Free Printable Algebra 2 Final Review

1.

What is the best classification for this number? -4

a)

natural

b)

whole

c)

integer

d)

rational

2.

What is the best classification for this number?
π

a)

integer

b)

rational

c)

irrational

d)

imaginary

3.

What is the best classification for this number? .78787878...

a)

integer

b)

rational

c)

irrational

d)

whole

4.

What is the best classification for this number? 10

a)

natural

b)

whole

c)

integer

d)

rational

5.

What is the best classification for this number? 0

a)

natural

b)

whole

c)

integer

d)

rational

6.

According to PEMDAS which part of an algebraic expression to solve first?

a)

addition from left to right

b)

The part of the expression in parentheses or brackets

c)

Parts of the expression with powers

d)

multiplication from left to right

e)

division from left to right

7.

According to PEMDAS which part of an algebraic expression to solve second?

a)

addition from left to right

b)

The part of the expression in parentheses or brackets

c)

Parts of the expression with powers

d)

multiplication from left to right

e)

division from left to right

8.

According to PEMDAS which part of an algebraic expression to solve third?

a)

addition from left to right

b)

The part of the expression in parentheses or brackets

c)

Parts of the expression with powers

d)

multiplication from left to right

e)

division from left to right

9.

According to PEMDAS which part of an algebraic expression to solve fourth?

a)

addition from left to right

b)

subtraction from left to right

c)

Parts of the expression with powers

d)

multiplication from left to right

e)

division from left to right

10.

According to PEMDAS which part of an algebraic expression to solve fifth?

a)

addition from left to right

b)

subtraction from left to right

c)

Parts of the expression with powers

d)

multiplication from left to right

e)

division from left to right

11.

Solve for x:

$-6x+23+2x=15$

a)

$x=2$

b)

$x=3$

c)

$x=4$

d)

$x=5$

12.

Solve for x:

$-4\left(2x+6\right)-12=4$

a)

$x=-5$

b)

$x=5$

c)

$x=-2$

d)

$x=2$

13.

Solve for y:

$2\left(y-4\right)=-4\left(y+8\right)$

a)

$y=4$

b)

$y=-4$

c)

No Solution

d)

Infinitely Many Solutions

14.

Solve for x:

$5\left(1+x\right)=5x+5$

a)

$x=1$

b)

$x=0$

c)

No Solution

d)

Infinitely Many Solutions

15.

Solve for n:

$3\left(n+4\right)=\frac{1}{2}\left(6n+4\right)$

a)

$n=1$

b)

$n=-1$

c)

No Solution

d)

Infinitely Many Solutions

16.

Solve for x:

$-6x+23+2x=15$

a)

$x=2$

b)

$x=3$

c)

$x=4$

d)

$x=5$

17.

Solve for x:

$-4\left(2x+6\right)-12=4$

a)

$x=-5$

b)

$x=5$

c)

$x=-2$

d)

$x=2$

18.

Solve for y:

$2\left(y-4\right)=-4\left(y+8\right)$

a)

$y=4$

b)

$y=-4$

c)

No Solution

d)

Infinitely Many Solutions

19.

Solve for x:

$5\left(1+x\right)=5x+5$

a)

$x=1$

b)

$x=0$

c)

No Solution

d)

Infinitely Many Solutions

20.

Solve for n:

$3\left(n+4\right)=\frac{1}{2}\left(6n+4\right)$

a)

$n=1$

b)

$n=-1$

c)

No Solution

d)

Infinitely Many Solutions

21.

| x + 3 | ≤ 2

a)

No Solution

b)

All Real Numbers

c)

-5 ≤ x ≤ -1

d)

1 ≤ x ≤ 5

22.

| x | ≤ 3.5

a)

No Solution

b)

All Real Numbers

c)

-3.5 ≤ x ≤ 3.5

d)

x ≤ -3.5 or x ≥ 3.5

23.

| 3c - 5 | < -2

a)

No Solution

b)

All Real Numbers

c)

1 < c < ⁷/₃

d)

c < 1 or c > ⁷/₃

24.

| 2w - 1 | < 11

a)

No Solution

b)

All Real Numbers

c)

-5 < w < 6

d)

-6 < w < 5

25.

| x + 1 | ≥ 3

a)

No Solution

b)

All Real Numbers

c)

x ≤ -4 or x ≥ 2

d)

-4 ≤ x ≤ 2

26.

The sum of seven and x

a)

7-x

b)

x-7

c)

7x

d)

7+x

27.

Product
The answer in...

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

28.

Less

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

29.

A letter that represents a number.

a)

Addition

b)

Expression

c)

Algebra

d)

Variable

30.

