Free Printable Math 3 Final Review

1.

In parallelogram ABCD, the measure of angle A is 40⁰. If the measure of angle C = 2x - 10, then what is the value of x?

a)

40

b)

75

c)

25

d)

45

2.

Which is true about consecutive angles in a parallelogram?

a)

Their sum is 90⁰

b)

Their sum is 180⁰

c)

They have the same measure

d)

There is no relationship

3.

What is the name of the point in a triangle where the medians intersect?

a)

Centroid

b)

Circumcenter

c)

Incenter

d)

Midpoint

4.

The volume of a cylinder is 150 in³. If the radius of the cylinder is 4 in, what is the approximate height?

a)

2 inches

b)

3 inches

c)

4 inches

d)

5 inches

5.

What is the volume of a cone with a diameter of 8 cm and a height of 18 cm?

a)

288π

b)

108π

c)

384π

d)

96π

6.

The density of a rectangular prism is 4 grams per cubic cm. If the mass of the box is 400 grams and its length 4 cm and width is 5 cm, what is the height of the box?

a)

3 cm

b)

4 cm

c)

5 cm

d)

6 cm

7.

What is the center of a circle with the following equation?

x² + y² - 8x + 10y - 8 = 0

a)

(-8, 10)

b)

(8, -10)

c)

(-4, 5)

d)

(4, -5)

8.

What is the radius of a circle with the following equation?

x² + y² - 8x + 10y - 8 = 0

a)

7

b)

14

c)

49

d)

24.5

9.

A sprinkler is spraying water in a radius of 10 yards at a rotation of 80 degrees. What is the approximate area of ground covered by the water from the sprinkler?

a)

62.4 square yards

b)

64.8 square yards

c)

69.8 square yards

d)

73.2 square yards

10.

A circle has a radius of 5 inches. What is the length of an arc that has a central angle of 2π/3 radians?

a)

10π/3 inches

b)

2π/15 inches

c)

π/5 inches

d)

5π/3 inches

11.

You start on the unit circle at (0, -1) and move 300° counterclockwise. Which angle (in degrees) will you end up on the unit circle?

a)

30

b)

330

c)

210

d)

120

12.

What is the coordinate on the unit circle at 30⁰?

a)

(1/2, √3/2)

b)

(√3/2, 1/2)

c)

(√2/2, √2/2)

d)

(√2/2, 1/2)

13.

What is the difference between the maximum and the minimum values of the trigonometric function shown?

y = -3cos(2x) + 8

a)

3

b)

6

c)

8

d)

2

14.

Describe how the function y = 2^x is transformed to make y = 2^{x - 5} + 3

a)

Translated left 5 and down 3

b)

Translated right 5 and down 3

c)

Translated left 5 and up 3

d)

Translated right 5 and up 3

15.

What is the range of the function: f(x) = -|x + 3| + 2

a)

y ≤ 2

b)

y ≥ 2

c)

y ≤ -3

d)

y ≥ -3

16.

Which is the inverse of y = (2x + 4)/8

a)

y = (-2x + 4)/8

b)

y = (8x - 4)/2

c)

y = (2x - 4)/8

d)

y = (8x + 4)/2

17.

a)

9

b)

-50

c)

150

d)

80

18.

Which is an equivalent expression?

a)

b)

c)

d)

19.

Which is a solution to the following equation?

a)

3/8

b)

-9/2

c)

-8/5

d)

-9/4

20.

For the following polynomial, k is an integer.

y = x³ + 4x² - 11x + k

If (x + 5) is a factor, which of the following is another factor?

a)

(x - 4)

b)

(x - 5)

c)

(x + 2)

d)

(x + 3)

21.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

22.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

23.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

24.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

9 - √17

b)

4

c)

2

d)

√8

27.

a)

9

b)

3

c)

5

d)

√15

28.

When f(x) = x²-3 and g(x) = 2x+8 , find g(f(2)).

a)

14

b)

10

c)

144

d)

141

29.

Find the inverse of $f\left(x\right)=\frac{1}{2}x+8$

a)

$f^{-1}\left(x\right)=2x+8$

b)

$f^{-1}\left(x\right)=2x-16$

c)

$f^{-1}\left(x\right)=2\left(x+8\right)$

d)

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

30.

Which graph is the inverse of the graph shown?

a)

b)

c)

d)

31.

