Free Printable Math 3 Exam Review

1.

What is the DOMAIN of the graph shown?

a)

(-4, 2]

b)

[-4, 2)

c)

[2, 5)

d)

(2, 5]

2.

What is the RANGE of the following graph?

a)

[0, ∞)

b)

[0, 3]

c)

(-∞, ∞)

3.

What is the DOMAIN of the function?

a)

[0, ∞)

b)

(-∞, ∞)

c)

(-∞, 0]

d)

[0, 3]

4.

What is the RANGE of the function?

a)

-7≤x≤6

b)

-7<x<6

c)

-8<y<2

d)

-8≤y≤2

5.

What is the RANGE for the following graph?

a)

(-∞, ∞)

b)

(-∞, 0]

c)

[-12, 12]

d)

[-4, 0]

6.

When f(x) = 9 - 3x and g(x) = 5x - 7

find f(x) + g(x).

a)

14x - 10

b)

-8x + 2

c)

2x + 2

d)

2x - 2

7.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

a)

8

b)

-8

c)

28

d)

None of these.

8.

When f(x) = x²+ 9 and g(x) = x - 9,

find f(x) - g(x).

a)

x²+ x + 9

b)

x²- x + 9

c)

x²- x

d)

x²- x + 18

9.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

10.

Are the following inverses of each other?

a)

True

b)

False

11.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

12.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

13.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

14.

What is the first step?

a)

Get absolute value alone by subtracting 5 from both sides

b)

Get absolute value alone by dividing by 5 on both sides

c)

Split into two equations

15.

After you split into two inequalities, what would they look like?

a)

x + 7 > 1

x + 7 > -1

b)

x + 7 > 1

c)

x + 7 > 1
X + 7 < -1

16.

Which inequality represents the graph?

a)

-8 < x < -6

b)

x < - 8 AND x > - 6

c)

x < - 8 OR x > - 6

17.

Solve |x – 12| - 3 = 11.

a)

-2, -26

b)

-2, 26

c)

3, 25

d)

4, -7

18.

| x + 2 | > 5

a)

x < - 7 or x > 3

b)

x > 7 or x < 3

c)

x < -7 and x > 3

d)

x > -3 and x < 7

19.

Describe the function's end behavior.

a)

$As\ x\rightarrow-\infty,\ y\rightarrow-\infty$
$As\ x\rightarrow\infty,\ y\rightarrow-\infty$

b)

$As\ x\rightarrow-\infty,\ y\rightarrow-\infty$
$As\ x\rightarrow\infty,\ y\rightarrow\infty$

c)

$As\ x\rightarrow-\infty,\ y\rightarrow\infty$
$As\ x\rightarrow\infty,\ y\rightarrow-\infty$

d)

$As\ x\rightarrow-\infty,\ y\rightarrow\infty$
$As\ x\rightarrow\infty,\ y\rightarrow\infty$

20.

Identify where the function is increasing and where it is decreasing.

a)

increasing (-1, ∞) and decreasing (-∞,-1)

b)

increasing (-∞, -1) and decreasing (-1, ∞)

c)

increasing (-∞,∞) and decreasing nowhere

d)

increasing (-1, -4) and decreasing (-3, 1)

21.

What are the domain and the range of the function?

a)

domain (-∞,∞) and range (-∞,∞)

b)

domain (∞,-∞) and range (∞,-∞)

c)

domain (-∞, 3] and range [3,∞)

d)

domain (-∞,1] and range [1,∞)

22.

Identify the function's x- and y-intercepts.

a)

x-int (-2,0), (1,0), and (3,0) and y-int (3,0)

b)

x-int (-2,0), (1,0), and (3,0) and y-int (0,3)

c)

x-int (0,-2), (0,1), and (0,3) and y-int (0,3)

d)

x-int (0,-2), (0,1), and (0,3) and y-int (3,0)

23.

What type of a function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

24.

What type of Function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

25.

What kind of function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

26.

What could be the equation for this graph?

a)

y = -2x³+ 1x + 3

b)

y = (x - 2)(x + 1)(x + 3)

c)

y = (x + 2)(x - 1)(x - 3)

d)

y = -2x² + 1x + 3

27.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

28.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

29.

What is f when x equals 8?

a)

0

b)

5

c)

11

d)

16

30.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

31.

What are the domain restrictions for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

32.

Match the graph with the correct equation.

a)

b)

c)

d)

33.

What does the model P=A(1+r)^t best represent?

a)

Exponential growth

b)

Simple Interest

c)

Compound Interest

d)

Exponential Decay

34.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

35.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

36.

