Free Printable Remediation 2025

1.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.5 feet

c)

13 feet

d)

11.6 feet

2.

A 10-foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which of the following is closest to the distance from the top of the ladder to the base of the wall?

a)

9ft

b)

11ft

c)

6ft

d)

14ft

3.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

75 cm²

b)

105 cm²

c)

135 cm²

d)

30 cm²

4.

a)

A.

b)

B.

c)

C.

5.

List in order from greatest to least.
56%, $\frac{\sqrt{3}}{5},$ $\frac{\pi}{10},$ 1.07

a)

56%, 1.07, $\frac{\sqrt{3}}{5}$ $\frac{\pi}{10}$

b)

56%, $\frac{\pi}{10}\$ , 1.07 ,

c)

$\frac{\pi}{10}$ , $\frac{\sqrt{3}}{5}$ 56%, 1.07

d)

1.07, 56%, $\frac{\sqrt{3}}{5},$ $\frac{\pi}{10}$

6.

What is the length of the hypotenuse in the triangle shown?

a)

3

b)

4

c)

5

d)

8

7.

a)

7 ft

b)

5 ft

c)

3 ft

d)

2 ft

8.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

9.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

10.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

11.

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

12.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

13.

You have a globe that has a radius of 11 inches. Find the volume of your globe.

a)

523 in³

b)

16,717 in³

c)

5,575 in³

d)

7,235 in³

14.

A cylinder shaped jar has a radius of 2 cm and a height of 6 cm. What’s the volume of the jar?

a)

301.44 cubic cm

b)

125.93 cubic cm

c)

75.36 cubic cm

d)

67.89 cubic cm

15.

Michael has a very large soup pot shaped like a cylinder that has a height of 15 inches and a radius of 6 inches. How much soup can Michael’s soup pot hold?

a)

4239 in³

b)

423.9 in³

c)

1695.6 in³

d)

1695.6 in²

16.

Choir is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches.

Which equation can be used to find the volume of the container?

a)

V = π(9)

b)

V = π(4.5)²(32)

c)

V = π(9)²(32)

d)

V = π(4.5)(32)

17.

Emily needs to make party hats in the shape of a cone. She wants the hat to have a radius of 6 inches and a height of 15 inches. What is the volume of the party hat?

a)

565.2

b)

94.2

c)

2260.8

d)

188.4

18.

Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

a)

21 cubic inches

b)

63 cubic inches

c)

66 cubic inches

d)

198 cubic inches

19.

Sarah needs a PVC cylinder pipe with a diameter of 10 inches and a height of 2 inches, how much material is needed to make 5 pipes?

a)

62.8 inches ²

b)

219.8 inches ²

c)

785 inches ²

d)

422 inches ²

20.

What kind of Function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

21.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

22.

Is the relation a function?
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

a)

Yes

b)

No

23.

Is this table a function or not a function?

a)

Function

b)

Not a Function

24.

Is this a function? Explain.

a)

Yes; it passes the horizontal line test.

b)

No; it is not a straight line.

c)

Yes; it passes the vertical line test.

d)

No; there is a line connecting the dots.

25.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

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

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

26.

Is this a function?

a)

Yes

b)

No

c)

I'm Confused

d)

May I phone a friend?

27.

Which set of values is not a function?

a)

(9,5) (10,5) (4,-5) (8,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (-5, -7) (1, 4)

28.

Vertical or horizontal?

x=4

a)

vertical

b)

horizontal

c)

neither

29.

Vertical or horizontal?

y=-3

a)

vertical

b)

horizontal

c)

neither

30.

What variable typically represents the domain?

a)

x

b)

y

31.

What variable typically represents the range?

a)

x

b)

y

32.

What is the domain?

a)

{0, 1, 2, 15}

b)

(0, 1, 2, 3}

c)

{3, 7, 11, 15}

d)

{3, 7, 11, 3}

33.

What is the range?

a)

{0, 1, 2, 15}

b)

(0, 1, 2, 3}

c)

{3, 7, 11, 15}

d)

{3, 7, 11, 3}

34.

What is the domain?

a)

{5, 10, 15}

b)

{(5,2), (5,4), (10,6), (15,8)}

c)

{2, 4, 6, 8}

d)

{5, 2, 4, 10, 15}

35.

Is the function represented by the table linear or nonlinear?

a)

Linear

b)

Nonlinear

36.

