Free Printable Final Exam Review (Algebra 2)

1.

a)

A

b)

B

c)

C

d)

D

2.

a)

M

b)

P

c)

R

d)

S

3.

a)

A

b)

B

c)

C

d)

D

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.

a)

A

b)

B

c)

C

d)

D

9.

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

a)

y = 1.5x + 12

b)

y = 12x + 1.5

c)

y = 0.67x - 8

d)

y = -8x + 0.67

10.

Find the quadratic regression equation for the relationship of the horizontal distance and the height of the ball in the provided table.

a)

$-18x^2+2.11x+4.21$

b)

$-0.06x^2+1.06x+7.9$

c)

$-6x^2+1.06x+79$

d)

$-0.12x^2+2.11x+4.22$

11.

Find the best fitting Quadratic model for the data

a)

$-0.26x^2-17.3x+222.8$

b)

$-0.26x2^2+22.59x+23.02$

c)

$2.6x^2+22.9x+20.03$

d)

$2.6x^2+2.3x+23.02$

12.

Write the exponential regression equation for the data.

a)

Y=8.16(2.7)^x

b)

Y=81.6(2.7)^x

c)

Y=8.16(.27)^x

d)

Y=8.16(27)^x

13.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

a)

y = 100(8.7)^x

b)

y = 100(1.87)^x

c)

y = 100(.87)^x

d)

y = 100(.13)^x

14.

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many chapters would be in a book with 180 pages.

a)

12 chapters

b)

15 chapters

c)

18 chapters

d)

21 chapters

15.

Find the slope for the trend line using points (2,2) and (4,3)

a)

2

b)

1/2

c)

-2

d)

-1/2

16.

a)

y= 8/7x+1

b)

y= 7/8x+1

c)

y= -7/8 +1

d)

y= -8/7+1

17.

Which of the following could be a possible line of best fit for the data?

a)

y = -5/2x + 20

b)

y = -x + 19

c)

y = x + 20

d)

y = 2/3x + 15

18.

What is the equation of the line of best fit?

a)

y = -25x + 170

b)

y = -5/8x + 170

c)

y = 25x + 170

d)

y = 5/8x + 170

19.

The equation of the trend line is y= 1/2x +1
How many laps can a bicycle make around the park in 23 minutes?

a)

44 laps

b)

12 1/2 laps

c)

23 laps

20.

The linear regression equation that best represents the line of best fit for the data is y=20.8x-35. Use the equation to predict the number of bacteria in 24 hours.

a)

35

b)

277

c)

464

d)

819

21.

The linear regression equation is y = 61.93x - 1.79. Use the equation to predict how far this person will travel after 10 hours of driving.

a)

10 miles

b)

617.5 miles

c)

0.19 miles

d)

500 miles

22.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=80\left(1.4\right)^x$

c)

$y=60\left(0.7\right)^x$

d)

$y=3\left(0.6\right)^x$

23.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ How many ants did you begin with?

a)

There was 2 ants

b)

There was 3 ants

c)

The equation doesn't tell us

24.

Give the rate of decay: *Hint: How far from 1*
y = 35(0.65)^x

a)

35%

b)

65%

c)

165%

25.

Give the rate of growth: (how far over 1)
y = 5(1.27)^x

a)

127%

b)

27%

c)

5

26.

f(x) = 30000(0.89)^x

What is the change in percent?

a)

11% decrease

b)

11% increase

27.

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(1 - 0.30)^x

b)

y=30(5000)^x

c)

y=5000(1 + 0.30)^x

d)

y=5000x^x

28.

The population of Townville is decreasing at a rate of 6% each year. If the starting population was 7,000 what equation represents the current population after x number of years?

a)

$f\left(x\right)=7000\left(0.6\right)^x$

b)

$f\left(x\right)=7000\left(0.4\right)^x$

c)

$f\left(x\right)=7000\left(0.06\right)^x$

d)

$f\left(x\right)=7000\left(0.94\right)^x$

29.

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

30.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^.08

b)

^1.08

c)

.92

d)

8

31.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

32.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

33.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

34.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

35.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

36.

