Free Printable Algebra 2 Final Exam Review # 2

1.

The period of a function is

a)

how long one cycle is before the function repeats

b)

how high and low the function goes from the center line

c)

the range of the function

2.

Amplitude refers to....

a)

how high and low the function varies from the center line.

b)

the length of the function

c)

how often the function repeats

3.

Midline refers to....

a)

how high and low the function varies from the center line.

b)

the length of the function

c)

how often the function repeats

d)

horizontal line half way between max and min of function

4.

Is the following function periodic?

a)

yes

b)

no

5.

What is the period of the function?

a)

6

b)

3

c)

2

d)

4

6.

What is the period of the function?

a)

4

b)

2

c)

3

d)

5

7.

What is the amplitude of the function?

a)

2

b)

1

c)

3

d)

5

8.

Is following periodic?

a)

Yes

b)

No

9.

What is the minimum height on the Ferris wheel?

a)

1

b)

4

c)

7

d)

0

10.

What is the equation of the midline of the graph?

a)

y = -3

b)

y = 2

c)

y = -2

d)

y = 3

11.

Find the amplitude of the graph shown.

a)

2

b)

4

c)

6

d)

8

12.

Find the period of the graph shown.

a)

2

b)

4

c)

6

d)

8

13.

What is the equation of the midline?

a)

5

b)

6

c)

y=5

d)

y=6

14.

What is the period?

a)

25 units

b)

24 units

c)

15 units

d)

12 units

15.

What is the coordinate of the y-intercept?

a)

[2, 0]

b)

[0, -1]

c)

(-∞, ∞)

d)

(-1, 0)

e)

(0, -1)

16.

Consider a Ferris wheel, moving in constant motion. At its lowest height of 2 meters above the ground, it loads passengers. It carries passengers to a height of at most 14 meters. How high is the hub of Ferris wheel off the ground (hint: height of the midline)?

a)

2m

b)

8m

c)

14m

d)

12m

17.

A section of a rollercoaster is in the shape of a sinusoidal curve shown below. It has a maximum height above the ground of 51 m and a minimum of 1 m. The equation can be written in the form h = Asin(Bd) + C:

What is the value of A?

a)

-20m

b)

50m

c)

25m

d)

15m

18.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

19.

Find h(f(x))

a)

4x²

b)

2x²

c)

4x⁴

d)

2x³

20.

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

21.

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+31

b)

g(f(x))= -6x²+24

c)

g(f(x))=18x²-84x+90

d)

g(f(x))=9x²-42x-41

22.

Convert 10^(x+5)=100 to logarithmic form.

a)

log₁₀₀=x+5

b)

log(x+5)=100

c)

log(100)=x+5

d)

log_(x+5)(100)=10

23.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

24.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

25.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$\tan\theta=-\sqrt{3}$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

26.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$6\sin\theta=3$

a)

$60\degree$

b)

$300\degree$

c)

$30\degree$

d)

$150\degree$

27.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers. $2\cos\theta\ -\frac{\sqrt[]{3}}{2}=3\cos\theta$

a)

$60\degree\ and\ 120\degree$

b)

$150\degree\ and\ 210\degree$

c)

$90\degree\ and\ 180\degree$

d)

$30\degree\ and\ 330\degree$

e)

$45\degree\ and\ 225\degree$

28.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-15+4\cos\theta=-15-2\sqrt{2}$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

29.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

30.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

31.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

32.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

33.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

34.

Use Law of Cosines to find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

35.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

a)

9285.73 ft

b)

96.36 ft

c)

24061.81 ft

d)

155.12 ft

36.

Parker must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B.

a)

707643.58

b)

841.22

c)

877.62

d)

842.01

37.

Which of these represents slope-intercept form of a linear equation?

a)

y - y₁ = m(x-x₁)

b)

Ax + By = C

c)

y = mx + b

d)

y=kx

38.

Which of these represents standard form of a linear equation?

a)

y - y₁ = m(x-x₁)

b)

Ax + By = C

c)

y = mx + b

d)

y=kx

39.

What is the slope of the line represented by $6x-5y=12$

a)

$-\frac{6}{5}$

b)

$\frac{5}{6}$

c)

$\frac{6}{5}$

d)

$-\frac{5}{6}$

40.

Given y=3/7x-1; write in standard form

a)

3x=7y=-7

b)

3x+7y=-7

c)

3x-7y=7

d)

-3x-7y=-7

41.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

42.

8x + 4y= 16

a)

y = -8x + 16

b)

y = 2x -4

c)

y = -2x + 4

d)

y = -8x + 12

43.

Which equation is written in STANDARD form?

a)

y = 1/2x + 2

b)

y - 3 = -5(x + 2)

c)

-7x + 2y = 9

d)

3x + 2 = y

44.

Simplify

a)

A. $\frac{4x^3}{\left(x+2\right)}$

b)

B. $\frac{4x³}{(x+10)}$

c)

C. $\frac{2x³}{(5x+1)}$

d)

D. $\frac{4x^3}{\left(x-2\right)}$

45.

