Free Printable 8th grade Year in Review 23-24

1.

$6^4\cdot6^2$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

2.

$\frac{9^8}{9^3}$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

3.

$8^{-2}$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

4.

$10^0$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

5.

$3^4\cdot3^6$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

6.

$\left(7^2\right)^4$ =

Your answer could be in exponential form or if you would like a challenge in its simplest form

7.

Enter the value of n for the equation

$2^5\cdot2^n=2^{15}$ .

a)

3

b)

10

c)

-10

d)

$\frac{1}{10}$

8.

Simplify:

$\frac{5^7}{5^4}$

a)

$5^{11}$

b)

$1^3$

c)

$5^3$

9.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.

Example: s⁶ ⋅ s⁴

a)

add

b)

subtract

c)

multiply

d)

divide

10.

According to exponent rules, when we raise the power to a power we _______ the exponents. Example: (e²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

11.

Anything raised to a power of zero is always:

(a)

12.

According to exponent rules, when we divide two powers with the same base we _______ the exponents. Example: a⁸/a³

a)

add

b)

subtract

c)

multiply

d)

divide

13.

Select the expression that is equivalent (equal) to (7⁶)⁴.

a)

7¹⁰

b)

7²

c)

7²⁴

14.

Select the expression equivalent (equal) to

6⁸ / 6³

a)

6¹¹

b)

6⁵

c)

6²⁴

15.

What is the correct way to equivalent 5² * 5³ ?

a)

5⁶

b)

5^-1

c)

5⁵

16.

What is 2654⁰?

(a)

17.

Which expression is equivalent (equal) to

10⁹ / 10³

a)

1/10^-6

b)

10⁶

c)

10^-6

d)

1 / 10⁶

18.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

19.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

20.

a)

b)

c)

d)

21.

A microgram is equal to 1 x 10 ^-6grams. How many times greater than a microgram is 1 x 10²grams?

a)

1 x 10^-8

b)

1 x 10^-4

c)

1 x 10⁴

d)

1 x 10⁸

22.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

23.

A TV show had 3.5 × 10⁶ viewers for their first episode and 8.5 × 10⁶ viewers for their second episode. How many viewers did they have overall?

a)

1.2 x 10⁷

b)

1.2 x 10^-7

c)

1.2 x 10⁶

d)

1.2 x 10^-6

24.

The mean distance from the sun to Earth is 9.29 x 10⁷ miles. Jupiter's mean distance from the sun is 4.8388 x 10⁸ miles. What is the difference between these two distances in miles?

a)

4.3092 x 10¹

b)

3.9098 x 10⁷

c)

3.9098 x 10⁸

d)

5.7678 x 10⁸

25.

Convert this number to standard notation:

1.4 x 10^-2

(a)

26.

Convert this number into scientific notation:

0.068

a)

6.9 x 10⁶

b)

6.8 x 10^-9

c)

6.8 x 10^-2

d)

None of the above

27.

Express the following in scientific notation:

.000457

a)

457 x 10⁶

b)

457 x 10^-6

c)

4.57 x10⁴

d)

4.57 x 10^-4

28.

Which of the following numbers is written in scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

29.

How do you write 8.317 x 10⁶in standard form?

(a)

30.

How would you write 0.0005 in scientific notation?

a)

50 x 10^-5

b)

5 x 10^-4

c)

5 x 10³

d)

.5 x 10³

31.

How would you write 4.3756 x 10⁴in standard form?

(a)

32.

a)

True

b)

False

33.

Find the slope of a line that passes through the given points:

(5,1) and (8,3)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{-2}$

d)

$\frac{3}{2}$

34.

Given that the slope is 2/3 and the y intercept is -3 what is the equation of the line?

a)

y = 2/3x - 3

b)

y = 2/3x + 3

c)

y = -2/3x - 3

d)

y = -2/3x + 3

35.

Which equation is being represented by this line?

a)

y = -x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

36.

Liam's class is planting bamboo seedlings in the school garden. The line represents the average height of a bamboo plant after itr has been planted. Write an equation in slope-intercept form that Liam could use to predict the height y of his bamboo after x days.