Find the slope:

a)

3/4

b)

4/3

c)

-3/4

d)

-4/3

37.

What is the zero(s) for the graph shown?

a)

-2

b)

-2 and 4

c)

4

d)

2

38.

The graph of f is shown. What are its zeros?

a)

-1 and 3

b)

0 and 1.5

c)

2

d)

-3 and 1

39.

Which graph represents a function?

a)

b)

c)

d)

40.

$h\left(x\right)=x^2-2x+4$

Find $h\left(3\right)$

(a)

41.

Which graph best represents $f\left(x\right)=2\left(5\right)^x$ ?

a)

b)

c)

d)

42.

Which graph could match the equation below?

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

a)

b)

c)

d)

43.

Which equation has a vertex of (4, 2)?

a)

$y=\left(x+2\right)^2-4$

b)

$y=\left(x-2\right)^2+4$

c)

$y=\left(x-4\right)^2+2$

d)

$y=\left(x+4\right)^2-2$

44.

Which equation is graphed above?

a)

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

b)

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

c)

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

d)

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

45.

Which equations matches the graph above?

a)

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

b)

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

c)

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

d)

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

46.

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

Choose the correct graph of the equation.

a)

b)

c)

d)

47.

What is the vertex of the following equation? $f\left(x\right)=-\frac{1}{2}\left(x-5\right)^2+6$

a)

$\left(-5,-6\right)$

b)

$\left(-5,6\right)$

c)

$\left(5,-6\right)$

d)

$\left(5,6\right)$

48.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

y intercept

49.

Does this graph show a maximum or a minimum?

a)

Maximum

b)

Minimum

50.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

51.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

52.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

53.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

54.

Use the given function or the graph to find the average rate of change

a)

3

b)

-3

c)

3/2

d)

-1/3

55.

Use the given function or the graph to find the average rate of change

a)

5

b)

-1/5

c)

-5

d)

15

56.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

57.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

58.

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

a)

-3

b)

-1

c)

1

d)

3

59.

What is the RANGE of the function?

a)

All real numbers

b)

y ≤ 4

c)

y < 4

d)

0 ≤ y ≤ 4

60.

What is the DOMAIN of the function?

a)

All real numbers

b)

x ≤ 4

c)

x < 4

d)

0 ≤ x ≤ 4

61.

How many pieces is this Piecewise Function composed of?

a)

1

b)

2

c)

3

d)

4

62.

What is the value of f(0)?

a)

-2

b)

2

c)

4

d)

0

63.

Evaluate f(-5)

a)

0

b)

2

c)

5

d)

-4

64.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

65.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

66.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

67.

Evaluate f(-3)=

a)

-1

b)

-7

c)

4

d)

5

68.

Evaluate f(3)=

a)

-1

b)

-7

c)

4

d)

5

69.

Find the value of $f\left(-8\right)$ .

a)

$21$

b)

$-8$

c)

$0$

d)

$9$

70.

What is g(4) if:

a)

-17

b)

-13

c)

13

d)

-5

71.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

72.

Which piecewise function matches this graph?

a)

b)

c)

d)

73.

Match the graph with the correct equation.

a)

b)

c)

d)

74.

Match the graph with the correct equation.

a)

b)

c)

d)

75.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

76.

(x+10)(x-10)

a)

x² - 100

b)

x² + 100

c)

x² + 20x - 100

d)

x² -20x + 100

77.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

78.

(4a + 2)(6a² − a + 2)

a)

24a³ + 16a² + 6a + 4

b)

24a³ + 8a² + 10a + 4

c)

24a³ + 8a² + 6a + 4

d)

24a³ - 8a² - 6a + 4

79.

Which system of equations represents lines f and g?

a)

y = 1.75x + 3.5

y = -4x - 8

b)

y = 1.75x + 3.5

y = -4x - 2

c)

y = 3.5x + 1.75

y = -4x - 8

d)

y = 3.5x + 1.75

y = -4x - 2

80.

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

a)

y = -x - 4

y = 2x - 2

b)

y = -x + 4

y = 2x - 4

c)

y = x - 4

y = -2x - 2

d)

y = x + 4

y = -2x - 4

81.

