Free Printable 8th Grade Math 1st Semester Exam Study Guide December 2025

1.

Evaluate ±√144

a)

±13

b)

±12

c)

±14

d)

±15

2.

Evaluate ³√1000

a)

10

b)

8

c)

9

d)

12

3.

Express the fraction 5/8 as a decimal.

a)

0.625

b)

0.65

c)

0.25

d)

0.66...

4.

Express the fraction 6/9 as a decimal. Round to the nearest hundredth.

a)

0.67

b)

0.76

c)

0.65

d)

0.6

5.

Express the decimal number 0.75 as a fraction in simplest form.

a)

13/4

b)

1/3

c)

2/5

d)

3/4

6.

Write the decimal number 0.625 as a fraction in simplest form.

a)

1/2

b)

3/8

c)

5/8

d)

3/4

7.

Name the point on the number line associated with the following real number: √15

a)

A

b)

B

c)

C

d)

D

8.

Name the point on the number line associated with the following real number: ³√560

a)

A

b)

B

c)

C

d)

D

9.

Simplify using exponents: (−3) × (−3) × (−3)

a)

-133

b)

-27

c)

-33

d)

-9

10.

Simplify (Hint: product rule of exponents) $x^5·x^3$

a)

$x^9$

b)

$x^8$

c)

$x^2$

d)

$x^{15}$

11.

Simplify (Hint: product rule of exponents)

$2x^5\cdot3x^2$

a)

$6x^7$

b)

$x^7$

c)

$5x^7$

d)

$x^{12}$

12.

Simplify (Hint: quotient rule of exponents) $\frac{n^{20}}{n^{15}}$

a)

$n^{35}$

b)

$n^{11}$

c)

1

d)

$n^5$

13.

Simplify (Hint: quotient rule of exponents) $\frac{30y^{1500}}{6y^{500}}$

a)

$5y^{2000}$

b)

$24y^{1000}$

c)

$5y^{1000}$

d)

$36y^{1000}$

14.

Simplify (Hint: zero rule of exponents) $(b^5)^0$

a)

1

b)

0

c)

$b^5$

d)

5

15.

Simplify (Hint: power rule of exponents) $(3b^5)^2$

a)

9b

b)

$6b^7$

c)

$9b^{10}$

d)

9

16.

Simplify (Hint: negative rule of exponents) $b^{-7}$ Write your answer.

a)

$1/b^{7}$

b)

$b^{7}$

c)

$-b^{7}$

d)

$-1/b^{7}$

17.

Simplify (Hint: power & negative rule of exponents) $(x^6y^{10})^{-3}$

a)

$\frac{1}{x^{18}y^{30}}$

b)

$x^{18}y^{30}$

c)

$\frac{1}{x^{2}y^{7}}$

d)

$x^{-18}y^{-30}$

18.

Simplify: $\frac{x^{15}y^{80}}{x^5y^{30}}$

a)

$xy^5$

b)

$x^{10}y^{50}$

c)

$x^{5}y^{110}$

d)

$x^{10}y^{110}$

19.

Simplify: $\frac{3x^4y^8}{6x^2y^3}$

a)

$\frac{x^2y^5}{2}$

b)

$\frac{x^6y^5}{3}$

c)

$\frac{x^2y^3}{2}$

d)

$\frac{x^4y^8}{6}$

20.

Simplify: $\frac{((a^3)^2b^8)}{(a^2b^3)}$

a)

$a^5b^{11}$

b)

$a^5b^6$

c)

$a^4b^5$

d)

$a^2b^4$

21.

Simplify: $\frac{((x^{8})^3x^{4})}{(4x^{10})}$

a)

$x^{14}/4$

b)

$x^{24}/4x^{10}$

c)

$x^{28}/4x^{14}$

d)

$x^{18}/4$

22.

Multiply. Write your final answer in Scientific Notation: $(5 \times 10^{-4})(2.2 \times 10^{-7})$

a)

$1.1 \times 10^{-10}$

b)

$1.1 \times 10^{-11}$

c)

$1.1 \times 10^{-1}$

d)

$1.1 \times 10^{-7}$

23.

Divide. Write your final answer in Scientific Notation: $(48.6 \times 10^{6})/(2.7 \times 10^{4})$

a)

$18 \times 10^{2} = 1.8 \times 10^{3}$

b)

$1.8 \times 10^{2} = 18 \times 10^{1}$

c)

$0.18 \times 10^{4} = 1.8 \times 10^{3}$

d)

180 × $10^{0}$ = 1.8 × $10^{2}$

24.

Add. Write your final answer in Scientific Notation: $(7.5 \times 10^{5}) + (2.5 \times 10^{3})$

a)

7.525 × $10^{5}$

b)

$1.0 \times 10^{6}$

c)

$7.75 \times 10^{6}$

d)

7.75 × $10^{4}$

25.

