Free Printable S2: 8th Grade Math Support Review

1.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

2.

Which number is the EXPONENT?
4^{2 =}16

a)

4

b)

2

c)

16

3.

3⁵

a)

15

b)

51

c)

125

d)

243

4.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

5.

Simplify the expression

x^5\cdot x^7

a)

x³⁵

b)

x¹²

c)

x²

d)

x^-2

6.

Simplify

2^4\cdot2^5

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

7.

a)

1¹⁰

b)

1²⁶

c)

z¹⁰

d)

z²⁶

8.

Simplify using only positive exponents: $5^{-8}$

a)

$5^8$

b)

$\frac{1}{5^8}$

c)

$\frac{1}{5^{-8}}$

d)

$-5^8$

9.

Simplify using only positive exponents: $y^{-3}$

a)

$3y$

b)

$-y^3$

c)

$\frac{1}{y^3}$

d)

$\frac{1}{y^{-3}}$

10.

Simplify using only positive exponents: $2^{-3}$

a)

$\frac{1}{8}$

b)

$\frac{1}{-8}$

c)

$-8$

d)

$\frac{1}{6}$

11.

Simplify using only positive exponents: $xy^{-3}$

a)

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

b)

$\frac{1}{xy^3}$

c)

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

d)

$xy^3$

12.

Simplify using only positive exponents: $a^{-2}b$

a)

$-a^2b$

b)

$\frac{b}{a^2}$

c)

$\frac{1}{a^2b}$

d)

$\frac{a^2}{b}$

13.

Simplify using only positive exponents: $x^{-1}y^3$

a)

$-xy^3$

b)

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

c)

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

d)

$xy^3$

14.

Simplify using only positive exponents: $\frac{1}{y^{-2}}$

a)

$-2y$

b)

$-y^2$

c)

$y^2$

d)

$y^{-2}$

15.

Simplify using only positive exponents: $\frac{1}{a^{-1}}$

a)

$a$

b)

$-a$

c)

$\frac{1}{a}$

d)

$\frac{1}{-a}$

16.

SImplify using only positive exponents: $a^{-2}bc^{-1}$

a)

$\frac{bc}{a^2}$

b)

$-a^2bc$

c)

$\frac{a^2b}{c}$

d)

$\frac{b}{a^2c}$

17.

SImplify using only positive exponents: $\frac{a^3b^{-2}}{c^{-5}}$

a)

$\frac{a^3c^5}{b^2}$

b)

$a^3b^2c^5$

c)

$\frac{a^3}{b^2c^5}$

d)

$\frac{b^2c^5}{a^3}$

18.

SImplify using only positive exponents: $\frac{a^2}{b^{-3}c^{-8}}$

a)

$\frac{b^3c^8}{a^2}$

b)

$a^2b^3c^8$

c)

$\frac{a^2b^3}{c^8}$

d)

$\frac{c^8}{a^2b^3}$

19.

Match the following:

a)

$\frac{a^{-3}b^{-5}}{c^{-1}}$

1.

$\frac{c}{a^3b^5}$

b)

$\frac{a^3c^{-1}}{b^{-5}}$

2.

$\frac{a^3b^5}{c}$

c)

$a^{-3}b^{-5}c^{-1}$

3.

$\frac{1}{a^3b^5c}$

d)

$\frac{a^3b^5}{c^{-1}}$

4.

$a^3b^5c$

e)

$\frac{1}{a^{-3}b^5c^{-1}}$

5.

$\frac{a^3c}{b^5}$

20.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

21.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

22.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

23.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

24.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

25.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

26.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

27.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

28.

a)

b)

c)

d)

29.

a)

b)

c)

d)

30.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

31.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

32.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

33.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

34.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

35.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

36.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

37.

What is the opposite (inverse operation) of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

38.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

39.

Find the length of the missing side.

a)

48 in.

b)

52 in.

c)

16 in.

d)

24 in.

40.

The legs form what type of angle?

a)

Acute

b)

Obtuse

c)

Reflex

d)

Right

41.

Sides a and b are called legs.

a)

true

b)

false

42.

The Pythagorean Theorem is

a² + b²= c²

a)

false

b)

true

43.

Find the missing length? *solve for x

a)

50 yards

b)

60 yards

c)

70 yards

d)

80 yards

44.

a = 2.1, b = 7.2, c = 7.5

Is this a right triangle?

*Hint - You could plug the values into the Pythagorean Theorem.

a)

yes

b)

no

45.

What is the formula for finding the hypotenuse?

a)

a² + b² = c²

b)

a + b = c

c)

a - b = c

d)

c - b = a

46.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

47.

Which of the following formulas best solves for a missing leg?

a)

a² + b² = c²

b)

c - b = a

c)

c² - b² = a²

d)

b² + c² = a²

48.

Which side is missing?

a)

Leg

b)

Hypotenuse

c)

Right Angle

49.

