)

b)

c)

d)

72.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

73.

Find the vertex of the PARABOLA with the given equation:

*TYPE ANSWER WITH NO SPACES

$\left(y+2\right)^2=-8\left(x+9\right)$

(a)

74.

What is the radius of this CIRCLE?

*Answer with JUST the numerical value

(a)

75.

Give the equation for the HYPERBOLA shown:

a)

$\frac{y^2}{4}-\frac{x^2}{16}=1$

b)

$\frac{x^2}{4}-\frac{y^2}{16}=1$

c)

$\frac{x^2}{16}-\frac{y^2}{4}=1$

d)

$\frac{y^2}{64}-\frac{x^2}{16}=1$

76.

Graph the HYPERBOLA with the given equation:

$\frac{\left(x-2\right)^2}{4}-\frac{\left(y+1\right)^2}{16}=1$

a)

b)

c)

d)

77.

Find the area of the sector, rounding your answer to 1d.p.

a)

176.7cm²

b)

23.6cm²

c)

156.7cm²

d)

88.4cm²

78.

Find the area of the sector, rounding your answer to 1d.p.

a)

67.1cm²

b)

67.0cm²

c)

16.8cm²

d)

134.0cm²

79.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

80.

Find the arc length of the bolded arc. Give your answer in terms of π.

a)

(65/12)π cm

b)

17.02 cm

c)

(845/24)π cm

d)

26π cm

Final Exam Review - Fall 2025

Total questions: 80

Worksheet time: 3hrs 3mins

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