Free Printable Final Exam Review # 3

1.

Is (0,0) a solution to the system?

a)

Solution

b)

Not a solution

2.

Is (-2, 0) a solution to the system?

a)

Solution

b)

Not a solution

3.

^{Which point is a solution to the system of inequalities?}

a)

(-8,2)

b)

(-2,-5)

c)

(0,6)

d)

(4, 3)

4.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(5, 1)

c)

(-1, -3)

d)

(20, -5)

5.

Which inequality is shown in the graph?

a)

y < 2x + 1

b)

y < -2x + 1

c)

y ≤ 2x + 1

d)

y ≤ -2x + 1

6.

The graph shows which inequality?

a)

y ≤ 3

b)

y ≥ 3

c)

y > 3

d)

x > 3

7.

What is the inequality symbol for the equation of this boundary line?

a)

less than

b)

less than or equal to

c)

greater than

d)

greater than or equal to

8.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

9.

Match

a)

y < x−2
y < 3

b)

y > -x+2
y > 3

c)

y < -x+2
y < 3

d)

y < -x+2
y > 3

10.

When graphed, the line will be...

5 ≥ x

a)

Solid

b)

Dashed

c)

Zig-Zag

11.

Write the slope intercept form of the equation 3x - 2y = -16

a)

y = -3x - 8

b)

y = -3x + 8

c)

y = -3/2x - 8

d)

y = 3/2 x + 8

12.

Write the slope intercept form of the equation 13x - 11y = -12

a)

y = 13/11x + 12/11

b)

y = 13x - 11

c)

y = -13/11x -12/11

d)

y = x + 1

13.

Write the slope intercept form of the equation 4x - y = 1

a)

y = -4x + 1

b)

y = 4x + 1

c)

y = 4x - 1

d)

y = -4x - 1

14.

What are the x- and y-intercepts of the linear function given by the equation 3x + 4y = -12

a)

(4, 0) and (0, -3)

b)

(-3, -4)

c)

(-4, 0) and (0, 3)

d)

(-4, 0) and (0, -3)

15.

On the graph, which portion of the piecewise function is represented in red?

a)

x

b)

0.5x + 2.5

c)

-1

d)

0.5x + 2

16.

a)

A

b)

B

c)

C

d)

D

17.

Find the vertex of

y=3\left(x-2\right)^2+3

a)

$\left(2,3\right)$

b)

$\left(-2,3\right)$

c)

$\left(2,-3\right)$

d)

$\left(-2,-3\right)$

18.

Find the axis of symmetry of

y=3\left(x-2\right)^2+3

a)

$x=2$

b)

$x=-2$

c)

$x=3$

d)

$x=-3$

19.

Find the vertex form of

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

a)

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

b)

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

c)

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

d)

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

20.

Find the x-intercepts of

f\left(x\right)=x^2-11x+30

a)

$x=5,6$

b)

$x=-6,-5$

c)

$x=-15,2$

d)

$x=-2,15$

21.

Find the x-intercepts of

h\left(x\right)=x^2-8x+12

a)

$x=2,6$

b)

$x=-6,-2$

c)

$x=-6,2$

d)

$x=-2,6$

22.

Find the y-intercept of

g\left(x\right)=x^2+5x-14

a)

-14

b)

14

c)

5

d)

-5

23.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

24.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

25.

Given f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

26.

(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

27.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

28.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

29.

Is the relation shown a function?

a)

No, because the x-value 11 is paired with 5 and 8.

b)

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

30.

Does the graph represent a function?

a)

Yes

b)

No

31.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

32.

Which is the set of all y-values or the outputs?

a)

Domain

b)

Range

c)

Relation

d)

Function

33.

What is the range of the table?

a)

{-4, 0, 1, 3}

b)

{-2, 0, 2, 3}

c)

{-4, -2, 0, 1, 2, 3}

d)

{ (0, 0), (2, -4), (3, 3), (-2, 1) }

34.

Is this a function?

a)

Function

b)

Not a Function

35.

Is this a function?

a)

Function

b)

Not a Function

36.

Is this set of ordered pairs a function or not a function?

a)

Function

b)

Not a Function

37.

Is this set of ordered pairs a function or not a function?

a)

Function

b)

Not a Function

38.

How do you predict your energy level and motivation is going to be for these last weeks of school?

a)

Going down more and more each day

b)

Leveled off to a medium level

c)

I'm going to get a "second wind" and feel great

d)

Hard to say, could go up or down.

39.

How many solutions does this Quadratic have?

a)

0

b)

1

c)

2

d)

3

40.

What is the value of the Discriminant?

a)

Positive

b)

0

c)

Negative

41.

What is the value of the Discriminant?

a)

Positive

b)

0

c)

Negative

42.

How many solutions will this quadratic have?

a)

None

b)

1

c)

2

43.

Let f(x)=√(x) and g(x)= -3√(x-2)+1. Describe g(x) in terms of f(x):

a)

reflects over x axis, vertical stretch by 3, right 2, up 1

b)

reflects over y axis, vertical compression by -3, left 2, up 1

c)

reflects over x axis, vertical stretch by -3, left 2, up 1

d)

reflects over y axis, vertical compression by 1/3, right 2, up 1

44.

Which of the following is the function shown in the graph?

a)

b)

c)

d)

45.