Is the function represented by the table linear or nonlinear?

a)

linear

b)

nonlinear

37.

List the types of intervals that the graph demonstrates in order.

a)

decreasing, constant, increasing, constant

b)

increasing, decreasing, constant

c)

increasing, constant, increasing, constant

d)

increasing, constant, decreasing, constant

38.

When is this function increasing?

a)

Between −2.5 and 2.5

b)

Between 0 and 5

c)

Between 0 and 55

d)

Between −5 and 0

39.

Find the interval(s) where the function is decreasing on the graph shown. Select all that apply.

a)

between -6 and -4

b)

between -4 and -2

c)

between -2 and 2

d)

between 2 and 5

e)

between 5 and 6

40.

On what intervals is this function linear? Select all that apply.

a)

Between -4 and -2

b)

Between -2 and 0

c)

Between 0 and 4

d)

Between -4 and 0

41.

On what intervals is this function nonlinear? Select all that apply.

a)

Between -4 and -2

b)

Between -2 and 0

c)

Between 0 and 4

d)

Between -4 and 4

42.

Is relation shown a function?

a)

YES

b)

NO

43.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

44.

Which graph represents a function?

a)

b)

c)

d)

45.

Which image is NOT the graph of a function?

a)

b)

c)

d)

46.

Which graph represents a linear function?

a)

b)

c)

d)

47.

Which of the following is nonlinear?

a)

$y=3x-4$

b)

$y=6$

c)

$y=2x^2+4$

d)

$y=x-\frac{3}{8}$

48.

All of these vocabulary words represent the X-value except _____________.

a)

Output

b)

Input

c)

Independent Variable

d)

Domain

49.

All of these vocabulary words represent the Y-value except _____________.

a)

Output

b)

Domain

c)

Dependent Variable

d)

Range

50.

The _______________________ is a visual way to determine if a curve is a graph of a function or not.

a)

Independent Variable

b)

Vertical Line Test

c)

Input

d)

Output

51.

Would this graph pass the vertical line test to be a function?

a)

Yes

b)

No

52.

Slope is another word for:

a)

Initial Value

b)

Rate of Change

c)

Change in Y's

d)

Y-intercept

53.

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)

54.

What is the slope of the equation?
y = -3x + 4

a)

-3

b)

4

c)

-4

d)

3

55.

Which statement BEST explains why the graphed relation is NOT a function?

a)

The graphed relation is not a line.

b)

There are infinitely many points on the graph.

c)

The domain of the graph does not include all real numbers.

d)

There are points on the graph with the same x-coordinate but different y-coordinates.

56.

Which relation below is a function?

a)

b)

c)

d)

57.

In which set of ordered pairs, (x, y), is y NOT a function of x?

a)

{(4,3), (3, 4)}

b)

{(4, 3), (7, 3)}

c)

{(7, 4), (4, 7), (4, 3)}

d)

{(7, 7), (4, 4), (3, 3)}

58.

The ordered pairs (x,y) define the relation Q.

Q: {(4, 5), (3, 2), (5, 5), (2, -3)}

Is Q a function?

a)

Yes, because there is exactly one x-value for every y-value.

b)

Yes, because there is exactly one y-value for every x-value.

c)

No, because there is more than one x-value for some y-values.

d)

No, because there is more than one y-value for every x-value.

59.

Which relation below is NOT a function?

a)

b)

c)

d)

60.

2x + 3(5x - 7) = 47

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

61.

-49 - x = -8x + 70

a)

15

b)

17

c)

14

d)

19

62.

What is the final answer to

4(x - 2) = -3 + 5x

a)

2

b)

-10

c)

-5

d)

-3

63.

Determine the number of solutions for this problem:
$5x+3\left(2-x\right)=10x+9-8x$

a)

no solution

b)

one solution

c)

infinite solutions

64.

Determine the number of solutions to this problem:
$5\left(3x+8\right)=10x+40$

a)

no solution

b)

one solution

c)

infinite solutions

65.

Determine the number of solutions to the problem:
$-4x+12+10x=6\left(x+2\right)$

a)

no solution

b)

one solution

c)

infinite solutions

66.

Solve:
2(4x-3) - 8 = 4 + 2x

a)

x = 5/3

b)

x = 3

c)

x = 1

d)

x = 2

67.

