Free Printable Math 3 Final Review

1.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

2.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

3.

Subtract the fractions

a)

a

b)

b

c)

c

d)

d

4.

a)

A

b)

B

c)

C

d)

D

5.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

6.

Simplify.

a)

A

b)

B

c)

C

d)

D

7.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

8.

Solve for x: $\frac{1}{x}=\frac{1}{5x}-\frac{x-1}{5x}$

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

9.

Solve by using the LCD.

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

10.

Solve for x: $\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

11.

Solve for x.

a)

-1

b)

2

c)

6

d)

No solution

12.

How do you find the x-intercept(s) for a rational function?

a)

Divide numerator by denominator.

b)

Evaluate f(0)

c)

Set the denominator = 0 and solve.

d)

Set the numerator = 0 and solve.

13.

How do you find the y-intercept for a rational function?

a)

Divide numerator by denominator.

b)

Evaluate f(0).

c)

Set the denominator = 0 and solve.

d)

Set the numerator = 0 and solve.

14.

What are the x-intercept and y-intercept of $y=\frac{2x-4}{x+4}$ ?

a)

(-2, 0) and (0, -1)

b)

(2, 0) and (0, -1)

c)

(-2, 0) and (0, 1)

d)

(2, 0) and (0, 1)

15.

Identify the vertical asymptote(s) of $y=\frac{4}{x^2+2x-3}$ .

a)

x = -3 and x = -1

b)

x = 3 and x = 1

c)

x = 3 and x = -1

d)

x = -3 and x = 1

16.

Find the domain of the function. f(x) = x³ / x+8

a)

x cannot equal to 2

b)

x cannot equal to -2

c)

x cannot equal to -8

d)

All real numbers

17.

Simplify (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)

18.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

19.

What is the x-Intercept?

a)

(0,0)

b)

(4,0)

c)

(5,0)

d)

(-5,0)

20.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

end behavior

d)

none

21.

Match the graph to the correct rational equation below.

a)

f(x)=x²/(x²+x-12)

b)

f(x)=4x²/(x²-x-12)

c)

f(x)=(2x²-2)/2x²

d)

f(x)=x/(x²+x-12)

22.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

$y=\frac{-6}{42}$

c)

y = -7

d)

y = 1

23.

What is the end behavior of the function?

a)

as x -> +/- infinity, f(x) -> 0

b)

as x -> - infinity, f(x) -> - infinity,

as x -> + infinity, f(x) -> infinity

c)

as x -> +/- infinity, f(x) -> 1

d)

as x -> +/- infinity, f(x) -> 9

24.

What is the end behavior of the function?

a)

as x -> - infinity, f(x) -> infinity,

as x -> + infinity, f(x) -> - infinity

b)

as x -> - infinity, f(x) -> - infinity,

as x -> + infinity, f(x) -> - infinity

c)

as x -> - infinity, f(x) -> infinity,

as x -> + infinity, f(x) -> infinity

d)

as x -> - infinity, f(x) -> - infinity,

as x -> + infinity, f(x) -> infinity

25.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

26.

Select ALL the information that applies to the given rational function.
$f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$

a)

Vertical Asymptote. at x = 1

b)

Horizontal Asymptote. at y = 0

c)

y-intercept at (0, 1/2)

27.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x+3}{-3x+6}$

a)

Vertical Asymptote at x = -6

b)

Horizontal Asymptote at y = -1/3

c)

y-intercepts at (0, 1/2)

28.

Graph the function.

$f\left(x\right)=\frac{-x+1}{x-4}$

a)

b)

c)

d)

29.

Select all the information that applies to the given rational function.

a)

V.A. at x = -1

b)

H.A. at y = -1/4

c)

x-intercepts at (0,0) and (-1,0)

d)

All the above are false.

30.

Graph the function.

a)

b)

c)

d)

31.

What is the domain and range?

a)

D : $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$
R: $\left(-\infty,1\right)\cup\left(1,\infty\right)$

b)

D : $\left(-\infty,1\right)\cup\left(1,\infty\right)$
R: $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$

c)

D : $\left(-\infty,3\right)\cup\left(3,\infty\right)$
R: $\left(-\infty,1\right)\cup\left(1,\infty\right)$

d)

D: $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$
R: $\left(-\infty,3\right)\cup\left(3,\infty\right)$

32.

a)

A

b)

B

c)

C

d)

D

33.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

34.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

35.

a)

A

b)

B

c)

C

d)

D

36.

Simplify.

a)

A

b)

B

c)

C

d)

D

37.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

38.

What is the rule for a 45-45-90 triangle?

a)

$x,\ x,\ x\sqrt{2}$

b)

$x,\ x\sqrt{3},\ 2x$

39.