Add. Write your final answer in Scientific Notation: $(2.45 \times 10^{7}) + (6.13 \times 10^{6})$

a)

$3.063 \times 10^{7}$

b)

$8.58 \times 10^{6}$

c)

$2.4513 \times 10^{7}$

d)

$2.45 \times 10^{6}$

26.

Subtract. Write your final answer in Scientific Notation: $(7.2 \times 10^{5}) − (4.5 \times 10^{4})$

a)

6.75 × $10^{5}$

b)

$6.75 \times 10^{4}$

c)

2.7 × $10^{5}$

d)

6.75 × $10^{4}$

27.

5x + 8 = 3x + 18 Solve for x.

a)

x = 5

b)

x = 7

c)

x = 3

d)

x = 10

28.

7x + 5 = 3x + 21 Solve for x.

a)

x = 4

b)

x = 2

c)

x = -4

d)

x = -2

29.

5x - 20 = 3x + 16 Solve for x.

a)

x = 18

b)

x = -18

c)

x = 9

d)

x = -9

30.

5x - 60 = 2x + 30 Solve for x.

a)

x = 30

b)

x = -30

c)

x = 20

d)

x = -20

31.

5x + 2 = 2(2x + 7) Solve for x.

a)

x = 2

b)

x = -14

c)

x = 12

d)

x = 0

32.

12 + 3h - 5 = 7 - 4h Solve for h.

a)

h = 2

b)

h = 0

c)

h = 7

d)

h = -2

33.

5(3h - 4) = -(8h + 7) Solve for h.

a)

h = 1.17

b)

h = 0.5

c)

h = 0

d)

h = 1

34.

3x + 7 = 2x + 12 Solve for x.

a)

x = 5

b)

x = -5

c)

x = 7

d)

x = -7

35.

-10 = -7(b + 3) + 7b Solve for b.

a)

No Solution

b)

b = 0

c)

b = -10

d)

Infinite Solutions

36.

5 = 7 - 2(5x - 3) + 15x Solve for x.

a)

x = 8/5

b)

x = -8/5

c)

x = 5

d)

x = -1

37.

Solve each proportion. Round to the nearest tenth, if necessary. $\frac{5}{m} = \frac{10}{4}$

a)

m = 2

b)

m = 4

c)

m = 5

d)

m = 8

38.

Solve each proportion. Round to the nearest tenth, if necessary. $\frac{3}{12} = \frac{6}{b-2}$

a)

b = 26

b)

b = 4.6

c)

b = 14

d)

b = 42

39.

Determine if the following relationship is proportional or non-proportional.

a)

Proportional

b)

Non-proportional

c)

Linear

d)

Exponential

40.

Determine if the following relationship is proportional or non-proportional.

a)

Proportional

b)

Non-proportional

c)

Linear but not proportional

d)

Non-linear

41.

Determine if the following relationship is proportional or non-proportional.

a)

The relationship is proportional.

b)

The relationship is non-proportional.

c)

The relationship is linear and proportional.

d)

The relationship is neither linear nor proportional.

42.

Determine if the following relationship is proportional or non-proportional.

a)

The relationship is proportional.

b)

The relationship is non-proportional.

c)

The relationship is linear and proportional.

d)

The relationship is neither linear nor proportional.

43.

What is the unit according to the graph?

a)

20 words per minute

b)

60 words per 3 minutes

c)

60 words per minute

d)

Cannot be determined

44.

Find the unit rate of price per pound.

a)

14 pounds for $2

b)

$7 per pound

c)

$1.70 per pound

d)

$14 per pound

45.

Write the slope as a fraction in simplest form based on this situation:

a)

Slope = 3/4

b)

Slope = 4/3

c)

Slope = 3

d)

Slope = 2/5

46.

Write the slope as a fraction in simplest form the table:

a)

Slope = -2

b)

Slope = -4

c)

Slope = -1/2

d)

Slope = Undefined

47.

Sam is hiking up a trail that rises 24 inches for every horizontal change of 4 inches to the right. What is the slope of the trail?

a)

6

b)

8

c)

12

d)

4

48.

A road climbs 15 feet vertically for every 20-foot horizontal distance. What is the slope of the road?

a)

0.75

b)

0.67

c)

1.33

d)

0.8

49.

Identify which store has the better deal by comparing unit rates.

a)

Store C has the better deal

b)

Store A has the better deal

c)

Store B has the better deal

d)

They all have the same price per shirt

50.

Find the slope and y-intercept from the given equation. y=5x-90

a)

Slope: 5 y-intercept: -90

b)

Slope: -5 y-intercept: 90

c)

Slope: 90 y-intercept: -5

d)

Slope: -90 y-intercept: 5

51.

Find the slope between 2 points: (5,7) and (1,4)

a)

3/4

b)

4

c)

-3

d)

-4/3

52.