Simplify.

a)

$\frac{x+6}{x+4}$

b)

$\frac{1}{x-5}$

c)

$\frac{x+6}{x+5}$

d)

$\frac{x+6}{x-5}$

e)

$\frac{x+6}{\left(x+5\right)\left(x-4\right)}$

46.

Divide the following expressions.

a)

$\frac{y^{\ 4}}{2x^2}$

b)

$\frac{9y^8}{2x^4}$

c)

$\frac{2x^2}{y^{\ 4}}$

d)

Can't be simplified

47.

Divide the following expressions.

a)

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

b)

$\frac{\left(x+4\right)^2\left(x-4\right)}{16\left(x+5\right)}$

c)

Can't be simplified

d)

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

48.

Multiply the following expressions.

\frac{x^2-8x+12}{x^2-16}\cdot\frac{4x+16}{x^2-4x+4}

a)

$\frac{4\left(x-6\right)}{\left(x-4\right)\left(x-2\right)}$

b)

$\frac{\left(x-4\right)\left(x-2\right)}{4\left(x-6\right)}$

c)

$\frac{x-6}{x-2}$

d)

$\frac{4}{x-4}$

49.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

50.

Divide the expression $\frac{x+8}{6\left(x+10\right)}\div\frac{\left(x+8\right)\left(x-8\right)}{\left(x+10\right)\left(x-8\right)}$

a)

$\frac{1}{6}$

b)

$\frac{\left(x+10\right)}{6x+60}$

c)

$\frac{x+8}{6x+60}$

d)

$\frac{\left(x+10\right)\left(x+8\right)}{6x+60}$

51.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

52.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

(0, -8)

b)

(0, 3)

c)

(0, 7)

d)

(0, -7)

53.

If given the equation
y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

54.

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

55.

What is the range of this function?

a)

(- ∞,+∞)

b)

[0, +∞)

c)

[-2, +∞)

d)

[2, +∞)

56.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

57.

Solve:
4x²= -4x -1

a)

x = -½

b)

x = -2

c)

x = 0

58.

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

59.

Convert to vertex form:
f(x) = x² + 10x + 24

a)

f(x) = ( x - 5 )² + 1

b)

f(x) = ( x + 5 )² - 1

c)

f(x) = ( x - 5 )² - 1

d)

f(x) = ( x + 5 )² + 1

60.

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

61.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

62.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

63.

Is there a hole or a vertical asymptote?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

64.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

65.

What is an asymptote?

a)

an imaginary line that your function never touches

b)

a part of your function

c)

a point on your graph

d)

a type of fruit

66.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

67.

Which of the following represents the graph below?

a)

b)

c)

d)

68.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

69.

A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.

a)

2.5%

b)

.15%

c)

2.35%

d)

2.25%

70.

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 2.3 and 3.5?

a)

68%

b)

99.7%

c)

95%

d)

84%

71.

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the GPA of the highest 2.5% of the students?

a)

4.1

b)

4.1 or higher

c)

4.7

d)

4.5 or higher

72.

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.

73.

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%

74.

Expand each Log

a)

A

b)

B

c)

C

d)

D

75.

Expand each Log

a)

A

b)

B

c)

C

d)

D

76.

Expand each Log

a)

A

b)

B

c)

C

d)

D

77.

Condense each Log

a)

A

b)

B

c)

C

d)

D

78.

Condense each Log

a)

A

b)

B

c)

C

d)

D

79.

Condense each Log

a)

A

b)

B

c)

C

d)

D

80.

A normally distributed set of data's graph resembles:

a)

A fire hydrant

b)

A bath tub

c)

A bell

d)

A tree

81.

The Empirical Rule's percents are:

a)

68-95.7-99

b)

68-95-99.7

c)

68.7-95-99

82.

What percent of the data is between 25 and 30 on the number line?

a)

25%

b)

`50%

c)

75%

d)

100%

83.

6. Which city has a higher median?

a)

Millersburg

b)

Arcadia

84.

Which box and whisker plot has the smallest lower quartile (Q1)?

a)

Top plot

b)

Bottom plot

85.

Find the median, first quartile, third quartile, and interquartile range of the data.

32, 53, 72, 66, 47, 54, 49, 67, 71

a)

Median: 54

First Quartile: 49

Third Quartile: 67

IQR: 18

b)

Median: 54

First Quartile: 48

Third Quartile: 69

IQR: 21

c)

Median: 54

First Quartile: 48

Third Quartile: 69

IQR: 22

d)

Median: 54

First Quartile: 49

Third Quartile: 69

IQR: 20

86.

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

87.

The masses of six children are 34.5 kilograms, 42.6 kilograms, 39.8 kilograms, 40.1 kilograms, 53.4 kilograms, and 33.8 kilograms. Find the mean mass.

a)

40.7 kg

b)

40

c)

41

d)

50

88.

In a population of five university students with GPAs of 2.5, 2.3, 1.7, 1.4, and 1.1, a sample of three students are considered. What would be the standard deviation of the resulting sampling distribution?

a)

0.53

b)

0.41

c)

0.35

d)

0.22

Algebra 2 Final Exam Review # 2

Total questions: 88

Worksheet time: 5hrs 9mins

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