Free Printable Fundamentals of Algebra Review

1.

If there is not a number in front of a variable, it is understood to be ....

a)

1

b)

0

c)

-1

d)

5

2.

How many terms are in this expression?

13t - 2x - 2² + 1/2y

a)

3 terms

b)

2 terms

c)

4 terms

d)

5 terms

3.

Evaluate: $\left(a^2+b\right)^2-ab$ if a = 4 and b = -2

a)

196

b)

316

c)

332

d)

204

4.

Evaluate when a = 15:
2(a - 5) + 2

a)

22

b)

27

c)

14

d)

7

5.

$9\left(-3\right)=-3\left(9\right)$

a)

Associative Property of Addition

b)

Commutative Property of Addition

c)

Associative Property of Multiplication

d)

Commutative Property of Multiplication

6.

What property allows this statement to be true?
(A + B) + C = A + ( B + C)

a)

Associative

b)

Commutative

c)

Distributive

d)

Identity

7.

Which property is demonstrated by 2 + 3 = 3 + 2

a)

Commutative Property of Multiplication

b)

Associative Property of Multiplication

c)

Commutative Property of Addition

d)

Associative Property of Addition

8.

Solve using distributive property of multiplication

5(a + 6)

a)

5a + 6

b)

a + 30

c)

5a + 30

d)

5a - 30

9.

Solve using distributive property of multiplication

$9\left(-5x+8\right)$

a)

$45x-72$

b)

$45x+72$

c)

$-45x-72$

d)

$-45x+72$

10.

Which expression is equivalent to:

10\left(y^2+2.45\right)

a)

$10y^2+2.45$

b)

$y^2+24.5$

c)

$10y^2+12.45$

d)

$10y^2+24.5$

11.

Choose the two expressions that are equivalent to:

2\left(6x+\frac{1}{2}\right)

a)

$12x+2$

b)

$12x+1$

c)

$6x+\frac{1}{2}+6x+\frac{1}{2}$

d)

$6x+1$

12.

What is the constant of this expression?

7x - 4y - 9

a)

7

b)

7x

c)

9

d)

-9

13.

Simplify:
3x - 2x - x

a)

6x

b)

x

c)

0

d)

5x

14.

Which expression is equivalent to:
d + d + d + 3 + 2

a)

3d + 5

b)

d + 5

c)

2d + 7

d)

3d + 4

15.

Simplify by combining like terms:
4x² - 3x + 11 -2x

a)

4x² - 5x + 11

b)

11x + 11

c)

16x² - 5x + 11

d)

10x²

16.

Simplify the following: $\left(a^3\right)^{7\ }$

a)

$a^{10}$

b)

$a^{21}$

c)

$a^4$

d)

$\frac{1}{a^4}$

17.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

18.

(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

19.

Find the product:
(n - 5)(n - 1)

a)

n² - 5n + 5

b)

n² - 6n + 5

c)

n²+ 5

d)

n² + 6n + 5

20.

"Subtracted from" and "less than" are terms that mean you need to "turn around" or "flip" the terms around.

a)

True

b)

False

21.

Match the clue word with the operation:
QUOTIENT

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

22.

Translate this phrase into an algebraic expression.

8 less than the product of 4 and a number

Use the variable m to represent the unknown number.

a)

8 − 4m

b)

8m − 4

c)

8m + 4

d)

4m − 8

23.

Which expression represents: "the product of 3 and x increased by 5"?

a)

5x - 3

b)

3 - 5x

c)

3x + 5

d)

3x(5)

24.

A _____________ is a symbol, usually a letter that stands for a number.

a)

coefficient

b)

algebraic expression

c)

variable

d)

term

25.

"Twice the quantity of" means you will use ____________ to write the expression.

a)

addition

b)

subtraction

c)

division

d)

parenthesis

26.

Determine whether the given value is a solution.

117 = 97 + n for n = 10

a)

yes

b)

no

27.

Mariah solved the following equation but did not get the correct answer. What step did she do incorrectly?
Step 1: -2(x - 4) - 6 = 12
Step 2: -2x - 8 - 6 = 12
Step 3: -2x -14 = 12
Step 4: -2x = 26
Step 5: x = -13

a)

Step 2 - she distributed incorrectly

b)

Step 3 - she combined like terms incorrectly

c)

Step 4 - she did not do the correct inverse operation

d)

Step 5 - she did not do the correct inverse operation

28.

Solve

a)

x = 1

b)

x = 10

c)

x = -1

d)

x = -10

29.