Choose two equations that make up the system represented by the graph.

a)

y=6−2.5x

b)

y=2.5x+6

c)

y=6−3x

d)

y=0.8x

82.

What is the solution to the system of equations below?

2x+y=7

3x+2y=16

a)

(2,5)

b)

(2,11)

c)

(-2,-11)

d)

(-2,11)

83.

What are the solutions to the system of equations below?

7x-5y=38

2x+10y=-12

a)

x = 4 and y = -2

b)

x = 4 and y = 2

c)

x = -4 and y = 2

d)

x = -4 and y = -2

84.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

85.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

86.

When 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

87.

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

88.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

89.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(g\left(x\right)\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-6x-5$

d)

$5x+7$

90.

$Find\ f\left(g\left(8\right)\right)$

a)

8

b)

1

c)

29

d)

22

91.

Given f and g in the graph,

what is f(g(2)) ?

a)

3

b)

8

c)

1

d)

4

92.

f(g(5)) =

(a)

93.

$Given\ f\left(x\right)\ =\ x^2\ +\ 4\ and\ g\left(x\right)\ =\ x+\ 5\ find\ f\circ g\left(x\right)$

a)

$x^2\ +\ 29$

b)

$x^{2\ }+\ 10x\ +29$

c)

$x^{2\ }+\ 9$

d)

$x\ +\ 9$

94.

Describe the transformation in each function as it relates to the graph of $f\left(x\right)=x.$

a)

stretched horizontally

reflected across y-axis

b)

compressed vertically

translated right

c)

stretched vertically

reflected across x-axis

d)

compressed vertically

translated left

e)

stretched vertically

translated up

95.

Describe the transformation in each function as it relates to the graph of $f\left(x\right)=x.$

a)

stretched horizontally

reflected across y-axis

b)

compressed vertically

translated right

c)

stretched vertically

reflected across x-axis

d)

compressed vertically

translated left

e)

stretched vertically

translated up

96.

Describe the transformation in each function as it relates to the graph of $f\left(x\right)=x.$

a)

stretched horizontally

reflected across y-axis

b)

compressed vertically

translated right

c)

stretched vertically

reflected across x-axis

d)

compressed vertically

translated left

e)

stretched vertically

translated up

97.

Describe the transformation in each function as it relates to the graph of $f\left(x\right)=x.$

a)

stretched horizontally

reflected across y-axis

b)

compressed vertically

translated right

c)

stretched vertically

reflected across x-axis

d)

compressed vertically

translated left

e)

stretched vertically

translated up

98.

Describe the transformation: (click on two answers)

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

a)

Reflection over the x-axis

b)

Reflection over the y-axis

c)

Shift 7 units up

d)

Shift 7 units down

99.

If the blue graph is the parent function, what is the equation of the red (transformed) function?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

100.

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?

a)

A. g(x)=3x²

b)

B. g(x)=-3x²

c)

C. g(x) = x² - 3

d)

D. g(x) = (x-3)²

101.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

f(x) = |x - 2| - 3

102.

a)

$y=\ \left|x\right|\ +\ 3$

b)

$y=\ \left|x\right|-\ 3$

c)

$y=\ \left|x+3\right|\$

d)

$y=\ \left|x-3\right|$

103.

What is the vertex of the function?

$f\left(x\right)=-2\left|x+3\right|-2$

a)

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

b)

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

c)

$\left(3,2\right)$

d)

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

104.

Which function is graphed?

a)

$f\left(x\right)=2\left|x+2\right|-4$

b)

$f\left(x\right)=2\left|x-4\right|+2$

c)

$f\left(x\right)=\left|x+2\right|-4$

d)

$f\left(x\right)=\left|x-4\right|+2$

105.

Which function is graphed?

a)

$f\left(x\right)=-3\left|x-1\right|+4$

b)

$f\left(x\right)=-\left|x-1\right|+4$

c)

$f\left(x\right)=-3\left|x+1\right|+4$

d)

$f\left(x\right)=-\left|x+1\right|+4$

106.

Which absolute value function shows the following transformations?