What is the rule for a 3-60-90 triangle?

a)

$x,\ x,\ x\sqrt{2}$

b)

$x,\ x\sqrt{3},\ 2x$

40.

What is the measure of side b?

a)

5

b)

10√2

c)

5√2

d)

10√3

41.

Find n.

a)

4

b)

6

c)

12

d)

2√3

42.

What is the value of y?

a)

3√2

b)

4√3

c)

6

d)

1

43.

Find the value of x and y

a)

x=10√3 y=30

b)

x=30√3 y=10

c)

x=10, y=30√3

d)

x=30 y=10√3

44.

BONUS - Solve for x.
You will need to use 45-45-90 and 30-60-90 triangles.

a)

10√3

b)

15

c)

5√3

d)

15√2

45.

From ∠C, what side is AB?

a)

Adjacent

b)

Hypotenuse

c)

Opposite

46.

Which trigonometric ratio is correct?

a)

cosC= adj/hyp

b)

sinC= adj/hyp

c)

tanC= adj/hyp

d)

tanC=adj/opp

47.

Which Trig function do you use?

a)

Sine

b)

Cosine

c)

Tangent

48.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

49.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

50.

$\cos\left(\theta\right)=?$

a)

$\frac{3}{5}$

b)

$\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

51.

What are the negative and positive coterminal angles of 120°?

a)

420°, -240°

b)

480°, -240°

c)

300°, -360°

d)

0°, -250°

52.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

53.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

54.

Graph the angle in standard position. $-220\degree$

a)

b)

c)

d)

55.

If the coordinates of the point are (0.755,0.656) find the measure of the angle of rotation. Round your answer to the nearest degree.

a)

41 degrees

b)

20 degrees

c)

123 degrees

d)

90 degrees

56.

What is the sine of the given angle shown?

a)

-3

b)

1

c)

$-\frac{3\sqrt{10}}{10}$

d)

$\frac{\sqrt{10}}{10}$

57.

How many degrees are in a circle?

a)

100

b)

180

c)

360

d)

1000

58.

What is the formula for the circumference of a circle?

a)

$\pi r^2$

b)

$360\cdot r$

c)

$2\pi r$

59.

What is the circumference of a circle with radius 1? Hint: $C=2\pi r$

a)

$\pi$

b)

$2\pi$

c)

$\pi^2$

60.

Angles in a circle can be measured in two ways, in degrees and in radians. 360 degrees is a full rotation in a circle just as 2pi radians in a full rotation in a circle. If 360 degrees = 2pi radians, then how many radians in 180 degrees?

a)

pi/2 radians

b)

pi radians

c)

3pi/2 radians

61.

If 360 degrees = 2 pi radians, how many degrees is 4 pi radians?

a)

180 degrees

b)

270 degrees

c)

720 degrees

62.

Now you know the basics of converting between degrees and radians. Both ways of measuring rotation in a circle are necessary to be successful in Math 3. Just remember that 360 degrees = 2 pi radians. Great work! Enjoy the freebie question and select the "correct" one.

a)

Correct Answer

b)

Why did you click here!?

63.

What is cos 60°?

a)

½

b)

^√3/₂

c)

^√2/₂

d)

1

64.

What is sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

65.

What is cos 90°?

a)

½

b)

undefined

c)

1

d)

0

66.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

67.

What is π/3 radians in degrees?

a)

30

b)

60

c)

360

d)

90

68.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

69.

tanθ 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

70.

What is the reciprocal of the sine function?

a)

cosecant

b)

cosine

c)

secant

d)

cotangent

71.

In what quadrant would Θ be in if:

Sin Θ < 0

Tan Θ > 0

a)

I

b)

II

c)

III

d)

IV

72.

What is the tan of 3π/2?

a)

-√3

b)

√3/3

c)

-1

d)

Undefined

73.

What is Θ when sec(Θ) = 2 between the interval 0 and 2π?

a)

π/6 and 5π/6

b)

π/3 and 5π/3

c)

π/4 and 7π/4

d)

2π/3 and 4π/3

74.

What is Θ when tan(Θ) = √3/3 between the interval π and 2π?

a)

π/6

b)

π/3

c)

4π/3

d)

7π/6

75.

What is the period of either graph?

y = sin(x) & y = cos (x)

a)

Pi

b)

2Pi

c)

Pi/2

d)

Pi/4

76.

What is the period of
y= 4 cos (5x)

a)

2π/5

b)

π

c)

5

d)

5π

77.

What is the midline of the following function? $y=\frac{1}{2}\cos\left(x\right)+2$

a)

$y=\frac{1}{2}$

b)

$y=2\pi$

c)

$y=\pi$

d)

$y=2$

e)

$y=\frac{\pi}{4}$

78.

What is the amplitude of the following function? $y=\frac{1}{2}\cos\left(x-\frac{\pi}{4}\right)+2$

a)

$\frac{1}{2}$

b)

$2\pi$

c)

$\pi$

d)

$2$

e)

$\frac{\pi}{4}$

79.