Isolate the variable by using __________ or opposite operations.

a)

intricate

b)

inverse

c)

similar

d)

the same

30.

To solve a - 4 = 35 you would ...

a)

subtract 4 from both sides of the equation.

b)

add 4 to both sides of the equation.

c)

add a to both sides of the equation.

d)

hope for the best.

31.

To solve x - 12 = 95 you would...

a)

add 12 to both sides of the equation.

b)

subtract 12 from both sides of the equation.

c)

add 95 to both sides of the equation.

d)

subtract 95 from both sides of the equation.

32.

Solve the following equation
18 = 3b

a)

15

b)

6

c)

21

d)

54

33.

Solve the following equation
c / 4 = 4

a)

1/4

b)

8

c)

1

d)

16

34.

Solve for x:
2x + 5 = 12

a)

7

b)

3

c)

3.5

d)

8.5

35.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

36.

Solve for x:
2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

37.

Which property justifies the work from Step 4 to Step 5?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Additive Inverse Property

d)

Substitution Property

38.

Which property justifies the work from Step 2 to Step 3?

a)

Addition Property of Equality

b)

Additive Inverse Property

c)

Identity Property of Addition

d)

Subtraction Property of Equality

39.

Graph 2x - y = 4

a)

A

b)

B

c)

C

d)

D

40.

How do you change

y-4=3(x+3) into slope-intercept form?

a)

y=23x-1/23

b)

y=3x+13

c)

y-7x=9

d)

y=13-3x

41.

Give the x-intercept

3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

42.

Given the following table, write the linear equation.

a)

y = 9x + 3

b)

y = 3x + 12

c)

y = 3x + 9

d)

y = 1x + 12

43.

s - 10 ≤ 1

a)

s ≤ 11

b)

s ≤ 9

c)

s ≥ 11

d)

s ≥ 9

44.

What inequality does the number line graph represent?

a)

$x\le-4$

b)

$x\ge-4$

c)

x < -4

d)

x < 4

45.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

46.

Solve the inequality.

$2\left(b\ -\ 8\right)\ >\ 12$

a)

b > 20

b)

b > 6

c)

b > 14

d)

b > 20

47.

Solve the inequality.

$-4d\ -\ 9\ \le\ 3$

a)

$d\ \le3$

b)

$d\ \le-3$

c)

$d\ \ge\ 3$

d)

$d\ \ge\ -3$

48.

Solve
-5m < 10

a)

m < -2

b)

m > -2

c)

m < -50

d)

m > -50

49.

A student must be at least 15 years old to obtain a driver’s permit. Let a represent the student's age.

a)

a > 15

b)

a < 15

c)

a ≤ 15

d)

a ≥ 15

e)

a = 15

50.

To order from the kid's menu a person must be no more than 12 years old. Let k represent the kid's age.

a)

k > 12

b)

k < 12

c)

k ≥ 12

d)

k ≤ 12

e)

k = 12

51.

a)

is greater than

b)

is less than

c)

is less than or equal to

d)

is greater than or equal to

52.

Write the following in interval notation.

x < 8

a)

(8, -∞)

b)

(-∞, 8]

c)

(-∞, 8)

53.

Can you use the symbols [ or ]
with infinity?

a)

Yes

b)

No

54.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

55.

Write this in interval notation.

$x>-9$

a)

$\left(-9,\ \infty\right)$

b)

$\left[-9,\ \infty\right]$

c)

$\left[-9.\ \infty\right)$

56.

Evaluate f(-2) if f(x) = x+3

a)

-1

b)

1

c)

5

d)

-5

57.

Given g(x) =
4x - 7, find g(-9).

a)

g(-9) = 29

b)

g(-9) = -43

58.

What is x if
f(x) = -2?

a)

4

b)

0

c)

3

d)

8

59.

For what value of t is H(t) = 4" ?

a)

0

b)

1

c)

2

d)

14

60.

At what point is the minimum of this graph?

a)

(4,1)

b)

(1,-4)

c)

(-1,0)

d)

(3,0)

61.

What is the relative max?

a)

(0, 36)

b)

(-2.55, -6.55), (2.55, -6.55)

c)

(-∞, ∞)

d)

None

62.

Identify where the function is decreasing.

a)

x < -4 , x > 1

b)

-4 < x < 1

c)

-6 < x < 7.5

d)

All Real Numbers

63.

When is this function increasing?

a)

−2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

−5 < x < 0

64.

Over what interval is the graph increasing?

a)

-2 < x < -1

b)

-1 < x < 2

c)

x > 4

d)

-4 < x < -2

65.