What side is missing?

a)

Hypotenuse

b)

Leg

50.

a)

$149.5\ cm^2$

b)

$150\ cm^2$

c)

$149\ cm^2$

d)

$299\ cm^2$

51.

a)

$105\ cm^2$

b)

$52.5\ cm^2$

c)

$52\ cm^2$

d)

$105.5\ cm^2$

52.

a)

$195\ cm^2$

b)

$195.5\ cm^2$

c)

$391.5\ cm^2$

d)

$391\ cm^2$

53.

a)

$135\ in^2$

b)

$54\ in^2$

c)

$130\ in^2$

d)

$125\ in^2$

54.

a)

Rectangle Table

b)

Trapezoid Table

c)

Both are the same

55.

a)

$18\ m^2$

b)

$81\ m^2$

c)

$54\ m^2$

56.

What is the area of the rectangle?

a)

$7\ m^2$

b)

$15\ m^2$

c)

$10\ m^2$

57.

Find the area of the rectangle

a)

$100\ cm^2$

b)

$25\ cm^2$

c)

$120\ cm^2$

58.

a)

$48\ m^2$

b)

$24\ m^2$

c)

$30\ m^2$

59.

a)

$30\ cm^2$

b)

$200\ cm^2$

c)

$175\ cm^2$

d)

$100\ cm^2$

60.

The formula for the area of a circle is...

a)

$A=\pi d^2$

b)

$A=2\pi r$

c)

$A=\pi\cdot d$

d)

$A=\pi r^2$

61.

I can calculate the area of a circle given its radius or diameter.

What is the area of the circle shown? Round your answer to the nearest tenth.

a)

$425.2\ cm^2$

b)

$37.7\ cm^2$

c)

$75.4\ cm^2$

62.

I can calculate the area of a circle given its radius or diameter.

What is the area of the circle shown? Round your answer to the nearest tenth.

a)

$31.4\ cm^2$

b)

$15.5\ cm^2$

c)

$78.5\ cm^2$

63.

I can calculate the area of a circle given its radius or diameter.

If the radius of a circle is 3 cm, what is the area of the circle?

a)

$9.4\ cm^2$

b)

$28.3\ cm^2$

c)

$18.7\ cm^2$

64.

I can calculate the area of a circle given its radius or diameter.

What is the area of the circle shown? Round your answer to the nearest tenth.

a)

$12.6\ cm^2$

b)

$24.1\ cm^2$

c)

$50.2\ cm^2$

65.

I can calculate the area of a circle given its radius or diameter.

What is the area of the circle shown? Round your answer to the nearest tenth.

a)

$113\ cm^2$

b)

$36.7\ cm^2$

c)

$18.8\ cm^2$

66.

I can calculate the area of a circle given its radius or diameter.

If the diameter of a circle is 11 m, what is the area of the circle?

a)

$95\ m^2$

b)

$34.5\ m^2$

c)

$379.9\ m^2$

67.

Identify the steps to solve for b

a)

Add 6 to both sides and divide both sides by 5

b)

Add 6 to both sides and multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

68.

$5x-1=19$

a)

$x=4$

b)

$x=10$

c)

$x=5$

d)

$x=15$

69.

$6x\ +\ 4\ =\ 9x\ -\ 5$

(a)

70.

$5x\ +\ 18\ =\ 12x\ +\ 4$

(a)

71.

$24\ =\ 3\left(3x\ -7\right)$

a)

$x\ =\ -9$

b)

$x\ =\ 5$

c)

$x\ =3$

d)

$x\ =\ 7$

72.

$r\ +\ 11\ +\ 8r\ =\ 29$

a)

$r\ =0$

b)

$r\ =\ 1$

c)

$r\ =\ 2$

d)

$r\ =\ 3$

73.

$-5\left(4x\ -\ 2\right)\ =\ -2\left(3\ +6x\right)$

a)

$x\ =\ 2$

b)

$x\ =\ 8$

c)

$x\ =\ -2$

d)

$x\ =\ -8$

74.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

75.

Determine the type of solution you will have if you get
-6=6

a)

one solution

b)

infinite solution=identity

c)

no solution

d)

I don't know. I need to study.

76.

14 + 35v = 3v + 14

a)

One Solution

b)

No Solution

c)

Infinite Solutions

77.

36 - 7p = -7p + 35

a)

One Solution

b)

No Solution

c)

Infinite Solutions

78.

-2v + 4 = -3 -2v

a)

No Solution

b)

Infinite Solutions

c)

One Solution

79.

3 + 5n = 5n + 3

a)

One Solution

b)

No Solution

c)

Infinite Solutions

80.

8x + 38 = -3 (-6 - 4x)

a)

No Solutions

b)

Infinite Solutions

c)

One Solution

81.

Solve:
3x + 15 = 3(x + 5)

a)

No Solution

b)

One Solution

c)

Infinitely Many Solutions

82.

9y+8=9y-8

a)

No Solution

b)

One Solution

c)

Infinite Solution

83.

-10y-6 = -10y-6

a)

No Solution

b)

One Solution

c)

Infinite Solutions

84.

3(x-8)=3x-24

a)

No Solution

b)

One Solution

c)

Infinite Solutions

85.

6(m+3)=2(m+5)

a)

No solution

b)

One Solution

c)

Infinite Solutions

86.

-5(2x - 4) = 2(10 - 5x)

a)

No Solution

b)

One Solution

c)

Infinite Solution

S2: 8th Grade Math Support Review

Total questions: 86

Worksheet time: 3hrs 52mins

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