Identify the graph of $y=\sin\left(2x\right)+2$ .

a)

b)

c)

d)

80.

Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

a)

y = 5cos(x - pi) + 3

b)

y = 3cos(x - pi) + 5

c)

y = 3cos(2x - pi) + 5

d)

y = 5cos(2x - pi) + 3

81.

What is the period for y = 4cos[¹/₂(x +π)] - 2?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

82.

What is the phase shift for the function

f(x) = -2sin4(x + π) - 1

a)

right π

b)

left π

c)

left 1

d)

left 4π

83.

Which is a correct equation for the graph shown?

a)

$y=\cos\left(\frac{1}{2}x\right)$

b)

$y=\sin\left(\frac{1}{2}x\right)$

c)

$y=\cos2x$

d)

$y=\frac{1}{2}\cos\left(x\right)$

84.

Which is a correct equation for the graph shown?

a)

$y=3\sin\left(\pi x\right)$

b)

$y=\pi\sin\left(3x\right)$

c)

$y=\sin\left(\pi x\right)+3$

d)

$y=-3\cos\left(\pi x\right)$

85.

Examine the equation $y=-\cos\left(x-\frac{\pi}{4}\right)+2$ and the graph above. Does the graph represent the equation?

a)

Yes

b)

No

86.

Which parent function is shown?

a)

y = tan x

b)

y = sin x

c)

y = csc x

d)

y = sec x

87.

Determine an equation for this graph:

a)

y=sec(x)

b)

y=2sec(x)

c)

y=2csc(x)

d)

y= csc(2x)

88.

Determine an equation for this graph:

a)

y=2csc(x)

b)

y=csc(x) + 1

c)

y=2csc(x) + 1

d)

y= csc(x) + 2

89.

Determine an equation for this graph:

a)

y=sec(x)

b)

y=2sec(x)

c)

y=2csc(x)

d)

y= csc(x)

90.

Which function below matches this graph?

a)

y=sec2x

b)

y=secx

c)

y=csc2x

d)

y=2-secx

91.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

92.

Name the graph

a)

y = cot x

b)

y = sinx

c)

y = tan x

d)

y = secx

93.

What is the value of d if the function above is in the form

f(x) = a tanx + d

a)

-2

b)

-1

c)

0

d)

1

e)

2

94.

What is the period length of y=tanx?

a)

π

b)

2π

c)

-2π

d)

π+1

95.

What is the period?

a)

$\frac{\pi}{2}$

b)

2

c)

1 up

d)

$2\pi$

96.

What is the equation of the function graphed?

a)

y = 4cotx

b)

y = tanx + 4

c)

y = 4tanx

d)

y = cotx + 4

97.

5. Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

a)

y = 5cos(x - pi) + 3

b)

y = 3cos(x - pi) + 5

c)

y = 3cos(2x - pi) + 5

d)

y = 5cos(2x - pi) + 3

98.

8. What is the period for y = 4cos¹/₂(x +π) - 2?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

99.

10. What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

100.

13. What is the equation of the graph?

a)

y = -2 cos x - 3

b)

y = 3 cos x - 2

c)

y = -7 cos x - 3

d)

y = -3 cos x - 4

101.

What is the equation for the graph shown.

a)

y = 4cotθ - 2

b)

y = 3cotθ - 1

c)

y = 2tanθ - 4

d)

y = -4tanθ + 2

102.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

103.

$1+\cot^2x\ =$

a)

$\csc^2x$

b)

$\sec^2x$

c)

$\cos^2x$

d)

$\tan^2x$

104.

Simplify
$\sec\theta\cot\theta\sin\theta$

a)

-1

b)

sin θ

c)

csc θ

d)

1

105.

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

106.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

107.

For which of these problems would multiplying by a conjugate be a helpful suggestion?

a)

b)

c)

d)

108.

Simplify.

a)

sinθ

b)

cos²θ

c)

sin²θ

d)

1- sin²θ

109.

Which of the following is not a pythagorean identity?

a)

cot²x + 1 = csc²x

b)

csc²x + 1 = cot²x

c)

cot²x - csc²x = -1

d)

csc²x - cot²x = 1

110.

a)

sin x

b)

cos x

c)

tan x

d)

1

111.

Which of the following is a solution to

sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

4π / 3

d)

5π / 3

112.

Solve sinθ = ½ on θ∈[0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

113.

a)

No solution

b)

π/3, 5π/3

c)

π/6, 11π/6

d)

2π/3, 4π/3

114.

Solve on the domain [0, 2π)
1/2sec x - 1 = 0

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

115.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

116.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

117.

Which of the following is NOT true about the graph?

a)

Potential outlier

b)

Centered at about 35

c)

skewed right

d)

not symmetric

118.