Find the zero(s) of the function.

a)

x = -3

b)

x = 1

c)

x = {-3, 1}

d)

y = 1

66.

Find the zero(s) of the function.

a)

x = 1

b)

x = -3

c)

x = {-1, 3}

d)

x = 2

67.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

68.

Find the zero(s) of the function.

a)

x = -3

b)

x = 3

c)

x = -12

d)

x = 12

69.

Find the zero(s) of the function.

a)

x = 10

b)

x = -10

c)

x = -8/5

d)

x = 8/5

70.

What is the equation for this table?

a)

y = -2x + 5

b)

y = 2x + 5

c)

y = 5x - 2

d)

y = 5x + 5

71.

Which equation best represents the relationship between x and y in the table shown?

a)

y= 5x+5

b)

y=1/5x+5

c)

y=15x+5

d)

y=10x+5

72.

Which equation matches the table?

a)

y = 3x + 9

b)

y = x + 9

c)

y = x + 3

d)

y = 12x - 3

73.

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

74.

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

75.

At what rate did the rain fall?

a)

2 cm per hour

b)

¹/₄ cm per hour

c)

¹/₂ cm per hour

d)

4 cm per hour

76.

What can be calculated from the slope of a distance vs. time graph?

a)

Acceleration

b)

Velocity

c)

Speed

d)

Motion

77.

What is the difference between average speed and instantaneous speed?

a)

Average speed and Instantaneous speed are the same

b)

Average speed is over time, Instantaneous speed is one instant

c)

Average speed is one instant, Instantaneous speed is over time

78.

What is the range of the mapping?

a)

{1, 2, 4}

b)

{0, 1, 2, 3}

c)

{0, 3}

d)

{1, 4}

79.

What is the domain of the relation shown in the table?

a)

{12}

b)

{6, 18}

c)

{3, 9, 15, 16}

d)

{13}

80.

What is the domain of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

81.

What is the Domain of this linear function?

a)

-6 ≤ x ≤ 6, real numbers

b)

0 ≤ x ≤ 7, integers

c)

2 ≤ x ≤ 7, real numbers

d)

No Solution

82.

What is the range of this function?

a)

All Real Numbers

b)

-1 ≤ x ≤ 1

c)

-1 ≤ f(x) ≤ 1

d)

1 ≥ x

83.

In the equation, y = mx + b, the letter b is the ___________.

a)

y-intercept

b)

x-intercept

c)

slope

d)

rate of change

84.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

85.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

86.

Bob has $150 in his savings account and saves $40 per month. Which function models his savings?

a)

y = 150 + 40

b)

y = 40x + 150

c)

y = 150x + 40

87.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

88.

What is the y-intercept in the equation x + 2y = 4

a)

(0, 0)

b)

(0, 2)

c)

(4, 0)

d)

(2, 0)

89.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

90.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

91.

What is the slope in the equation: y=4x+3

(a)

92.

Write the following equation in slope-intercept form:
4x - 3y = 12

(a)

93.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

(a)

94.

Name the x- and y-intercepts for the equation:
2x + y = 6

(a)

95.

Graphing:
Graph 2x - y = 4

a)

A

b)

B

c)

C

d)

D

96.

Solving Equations:
2(6b + 1) = 4(b - 5) -2

a)

b = - 2.75

b)

b = -7/8

c)

b = 3

d)

b = -3

97.

Writing Equations:
Given the following table, write the linear equation.

a)

y = 9x + 3

b)

y = 3x + 12

c)

y = 3x + 9

d)

y = 1x + 12

98.

Linear Modeling:
A local donut shop charged $6.50 for a dozen and provided a coupon in the newspaper for $1.50 off an order. Since the donut shop has gained popularity they have changed their coupon which now provides a discount of only half their original coupon's value. What is the equation that represents the value of a customer's order who uses the new coupon with their order?

a)

y = 6.50x - 0.75

b)

y = 6.50x + 0.75

c)

y = 6.50x - 1.50 - 0.75

d)

y = 5x - 0.75

99.

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

a)

c = 2.75b + 4

b)

c = 2.75b

c)

c = 4b- 2.75

d)

c = 2.75b - 4

100.

Wendy’s is currently hiring workers at $14 an hour. To increase the number of applicants, they are offering a $500 initial hiring bonus. Let x be the number of hours worked, and y be the total amount of money made. Write an equation that models this situation.

How much will you have made after working 30 hours?

(a)

Fundamentals of Algebra Review

Total questions: 100

Worksheet time: 2hrs 40mins

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