Solve for x:

4(1 - x) + 3x = -2(x + 1)

a)

x = -6

b)

x = 6

c)

x = 3

68.

a)

-2

b)

-4

c)

2

d)

4

69.

a)

0

b)

1

c)

2

d)

-2

70.

a)

-4

b)

-2

c)

-6

d)

-8

71.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

72.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

73.

x + 8 < 3 or - 8x < -40

a)

x > -5 or x < 5

b)

x < -5 and x > 5

c)

x < -5 or x > 5

d)

x > -5 and x < 5

74.

Solve:

3x + 2 < -7 or -4x + 5 < 1

a)

All real numbers

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

75.

Give the solution set for: -13<2x+5<15

a)

-9>x>5

b)

-9<x<5

c)

-4<x<5

d)

-4>x>5

76.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

77.

2x − x + 7 = x + 3 + 4

a)

No Solutions

b)

Infinitely Many Solutions

c)

One Solution

78.

4(2x + 1) = 5x + 3x + 9

a)

One Solution

b)

Infinitely Many Solutions

c)

No Solutions

79.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 8 = 3(x - 4) + 1

a)

one

b)

no solutions

c)

infinite solutions

80.

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 7 = 3(x - 3) + 2

a)

one

b)

no solutions

c)

infinite solutions

81.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

82.

-2(3m + 6) = -3(4 +2m)

a)

No Solution

b)

One Solution

c)

Infinite Solution

83.

What type of slope is shown?

a)

positive

b)

negative

c)

zero

d)

undefined

84.

What is the y-intercept of this graph?

a)

$b=4$

b)

$b=-4$

c)

$b=-2$

d)

$b=2$

85.

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

a)

A

b)

B

c)

C

d)

D

86.

Identify the correct slope for the table shown.

a)

$m=10$

b)

$m=5$

c)

$m=\frac{5}{2}$

d)

$m=2$

87.

Identify the correct y-intercept shown on this table.

a)

$b=5$

b)

$b=0$

c)

$b=10$

d)

$b=2$

88.

Based on the table, write the equation in slope-intercept form.

a)

$y=5x+5$

b)

$y=\frac{1}{5}x+5$

c)

$y=15x+5$

d)

$y=10x+5$

89.

What is the y-intercept?

a)

7

b)

0

c)

2

d)

1

90.

Jackson started with $800 in his savings account, but has to pay $30 a month for his electricity bill. Write an equation that relates his savings, y, to the amount of months, x.

a)

$y=-30x+800$

b)

$y=30x-800$

c)

$y=-30x$

d)

$y=12x-30$

91.

Stephanie owes her mom $80 for a recent trip to the mall. She plan to pay back $15 a month until it is all paid back. Write an equation in slope-intercept form that relates the amount she owes, y, to the amount of months, x.

a)

$y=15x-80$

b)

$y=15x+80$

c)

$y=-15x+80$

d)

$y=-15x-80$

92.

Find the slope of the line that passes through: $\left(-3,-4\right)\ and\ \left(7,6\right)$

a)

0

b)

Undefined

c)

-1

d)

1

93.

Find the slope of the line that passes through: $\left(6,7\right)\ and\ \left(4,2\right)$ .

a)

$\frac{2}{5}$

b)

$\frac{-5}{2}$

c)

$\frac{5}{2}$

d)

$\frac{-1}{2}$

94.

The graph shows a linear relationship between x

and y. x represents the number of comic books Priya buys at the store, all at the same price, and y represents the amount of money (in dollars) Priya has after buying the comic books.

How much money will she have after she buys 3 books?

a)

12

b)

3

c)

8

d)

24

95.

A container of fuel dispenses fuel at the rate of 5 gallons per second. If y represents the amount of fuel remaining in the container, and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship. In the coordinate plane, will the slope of the line representing that relationship have a positive, negative, or zero slope?

a)

positive

b)

negative

c)

zero

96.

Which situation could NOT represent a proportional relationship?

a)

The number of gallons of water in x barrels with 42 gallons of water in each barrel.

b)

The amount an employee who makes $8.50 per hour earns in h hours.

c)

The weight in x weeks of a puppy that gains 2 pounds per week if its starting weight is 8 pounds.

d)

The cost of purchasing p pounds of bananas for $0.55 per pound.

97.

Mr. Leonard is renting a car for one day. The table below shows the total amount he will be charged for the car based on the number of miles he drives.