Solve for x
3 l 4w−1 l −5 = 10

a)

x = 1.5 and x =-1

b)

x = -1.5 and x = 1

c)

x =1 and x = -1

d)

No Solution

32.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

33.

a)

no solution

b)

(-∞, -22) u (2, ∞)

c)

(-22, 2)

d)

all real numbers

34.

Solve and Graph:

a)

b)

c)

d)

35.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

36.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

37.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

38.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.

a)

x+y≤300
7.5x+5.5y≥2000

b)

x+y<300
7.5x+5.5y≥2000

c)

x+y≤300
7.5x+5.5y≤2000

d)

x+y>2000
7.5x+5.5y≤300

39.

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

40.

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

a)

-3

b)

-1

c)

1

d)

3

41.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

42.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

43.

f(x) = 2x³ - 3x² + 4x -10

State the maximum and minimum number of zeros for f(x).

a)

Max: 3 Min: 0

b)

Max 2 Min: 0

c)

Max: 1 Min: 1

d)

Max: 3 Min: 1

44.

f(x) = -3x⁴ + x³ - 2x² + x - 1

What is the y-intercept of f(x)?

a)

(-1, 0)

b)

(0, -1)

c)

(-3, 0)

d)

(0, -3)

45.

f(x) = x³ - 3x² - 4x

Find the zeros of f(x).

a)

{-4, 0, 1}

b)

{-1, 4}

c)

{-1, 0, 4}

d)

{-4, 1}

46.

Write a polynomial function with the given zeros.

a)

A

b)

B

c)

C

d)

D

47.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

48.

Find a polynomial function of degree 3 with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

49.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

a)

6, 3, -3

b)

-6, 3, -3

c)

-6, 3i, -3i

d)

6, 3i, -3i

50.

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0

d)

The end behavior of the graph is x →∞,y→∞and x→⁻∞, y→⁻∞

51.

Find the factored form of the function graphed:

a)

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

b)

y= (x + 1)²(2 - x)

c)

y = (-x + 1)²(x - 2)

d)

y = -(x - 1)²(x + 2)

52.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

53.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

54.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

55.

Divide using synthetic division

(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 - 12/(x + 3)

b)

2x² - 2x + 6 - 23/(x + 3)

c)

2x² - 2x + 8 - 20/(x + 3)

d)

2x² - 4x + 1

56.

2x³ - 5x² + 3x + 7 ÷ x - 2

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/(x - 2)

d)

2x² - 9x - 15 - 23/(x - 2)

57.

Decide if (x - 3) is a factor of 3x³+ 10x²- x - 12.

a)

Yes, it is a factor

b)

No, it is not a factor

58.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

59.

2x³ - 5x² + 3x + 7 ÷ x - 2

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

60.

What is the remainder when

2x^2−5x−1\ is\ divided\ by\ x−3

(a)

61.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

62.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

63.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

64.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

65.

a)

A

b)

B

c)

C

d)

D

66.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

67.

Which statements are true for the given rational function. Select all that apply.

a)

The horizontal asymptote is at y = 0.

b)

There is a hole at (6, ¾ ).

c)

The vertical asymptote is at x = -2.

d)

The x and y intercepts are at the origin.

e)

The domain is all real numbers except -2.

68.

Find the y-intercept.

a)

(0, -2)

b)

(0, 2)

c)

(0, 4)

d)

it is undefined

69.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

70.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

71.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

72.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

73.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

None

74.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

75.

Is the following function and example of decay or growth?

f(x)=2(0.85)^x

a)

Exponential Decay

b)

Exponential Growth

76.

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

a)

125

b)

11

c)

1398

d)

140

77.

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

a)

$0.29

b)

$2,900,000,000

c)

$46,704.79

d)

$145,000

78.

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

79.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

80.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

81.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

82.

Find the corresponding graph of
$\log_2\left(-x+1\right)$

a)

b)

c)

d)

83.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

84.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

85.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

86.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

87.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

88.

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

89.

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

a)

4

b)

2

c)

3

d)

16

90.

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)

91.

Find the center if the endpoints of the diameter are at (-12, -7) and (3, 5)

a)

(-9/2, -1)

b)

(-15/2, -6)

c)

(9/2, 1)

d)

(15/2, 6)

92.

Find the VOLUME of the box

a)

3x²+7x+2

b)

3x³+7x²+2x

c)

x²+2x

d)

3x³+7x+2

93.

What shape will the horizontal cross-section of a cone be?

a)

Dome

b)

Circle

c)

Pyramid

d)

Triangle

94.

Identify the cross section formed in the picture.

a)

square

b)

rectangle

c)

parallelogram

d)

pentagon

95.