Given a set of skewed data, which would be the most appropriate measure of center?

a)

Mean

b)

Median

c)

Mode

119.

Which describes the data that would be outliers for a given set?

a)

Any data after median+IQR or before median-IQR

b)

Any data after Q3+IQR or before Q1-IQR

c)

Any data after Q3+IQR*1.5 or before Q1-IQR*1.5

d)

Any data after median+IQR*1.5 or before median-IQR*1.5

120.

Given the 5 number summary, is the minimum an outlier? If it is, why is it?

a)

Yes, an outlier as it is less than 15.5.

b)

Yes, an outlier as it is less than 19.5.

c)

Yes, an outlier as it is less than 23.

d)

No, the minimum is not an outlier.

121.

A way to describe the shape of a data display that has two modes or peaks.

a)

unimodal

b)

bimodal

c)

multimodal

d)

uniform

122.

Describing the shape of a data set that has the same values across the entire display.

a)

symmetric

b)

unimodal

c)

skewed

d)

uniform

123.

Which of the following is a measure of variability?

a)

mean

b)

median

c)

mode

d)

standard deviation

124.

According to the empirical rule, what percentage of data falls within 1 standard deviation?

a)

25%

b)

68%

c)

95%

d)

99.7%

125.

According to the empirical rule, how much of the data falls within 3 standard deviations?

a)

25%

b)

68%

c)

95%

d)

99.7%

126.

Which of the following is a disadvantage of the Empirical Rule?

a)

There is no result for 3 standard deviations.

b)

It is very conservative.

c)

There is no result for 1 standard deviation.

d)

The data has to be approximately normal.

127.

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 1.7 and 4.1?

a)

68%

b)

99.7%

c)

95%

d)

84%

128.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

a)

28,000 km and 32,000 km.

b)

24,000 km and 34,000 km.

c)

26,000 km and 34,000 km.

d)

27,000 km and 31,000 km.

129.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

a)

68%

b)

34%

c)

16%

d)

2.5%

130.

What is the purpose of z-scores?

a)

to describe the exact location of a score within a distribution

b)

to find the mean of the distribution

c)

to describe the shape of the distribution

d)

to find the standard deviation of the distribution

131.

What is the formula to find the z-score for population?

a)

z=X-M

b)

z=σ-M/μ

c)

^z/M=μ

d)

z=X-μ/σ

132.

Find the z-score value corresponding if the location is below the mean by 2 standard deviations

a)

+2.00

b)

-2.00

c)

+1.25

d)

-1.00

133.

A data set has a mean of 290 and a standard deviation of 20. Calculate the z-score for 265.

a)

$z=250.5$

b)

$z=1.25$

c)

$z=-1.02$

d)

$z=-1.25$

134.

What does it mean to have a z-score of $z=0$ on a quiz?

a)

It means you did better than zero people.

b)

It means you scored the same grade as the average grade.

c)

It means you earned a zero on the quiz.

d)

It means the average score was a zero.

135.

What percent of scores are below a z-score of $z=-1.02$ ? (Use either the attached image of a z-table or use your own copy of the z-table from your notes)

a)

15.87%

b)

15.39%

c)

9.68%

d)

84.61%

136.

What is the probability that a score is above (right of) 2.37?

a)

.0116

b)

.0089

c)

.0068

d)

.0051

137.

The author of the statistical study was an observer at a police sobriety checkpoint at which every 5th driver was stopped and interviewed. Which sampling type is this?

a)

random

b)

systematic

c)

convenience

d)

stratified

e)

cluster

138.

On Days of presidential elections, the news media organize an exit poll in which specific polling stations are randomly selected and all voters are surveyed as they leave the premises. Which sampling type is this?

a)

random

b)

systematic

c)

convenience

d)

stratified

e)

cluster

139.

An engineering student measures the strength of fingers used to push buttons by testing family members. Which sampling type is this?

a)

random

b)

systematic

c)

convenience

d)

stratified

e)

cluster

140.

In a Gallup poll of 1059 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers that were then called. Which sampling type is this?

a)

random

b)

systematic

c)

convenience

d)

stratified

e)

cluster

141.

A market researcher has partitioned all California residents into categories of unemployed, employed full time, and employed part time. She is surveying 50 people from each category. Which sampling type is this?

a)

random

b)

systematic

c)

convenience

d)

stratified

e)

cluster

142.

If I wanted to know how many blades of grass are inside the track, I can divide the grassy area into 1 inch sections, randomly pick several sections to count, average them together and multiply that by the total square inches. Which sampling method did I use?

a)

simple random sample

b)

convenience

c)

stratified random sample

d)

systematic random sample

Math 3 Final Review

Total questions: 142

Worksheet time: 5hrs 24mins

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