What equation best represents c, the number of dollars Mr. Leonard should be charged for driving m miles?

a)

$c=0.10m+30$

b)

$c=30m+0.10$

c)

$c=0.50m+30$

d)

$c=30m+0.50$

98.

Emily sells greeting card. The graph models the linear relationship between the number of boxes of cards she sells and her profit.

What is the cost per box of greeting cards?

(a)

99.

What is an example of an irrational number?

a)

-2/3

b)

.75575557654..

c)

23

d)

0

100.

A repeating decimal or decimal that terminates is called a

a)

Natural Number

b)

Irrational Number

c)

Rational Number

d)

Whole Number

101.

The square root of 5 is between what two integers?

a)

4 and 5

b)

2 and 3

c)

3 and 4

d)

9 and 10

102.

Which list of numbers is in order from least to greatest?

a)

A √23, 5, 6, 43%

b)

B 5, √23, 6, 43%

c)

C 43%, 5, √23, 6

d)

D 43%, √23, 5, 6

103.

π or PI is classified as which?

a)

Rational

b)

Irrational

c)

Rational, Real

d)

Irrational, Real

104.

√121

a)

12

b)

10

c)

11

d)

3

105.

numbers that are non-terminating and non-repeating decimals [example: π]

a)

Rational Numbers

b)

Decimal Expansion

c)

Irrational Numbers

d)

Radical

106.

Solve 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

107.

3⁻⁴

a)

1 ⁄ 81

b)

-81

c)

81

d)

1 ⁄ 12

108.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

109.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

110.

Are these two equivalent: 2² = (-2)²

a)

Yes

b)

No

111.

$m\cdot m^3$

a)

$m^2$

b)

$m^3$

c)

2m

d)

$m^4$

112.

Find the value of x.

$\left(3^x\right)^3=\ 3^{15}$

a)

x = 5

b)

x = 12

c)

x = 45

113.

Which expression is equivalent (equal) to

a)

6³

b)

6⁴

c)

6²

d)

6⁶

114.

$\frac{8^5}{8^2}$

a)

$8^3$

b)

$8^7$

c)

$8^{10}$

115.

$\frac{10^{24}}{10^2}$

a)

$10^{22}$

b)

$10^{26}$

c)

$10^{48}$

116.

$\frac{\left(4^7\cdot4^3\right)^4}{4^5}$

a)

$4^9$

b)

$4^8$

c)

$4^{35}$

d)

$4^{14}$

117.

Simplify using exponent properties: (b⁴)⁵

a)

b²⁰

b)

b¹

c)

1

d)

b⁹

118.

Simplify using exponent properties: x⁵/x^-2

a)

1

b)

x¹⁰

c)

x⁷

d)

x³

119.

Simplify using exponent properties: b⁰

a)

???

b)

b²

c)

b

d)

1

120.

Which number is between 7 and 8?

a)

√7

b)

√42

c)

√59

d)

√68

121.

Put in order of least to greatest.
√5, 3, 2½, √8

a)

3, 2½, √8, √5

b)

2½, 3, √5, √8

c)

√5, 3, 2½, √8

d)

√5, 2½, √8, 3

122.

What is the answer to the problem in the picture?

a)

3/4

b)

4/5

c)

5/6

d)

6/7

123.

between which if these does √27 lay on a number line

a)

5 and 6

b)

6 and 7

c)

4 and 5

d)

8 and 9

124.

Includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

125.

Identify the rational numbers.

a)

$\sqrt{4}$

b)

$\pi$

c)

$3.5$

d)

$\sqrt{2}$

e)

$\frac{2}{3}$

126.

Which of the following numbers is irrational?

a)

$\sqrt{50}$

b)

$\sqrt{36}$

c)

$\sqrt{169}$

d)

$\sqrt{225}$

127.

Select ALL numbers that are irrational.

a)

10

b)

-21

c)

$\pi$

d)

$\frac{10}{2}$

e)

$\sqrt{10}$

128.

Select ALL numbers that are rational.

a)

55

b)

$\sqrt{289}$

c)

$\sqrt{6}$

d)

$\pi$

e)

$6\frac{7}{9}$

129.

Is this is a function or not a function?

a)

Function

b)

Not a Function

Remediation 2025

Total questions: 129

Worksheet time: 11hrs 41mins

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