Simplify the following rational function:

$\frac{\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x-4\right)}{\left(x+4\right)\left(x+3\right)\left(x+1\right)\left(x+2\right)\left(x-2\right)}$

a)

$\frac{1}{x+2}$

b)

$\frac{\left(x+3\right)}{\left(x-2\right)\left(x-4\right)}$

c)

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

d)

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

46.

Simplify by factoring:

$\frac{x^2+5x-14}{x^2-4}$

a)

$\frac{x+7}{x-2}$

b)

$\frac{x+7}{x+2}$

c)

$\frac{x-7}{x-2}$

d)

$\frac{x-7}{x+2}$

47.

Multiply the following rational expressions, simplifying the answer if needed.

$\frac{3x+3}{x+2}\cdot\frac{4x-8}{x+1}$

a)

$\frac{7x-5}{\left(x+2\right)\left(x+1\right)}$

b)

$\frac{12\left(x-2\right)}{\left(x+2\right)}$

c)

$12$

d)

$\frac{12\left(x^2-2\right)}{\left(x+2\right)\left(x+1\right)}$

48.

Multiply the following rational expressions, simplifying the answer if needed:

\frac{n^2-6n+5}{2n+6}\cdot\frac{3n+9}{n-5}

a)

$3n-2$

b)

$\frac{2\left(n+3\right)}{n-5}$

c)

$\frac{3\left(n-1\right)}{2}$

d)

$1$

49.

Divide the Rational Expression

\frac{6}{k-4}\div\frac{k+6}{k^2+2k-24}

a)

$\frac{9}{k-4}$

b)

$\frac{k+7}{8}$

c)

$6$

d)

$k-3$

50.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

51.

What is the Horizontal Asymptote?

a)

y= 5

b)

y= -6

c)

y= 1

d)

y= 5/-6

52.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

53.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

54.

Find the length of Side BC.

a)

33

b)

24

c)

12

d)

29

55.

Find the length of side AB.

a)

10

b)

8

c)

6.1

d)

4.9

56.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

57.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

58.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

59.

Use the Law of Cosines to find the value of x. (Level 1)

a)

41.7

b)

51.7

c)

61.7

d)

71.7

60.

What is the sample standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

6.89

b)

10.1

c)

7.26

d)

9

61.

All of the below sets have the same mean.

Set 1-Standard Deviation=3.1

Set 2-Standard Deviation=4.9

Set 3-Standard Deviation=1.7

Set 4-Standard Deviation=3.2

Which set of data probably has the points closest to the mean?

a)

1

b)

2

c)

3

d)

4

62.

Four data sets are shown below.
Set 1: {10, 19, 38, 50, 51}
Set 2: {5, 21, 26, 39, 51}
Set 3: {9, 38, 50, 50, 51}
Set 4: {5, 28, 28, 28, 51}
Which data set has the largest standard deviation?

a)

Set 1

b)

Set 2

c)

Set 3

d)

Set 4

63.

To find the _________ you add up all the numbers and then divide by how many numbers you have.

a)

Mean

b)

Median

c)

Mode

d)

Range

64.

The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for

snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1,

14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6

What are the mean and population standard deviation for these data, to the nearest hundredth?

a)

mean = 9.46; standard deviation = 3.74

b)

mean = 9.46; standard deviation = 3.85

c)

mean = 9.45; standard deviation = 3.74

d)

mean = 9.45; standard deviation = 3.85

65.

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

a)

1084 to 1216 pounds

b)

1106 to 1150 pounds

c)

1106 to 1194 pounds

d)

1128 to 1172 pounds

66.

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.

67.

Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3?

a)

9 to 21

b)

12 to 18

c)

6 to 24

d)

13 to 16

68.

Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3?

a)

9 to 21

b)

12 to 18

c)

6 to 24

d)

13 to 16

69.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

70.

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

71.

Solve on the Interval [0,2π)
tan(x)+1=2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

72.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

73.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

74.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

75.

Expand

a)

A

b)

B

c)

C

d)

D

76.

Expand

a)

A

b)

B

c)

C

d)

D

77.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

78.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

79.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

80.

ln(9x-2)=ln(x+14)

a)

x=2

b)

x=.156

c)

x=-3

d)

x=0

81.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

82.

log₈(9)-log₈(-4x-2) =log₈(36)

a)

No Solution

b)

{-113/80}

c)

{17/4}

d)

{-9/16}

83.

log(x+6)-log(x) =log(20)

a)

1/135

b)

27/4

c)

No solution

d)

6/19

84.

Determine the period of the sinusoidal graph shown.

a)

15 m

b)

40 s

c)

140 s

d)

80 s

85.

Which of the following equations has a period of

720\degree

a)

$g\left(x\right)=2\sin\left(x\right)$

b)

$g\left(x\right)=2\sin\left(2x\right)$

c)

$g\left(x\right)=\cos\left(720x\right)$

d)

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

86.

a)

The Equation is:
$f\left(x\right)=2\sin\left(4x\right)$

b)

The Equation is:
$f\left(x\right)=2\sin\left(90x\right)-3$

c)

The Equation is:
$f\left(x\right)=2\cos\left(90x\right)$

d)

The Equation is:
$f\left(x\right)=2\cos\left(4x\right)-3$

87.

Determine the amplitude of the function:

y=5\sin\left(2\left(x-30\right)\right)+3

a)

a = 2

b)

a = 8

c)

a = 5

d)

a = 30

88.

(a)

Final Exam Review # 3

Total questions: 88

Worksheet time: 5hrs 49mins

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