Identify the cross section formed in the picture.

a)

square

b)

rectangle

c)

parallelogram

d)

pentagon

96.

a)

b)

c)

d)

97.

Which 3-D solid is created when the rectangle is rotated about the horizontal line?

a)

b)

c)

d)

98.

Jack has a rock. The rock has a mass of 14g and a volume of 2cm³. What is the density of the rock?

a)

7 mL

b)

7 g/cm³

c)

28 g/cm³

d)

1/7 g/cm³

99.

Which of the following points of concurrency are formed by the intersection of medians?

a)

Incenter

b)

Circumcenter

c)

Centroid

d)

Orthocenter

100.

The figure is an example of a(n) ...

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

101.

Which point is equidistant from the vertices?

a)

Circumcenter

b)

Incenter

c)

Neither

d)

Bilateral

102.

Name the point of concurrency shown.

a)

Circumcenter

b)

Incenter

c)

Supercenter

d)

Neither

103.

The figure is a parallelogram.
Solve for x.

a)

7

b)

2

c)

0

d)

4

104.

The figure is a parallelogram.
Solve for x.

a)

0

b)

6

c)

5

d)

9

105.

Is the quadrilateral a parallelogram? If yes, state how you know.

a)

Opposite sides equal

b)

Opposite sides parallel

c)

Diagonals bisect each other

d)

Not enough info

106.

The figure is a parallelogram.
Solve for x.

a)

7

b)

1

c)

5

d)

2

107.

Find the total surface area of the cylinder.

a)

100.53 square inches

b)

351.86 square inches

c)

251.33 square inches

d)

50.27 square inches

108.

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

a)

4

b)

8

c)

12

d)

24

109.

Find the length of AD

a)

2

b)

4

c)

6

d)

8

110.

If the circumference of a circle is 22 π ft, what is the radius?

a)

22 ft

b)

11ft

c)

π ft

d)

no ft

111.

What is the part of the circle highlighted in red called?

a)

semi-circle arc

b)

major arc

c)

minor arc

d)

sector

112.

What is the part of the circle highlighted in red called?

a)

semi-circle arc

b)

major arc

c)

minor arc

d)

sector

113.

A chord is a segment that connects ___________

a)

the center to the endpoint

b)

to one point outside the circle

c)

a central angle

d)

2 endpoints of a circle

114.

An angle whose vertex lies on the circle and whose sides are chords of the circle

a)

inscribed angle

b)

central angle

c)

arc

d)

radius

115.

A line that intersects a circle at exactly one point

a)

secant

b)

circle

c)

chord

d)

tangent

116.

Determine the measure of ∠NOP

a)

15°

b)

20°

c)

40°

d)

50°

117.

Determine the measure of ∠UVS

a)

19.5°

b)

39°

c)

78°

d)

102°

118.

Find the measure of arc NL

a)

21°

b)

42°

c)

45°

d)

84°

119.

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

a)

36

b)

35

c)

30

d)

41

120.

Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

121.

What is the measure of arc KL?

a)

108

b)

106

c)

110

d)

112

122.

Find the m∠MNQ.

a)

89⁰

b)

45⁰

c)

158⁰

d)

22⁰

123.

What is the measure of angle HKI?

a)

72

b)

73

c)

74

d)

75

124.

How do I find the circumference of a circle?

a)

C=r^2

b)

C=pi

c)

C=2pi*r

d)

C=pi*d

125.

cos(60°)

a)

0

b)

1/2

c)

√3/2

d)

1

126.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

127.

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)

128.

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

129.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

130.

a)

-1

b)

0

c)

undefined

d)

√3

131.

a)

√3/3

b)

√3

c)

1

d)

undefined

132.

$\tan\left(\theta\right)$ of an angle, $\theta$ can be expressed as which of the following?

a)

$\frac{opposite}{hypotenuse}$

b)

$\frac{opposite}{adjacent}$

c)

$\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

d)

$\frac{hypotenuse}{adjacent}$

133.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

134.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

135.

What is 225 degrees in radians?

a)

7π/4

b)

5π/4

c)

3π/4

d)

5π/3

136.

What are the negative and positive coterminal angles of -225 degrees?

a)

375°, -600°

b)

125°, -356°

c)

135°, -585°

d)

60°, -120°

137.

Find a coterminal angle to -180 degrees.

a)

180

b)

90

c)

270

d)

360

Math 3 Final Review

Total questions: 137

Worksheet time: 8hrs 37mins

Similar Resources on Wayground