Which equation matches the graph?

a)

y=2(2)^x

b)

y=2(1/2)^x

c)

y=2^x

d)

y=1/2(2)^x

37.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

38.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

39.

Change 6.5% to a decimal

a)

.65

b)

6.5

c)

.065

d)

.065%

40.

Caiden deposited $475 in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

41.

Krystal has $3000 invested at a 2% interest rate. Which expression can be used to determine how much money Krystal had after 16 years?

a)

$A=3000\left(1+.02\right)^{16}$

b)

$A=3000\left(1-.02\right)^{16}$

c)

$A=16\left(1+.2\right)^{3000}$

d)

$A=3000\left(.2\right)^{16}$

42.

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

43.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

44.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

45.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

46.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

47.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

48.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

49.

Solve: 7^-x = 49

a)

1

b)

-1

c)

2

d)

-2

50.

7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

51.

ln (5x + 6) = 5

a)

154.413

b)

30.883

c)

147.213

d)

28.483

52.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

53.

3e^2x + 10 = 25

a)

{-3.940}

b)

{1.228}

c)

{0.451}

d)

{0.805}

54.

Solve by factoring.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

55.

Solve x²− 4 = 0 (solve using square roots)

a)

2 and -2

b)

4 and -4

c)

16 and -16

d)

8 and -8

56.

Solve by taking square roots:
5m² + 1 = 6

a)

m = 0

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

57.

Factor

x^{3\ }-\ 27

a)

$\left(x-3\right)\left(x^{2\ }+3x+9\right)$

b)

$\left(x+3\right)\left(x^{2\ }+3x+9\right)$

c)

$\left(x-3\right)\left(x^{2\ }-3x+9\right)$

58.

Factor

x^{4\ }+5x^{2\ }+4

a)

$\left(x^2-1\right)\left(x^{2\ }+\ 4\right)$

b)

$\left(x^2-1\right)\left(x^{2\ }-\ 4\right)$

c)

$\left(x^2+1\right)\left(x^2+4\right)$

59.

The perimeter of a circle is usually called the...

a)

radius

b)

diameter

c)

circumference

d)

area

60.

The space contained inside of a circle is called the...

a)

radius

b)

diameter

c)

circumference

d)

area

61.

Steven purchases a bowl. The diameter of the
bowl is 14 cm. What is the circumference of the
bowl?

a)

28 cm

b)

43.98 cm

c)

87.96 cm

d)

7 cm

62.

Find the area of the circle

a)

56.52

b)

254.34

c)

1017.36

d)

113.04

63.

A region bounded by two radii of the circle and their intercepted arc is a ....

a)

arc of a circle

b)

arc length of a circle

c)

sector of a circle

d)

segment of a circle

64.

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

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

65.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

66.

Find the length of the bold arc.Leave pi in your answer.

a)

5688π ft

b)

15.8π ft

c)

150.4π ft

d)

54,150 ft

67.

Write the equation of the circle.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

68.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

69.

In the equation
(x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

70.

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

71.

a)

A

b)

B

c)

C

d)

D

72.

a)

A

b)

B

c)

C

d)

D

73.

Solve for x.

a)

5

b)

20

c)

40

d)

85

74.

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

75.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

76.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

77.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

78.

Find the least common denominator of the expression

a)

18

b)

6x

c)

3xy

d)

6xy

79.

Simplify the expression

a)

(12n² + 28n + 4) / (2n-5)(n+2)

b)

(12n² - 28n + 4) / (2n-5)(n+2)

c)

(8n) / (3n + 3)

d)

(12n² + 2n -3) / (2n-5)(n+2)

80.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

81.

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

a)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

b)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

c)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

d)

$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

82.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

83.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

84.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

85.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

86.

If ABCD is a parallelogram, what is the length of BD?

a)

10

b)

11

c)

7

d)

5

87.

a)

x = 70, y = 80

b)

x = 70, y = 30

c)

x = 80, y = 70

d)

x = 80, y = 30

88.

The figure is a parallelogram.
Solve for x.

a)

12

b)

4

c)

6

d)

2

89.

HIJK is a parallelogram
solve for Y

a)

20

b)

15

c)

60

d)

12

90.

What is $225\degree$ in radians?

a)

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

b)

$\frac{5\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

$\frac{5\pi}{3}$

91.

What is $\frac{11\pi}{6}$ radians in degrees?

a)

30

b)

330

c)

360

d)

300

92.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

93.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

94.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

95.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

96.

What is the value of cosine at 270

a)

0

b)

1

c)

-1

97.

What is the value of cosine at 315

a)

0

b)

1

c)

√2 / 2

d)

-√2 /2

98.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

Math 3 Exam Review

Total questions: 98

Worksheet time: 6hrs 48mins

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