Find the slope between 2 points. (2,5) and (6,4)

a)

-4

b)

-1/4

c)

0

d)

1/4

53.

Find the slope as a fraction in simplest form using the given graph. Points: (1, 2) and (3, -2)

a)

-2

b)

2

c)

1/2

d)

-1/4

54.

Find the slope as a fraction in simplest form using the given graph. Points: (2, 4) and (8, 7)

a)

1/2

b)

1/3

c)

1/4

d)

1/6

55.

Write the equation in slope-intercept form. 2x - 4y = 8

a)

y = 1/2x - 2

b)

y = -1/2x + 2

c)

y = 2x + 4

d)

y = -2x + 4

56.

Write an equation in slope-intercept form that has the following slope and y-intercept: slope: -2 and y-intercept: 4

a)

y = -2x + 4

b)

y = 4x - 2

c)

y = -2x - 4

d)

y = 2x + 4

57.

Write an equation in slope-intercept form that has the following slope and y-intercept: slope: 3 and y-intercept: 5

a)

y = 3x + 5

b)

y = -3x + 5

c)

y = 3x - 5

d)

y = -3x - 5

58.

Write the slope-intercept form of the equation of the given line.

a)

y = x - 1

b)

y = 2x - 2

c)

y = 1/2x - 1

d)

y = -x + 2

59.

Write the slope-intercept form of the equation of the given line.

a)

y = -5/3 - 3

b)

y = 3x - 2

c)

y = -3/5x + 3

d)

y = x + 2

60.

Write the slope-intercept form of the equation of the line through the given points. (1, 3) and (4, 9)

a)

y = 2x + 1

b)

y = x + 2

c)

y = 3x - 1

d)

y = 2x + 3

61.

Graph the equation: y = 2x

a)

A line passing through (0,0) with slope 2 (steep upward from left to right)

b)

A line passing through (0,0) with slope -2 (steep downward from left to right)

c)

A horizontal line passing through (0,0)

d)

A vertical line passing through (0,0)

62.

Graph the equation: y = -3/4x + 2

a)

A line with slope -3/4 and y-intercept 2

b)

A line with slope 3/4 and y-intercept -2

c)

A line with slope -4/3 and y-intercept 2

d)

A line with slope 3/4 and y-intercept 2

63.

Choose which type of solution fits the system of equations: one solution, no solution, infinitely many solutions.
y = 3x + 5
6x - 2y = -10

a)

One solution

b)

No solution

c)

Infinitely many solutions

64.

Determine the type of solution for the following system of equations: one solution, no solution, or infinitely many solutions.
y = 3x - 5
6x - 2y = 10

a)

One solution

b)

No solution

c)

Infinitely many solutions

65.

Does this set of ordered pairs represent a function? {(2, 5), (3, 6), (4, 7), (5, 8)}

a)

True

b)

False

66.

Does this set of ordered pairs represent a function? {(2, 3), (4, 5), (6, 7), (8, 9), (2, 4)}

a)

True

b)

False

67.

Does the graph shown represent a function?

a)

True

b)

False

68.

Does the graph shown represent a function?

a)

True

b)

False

69.

Consider the function h(x) = 4x + 7 + x. Evaluate h(2).

a)

15

b)

13

c)

17

d)

11

70.

Consider the function h(x) = 3x + 2 + x. Evaluate h(-2).

a)

-4

b)

-2

c)

-6

d)

0

71.

Consider the function n(x) = √4x + 5. Evaluate n(9).

a)

-11

b)

6.4

c)

64

d)

11

72.

Determine if the function below is linear or nonlinear.

a)

Linear

b)

Nonlinear

73.

Determine if the function below is linear or nonlinear.

a)

Linear

b)

Nonlinear

74.

y = -3x + 5

a)

Linear

b)

Nonlinear

75.

$y = 5x^2$

a)

Linear

b)

Nonlinear

76.

Write an equation that represents the following: Blockbuster used to be a popular movie rental company. They charged $15 a month to be a member in addition to $3 per movie you rented.

a)

y = 3x + 15

b)

y = 15x + 3

c)

y = 18x

d)

y = 15 + 3

77.

Write an equation that represents the following: A gym charges a $20 monthly membership fee plus $5 for each fitness class you attend.

a)

y = 5x + 20

b)

y = 20x + 5

c)

y = 25x

d)

y = 20 + 5

78.

What is happening in the graph between 30 and 40 minutes?

a)

Sara is not moving.

b)

Sara is accelerating

c)

Sara is slowing down

79.

What does the graph show about Sara's movement between 10 and 30 minutes?

a)

Sara is moving at a constant speed.

b)

Sara is moving faster and faster.

c)

Sara is moving back toward the school.

8th Grade Math 1st Semester Exam Study Guide December 2025

Total questions: 79

Worksheet time: 4hrs 57mins

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