Opening downward

Horizontal shift right 2 units

Vertical shift down 7 units

a)

$y=-\left|x+2\right|-7$

b)

$y=\left|x-2\right|-7$

c)

$y=-\left|x-2\right|-7$

d)

$y=-\left|x-2\right|+7$

107.

Describe the transformations compared to the parent function f(x) = |x|.

f(x) = 3|x + 4|- 5

a)

Wider, shifted right 4 units, and down 5 units

b)

Wider, shifted right 4 units, and up 5 units

c)

More narrow, shifted left 4 units, and down 5 units

d)

More narrow, shifted right 4 units, and down 5 units

108.

What is the vertex?

a)

(3, 1)

b)

(0, 1)

c)

(1, 3)

d)

No vertex

109.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

110.

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

111.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

112.

Find the inverse of $f\left(x\right)=3x+2$

a)

$f^{-1}\left(x\right)=\frac{x-2}{3}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{2}$

c)

$f^{-1}\left(x\right)=\frac{3x}{2}$

d)

$f^{-1}\left(x\right)=\frac{2+x}{3}$

113.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

114.

Find the inverse of $f\left(x\right)=4x-9$

a)

$f^{-1}\left(x\right)=\frac{1}{4}x+\frac{9}{4}$

b)

$f^{-1}\left(x\right)=-\frac{1}{4}x+\frac{9}{4}$

c)

$f^{-1}\left(x\right)=\frac{1}{4}x-\frac{9}{4}$

d)

$f^{-1}\left(x\right)=4x+36$

115.

a)

b)

c)

d)

116.

Find the inverse of $f\left(x\right)=x^2-5$ ,

a)

$f^{-1}\left(x\right)=\sqrt[]{x+5}$

b)

$f^{-1}\left(x\right)=\sqrt[]{x-5}$

c)

$f^{-1}\left(x\right)=\sqrt[]{x}+5$

d)

$f^{-1}\left(x\right)=x^2-5$

117.

Determine whether the pair of functions are inverse functions.

$f\left(x\right)=\sqrt[3]{x-1}$

$g\left(x\right)=x^3+1$

a)

Inverse Functions

b)

Not Inverse Functions

118.

Determine whether the pair of functions are inverse functions.

$f\left(x\right)=\frac{-x-4}{7}$

$g\left(x\right)=-7x-4$

a)

Inverse Functions

b)

Not Inverse Functions

119.

Find the inverse function

a)

b)

c)

d)

120.

Find the inverse function

a)

b)

c)

d)

121.

Find the inverse function

a)

b)

c)

d)

122.

Find the inverse function

a)

b)

c)

d)

123.

Hint: Pay extra attention to what you are distributing

a)

x = - 6

b)

x = - 3

c)

x = 6

d)

x = 3

124.

Solve:

7(-3x + 10) = 5(-4x + 15)

a)

x = 7

b)

x = -5

c)

x = 5

d)

x = -7

125.

Solve the inequality and graph its solution.

a)

b)

c)

d)

126.

Solve the inequality: 2(x + 3) + 4 > 3(x - 2) - 5

a)

x < -21

b)

x < 21

c)

x > -21

d)

x > 21

127.

Solve the following equation for y

Ax + By = C

a)

y = $\frac{\left(Ax\ +\ C\right)}{B}$

b)

y = $\frac{\left(Bx\ +\ C\right)}{A}$

c)

y = $\frac{\left(C-Bx\right)}{A}$

d)

y = $\frac{\left(C\ -Ax\right)}{B}$

128.

Solve -2 = 4r + s for s.

a)

s = -2 + 4r

b)

s = 2 - 4r

c)

s = -2 - 4r

d)

s = 2 + 4r

129.

Solve for w undefined

a)

$w=\frac{2P}{l}$

b)

$w=\frac{2l+P}{2}$

c)

$w=\frac{l+P}{2}$

d)

$w=\frac{P-2l}{2}$

130.

Solve for m $y=mx+b$

a)

$m=x+b-y$

b)

$m=y-b-x$

c)

$m=\frac{x-b}{y}$

d)

$m=\frac{y-b}{x}$

Final Exam Review (Algebra 2)

Total questions: 130

Worksheet time: 11hrs 46mins

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