Five less than y

a)

5+y

b)

5y

c)

5-y

d)

y-5

31.

Which statement below accurately represents the graph?

a)

$100 is earned for each hour worked

b)

$100 is earned for every 2 hours worked

c)

$500 is earned for every 8 hours worked

d)

$400 is earned for every 6 hours worked

32.

The equation below represents an elevator's height after an amount of seconds. Using this equation, what should the height of the elevator be after 14 seconds?
h(s) = -3.8s + 290

a)

80

b)

236.8

c)

-80

d)

72.6

33.

The following scatter plot shows Pam's training as she prepares to run a 6 mile race at the end of the month. Which of the following would be a reasonable approximation for the length of time it would take for her to run 6 miles?

a)

A. 50 min

b)

B. 80 min

c)

C. 45 min

d)

D. 60 min

34.

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

35.

1. Mrs. Collins made a scatterplot to show the relationship between the number of absences and a student’s final exam score. Based on this scatterplot, a student with 6 absences should get approximately what score on the final exam?

a)

65

b)

92

c)

70

d)

76

36.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

37.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

38.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?

a)

$394

b)

$440

c)

$472.80

d)

$512.20

39.

The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?

a)

34.04

b)

90.00

c)

1,285.35

d)

44,444.44

40.

The amount of money earned on a job is directly proportional to the number of hours worked. if $36 is earned for 8 hours of work, how much is earned for 30 hours of work?

a)

135

b)

6.667

c)

1080

41.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

42.

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

a)

Vertical Compression by a factor of 2

b)

Vertical Stretch by a factor of 2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

43.

Which transformation will occur if f(x) = x² is replaced with 1/2⋅f(x)?

a)

Vertical Compression by a factor of 1/2

b)

Vertical Stretch by a factor of 1/2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

44.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

a)

Translation left 2 units

b)

Narrower

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

45.

Describe the transformation of y = f(x) for the new function
y = f(x) + 5

a)

The graph of y = f(x) was shifted to the right 5 units.

b)

The graph of y = f(x) was shifted to the left 5 units.

c)

The graph of y = f(x) was shifted up 5 units.

d)

The graph of y = f(x) was shifted down 5 units.

46.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

47.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

48.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?

a)

$394

b)

$440

c)

$472.80

d)

$512.20

49.

The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?

a)

34.04

b)

90.00

c)

1,285.35

d)

44,444.44

50.

The amount of money earned on a job is directly proportional to the number of hours worked. if $36 is earned for 8 hours of work, how much is earned for 30 hours of work?

a)

135

b)

6.667

c)

1080

51.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

52.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

53.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

54.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

55.

What is the inequality graphed here?

a)

y ≤ | x + 3 | + 2

b)

y ≥ | x + 3 | + 2

c)

y > | x - 3 | + 2

d)

y < | x + 3 | - 2

56.

Solve by factoring:

x^2-11x+19=-5

a)

$x=4,6$

b)

$x=-8,\ -3$

c)

$x=3,8$

d)

$x=-12,-2$

57.

Solve by factoring:

-6c^2+19c+7=0

a)

$c=-\ \frac{1}{3},\ \frac{7}{2}$

b)

$c=\ \frac{1}{3},\ -\frac{7}{2}$

c)

$c=-\ 3,\ \frac{2}{7}$

d)

$c\ =\ -\ \frac{2}{7},\ 3$

58.

Solve by factoring:

6v^2-18v-18=6

a)

$c=-2,\ 2$

b)

$c=\ -4,\ 1$

c)

$c=24,\ -1$

d)

$c\ =\ -\ 1,\ 4$

59.

Solve by factoring:

7r^2-14r=-7

a)

$r=-1,\ 1$

b)

$r=\ -7,\ 1$

c)

$r\ =-1$

d)

$r\ =\ 1$

60.

Solve by factoring:

28y^2-63=0

a)

$y=-\ \frac{2}{3},\ \frac{2}{3}$

b)

$y=-\ \frac{3}{2},\ \frac{3}{2}$

c)

$y\ =\ -4,\ 9$

d)

$y\ =\ -4,\ -9$

61.

Solve using substitution.

a)

(1,3)

b)

(3,-1)

c)

(7,3)

62.

Solve using elimination.

a)

(4,5)

b)

(3,4)

c)

(5,4)

63.

Solve using the most efficient method.

a)

(2,1)

b)

(1,-2)

c)

(2,-1)

64.

Solve using your preferred method.

a)

(3,7)

b)

(5,7)

c)

(6,6)

65.

Solve using the most efficient method.

a)

(3,4)

b)

(4,12)

c)

(14,17)

66.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

67.

Factor: x² + 13x + 30

a)

(x + 3)(x + 10)

b)

(x + 5)(x + 6)

c)

(x + 2)(x + 15)

d)

(x + 1)(x + 30)

68.

Factor: x² + 13x - 48

a)

(x + 3)(x - 16)

b)

(x + 16)(x - 3)

c)

(x + 4)(x - 12)

d)

(x + 12)(x - 4)

69.

w³ + 3w

a)

3w(1)

b)

w(w² + 3)

c)

w³(w + 3)

70.

Factor:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

12c³(2c² - 0)

71.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

72.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

73.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

74.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

75.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

76.

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

a)

horizontal shift right 5 units

b)

horizontal shift left 5 units

c)

vertical shift up 5 units

d)

vertical shift down 5 units

77.

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

78.

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

a)

Vertical stretch by a factor of 5

b)

Vertical shrink/compress by a factor of 5

c)

Reflect over x-axis

d)

Vertical shift up 5 units

79.

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

a)

Vertical Stretch by a factor of 2 and vertical shift up 4 units

b)

Vertical Shrink/Compress by a factor 2 and vertical shift up 4

c)

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

d)

Vertical Shrink/Compress by a factor of 2 and horizontal shift right 4 units

80.

If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

81.

Which inequality is graphed on the given coordinate plane?

a)

y > x + 1

b)

y < x + 1

c)

y ≥ -x + 1

d)

y ≤ -x + 1

82.

Which inequality is graphed on the given coordinate plane?

a)

y < 2x +2

b)

y > ¹/₂x - 2

c)

y ≥ - 2x +2

d)

y ≥ 2x - 2

83.

This graph represents the inequality y < 3, TRUE or FALSE?

a)

TRUE

b)

FALSE

84.

The given graph represents the inequality x < -1, TRUE or FALSE?

a)

TRUE

b)

FALSE

85.

Which ordered pair(s) is a solution to the given system?

a)

(5, -5)

b)

(0,0)

c)

(-5, -2)

d)

(3,-3)

86.

Write the equation in standard form of the parabola passing through the points (1, -1), (2, -5), (3, -7).

a)

$y=x^2-7x+5$

b)

$y=-x^2+4x-7$

c)

$y=x^2-5x-2$

d)

$y=-x^2+3x-8$

87.

Write the equation in standard form of the parabola passing through the points (2, -8), (3, -8), (6, 4).

a)

$y=x^2-7x+5$

b)

$y=-x^2+4x-7$

c)

$y=x^2-5x-2$

d)

$y=-x^2+3x-8$

88.

Write the equation in standard form of the parabola passing through the points (1, -4), (2, -3), (3, -4).

a)

$y=x^2-7x+5$

b)

$y=-x^2+4x-7$

c)

$y=x^2-5x-2$

d)

$y=-x^2+3x-8$

89.

Write the equation in standard form of the parabola passing through the points (-1, -12), (2, -6), (4, -12).

a)

$y=x^2-7x+5$

b)

$y=-x^2+4x-7$

c)

$y=x^2-5x-2$

d)

$y=-x^2+3x-8$

90.

The table gives the number of pairs of skis sold at a sporting goods store in Durango, Colorado last year. Find a quadratic model for the data.

a)

$s=-2t^2+24t+10$

b)

$s=-2t^2-28t+108$

c)

$s=2t^2-28t+108$

d)

$s=24t^2+24t+10$

91.

1) Solve the system of linear equations.

a)

(-1, 5, 2)

b)

(1, -5, -2)

c)

no solution

d)

infinitely many solutions

92.

2) Solve the system of linear equations.

a)

(-1, 1, 2)

b)

(2, 1, -1)

c)

no solution

d)

infinitely many solutions

93.

3) Solve the system of linear equations.

a)

(3, 1, -5)

b)

(-3, 1, -1)

c)

no solution

d)

infinitely many solutions

94.

4) Solve the system of linear equations.

a)

(1, -3, -4)

b)

(-1, 3, -4)

c)

no solution

d)

infinitely many solutions

95.

5) Solve the system of linear equations.

a)

(1, 0, -1)

b)

(-2, 1, 0)

c)

no solution

d)

infinitely many solutions

96.

What is the solution to this system of equations?

a)

(-4,3)

b)

(5,-4)

c)

(-4, -5)

d)

(-4, 5)

97.

What is the solution to this system of equations?

a)

(1,0)

b)

(-3, -1)

c)

(-1,-3)

d)

(1,3)

98.

What is the solution to this system?

a)

(-2, -2)

b)

(2, -2)

c)

(-2,2)

d)

(2, 2)

99.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

100.

What is the solution?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

Algebra 2 Final Review

Total questions: 100

Worksheet time: 4hrs 34mins

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