37.

The slope represents the average number of (a) grows each day. The (b) represents the (c) when it is first planted.

Choose from the below words

inches a bamboo plant

y-intercept

height of the plant

x-intercept

number of days

38.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

39.

Find the slope of a line that passes through the given points:

(5,1) and (8,3)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{-2}$

d)

$\frac{3}{2}$

40.

Given that the slope is 2/3 and the y intercept is -3 what is the equation of the line?

a)

y = 2/3x - 3

b)

y = 2/3x + 3

c)

y = -2/3x - 3

d)

y = -2/3x + 3

41.

Which equation is being represented by this line?

a)

y = -x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

42.

Liam's class is planting bamboo seedlings in the school garden. The line represents the average height of a bamboo plant after itr has been planted. Write an equation in slope-intercept form that Liam could use to predict the height y of his bamboo after x days.

43.

The slope represents the average number of (a) grows each day. The (b) represents the (c) when it is first planted.

Choose from the below words

inches a bamboo plant

y-intercept

height of the plant

x-intercept

number of days

44.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

45.

A meteorologist tracks the amount of snowfall over a 5-Hour period.She graphs her measurements. What is the equation of the meteorologist's line in slope-intercept form?

a)

y=mx+b

b)

y=2x+3

c)

y=3x+2

d)

y=2/3x+3

46.

What is the y-intercept of
2x-5y=35?

a)

(0,-7)

b)

(-7,0)

c)

(35/2, 0)

d)

(0,35/2)

47.

Julio sells hand-painted skateboards. The graph shows how the price of a skateboard is related to the amount of time Julio spends painting it. Write Write an equation in slope-intercept form that Julio could use to predict the price y of a skateboard in relation to the amount of time x he spends painting.

48.

Write the slope intercept form of the equation 9x - 7y = -7

a)

y = -9/7x + 1

b)

y = 9/7x + 1

c)

y = -9/7x - 7/9

d)

y = 9/7x + 7/9

49.

The graph shows the costs of lotion C, represented by line C, and lotion D, represented by line D. Decide of the following statements are true or false.

Categorize the following

The cost of lotion C is $0.50 per ounce.

The cost of lotion D is $2.00 per ounce.

Lotion C cost more than Lotion D

Lotion D costs more than Lotion C

TRUE

FALSE

50.

Solve the following equation:

7x + 8 - 2x = 20

(a)

51.

6 + 9r = 9r + 6

a)

One Solution

b)

No Solution

c)

Infinite Solutions

52.

2b ‒ 5 = 9

a)

One Solution

b)

No Solution

c)

Infinite Solutions

53.

–2q ‒ 3 = –2q ‒ 8

a)

One Solution

b)

No Solution

c)

Infinite Solutions

54.

8p ‒ 1 = 1 + 8p

a)

One Solution

b)

No Solution

c)

Infinite Solutions

55.

6e ‒ 10 = 10 ‒ 2e + 10e

a)

One Solution

b)

No Solution

c)

Infinite Solutions

56.

4(x ‒ 5) = 4x ‒ 20

a)

One Solution

b)

No Solution

c)

Infinite Solutions

57.

2(3g + 1) = 3g + 1 + 3g

a)

One Solution

b)

No Solution

c)

Infinite Solutions

58.

Solve the following equation:

8x + 4 = 3x + 14

(a)

59.

Solve the following equation:

0.5(2x + 14) = 10

a)

x = 3

b)

x = 17

c)

x = -2.25

d)

x = - 4

60.

Solve the following equation:

-3x = 9

a)

x = 3

b)

x = 12

c)

x = -3

d)

x = 6

61.

Solve the following equation:

$-2\left(3x\ -\ 7\right)\ =\ 2x\ -\ 2$

a)

x = 3

b)

x = 4

c)

x = 5/7

d)

x = 2

62.

What is the formula for finding the hypotenuse of a right triangle using the Pythagorean theorem?

a)

c = √(a^2 + b^2)

b)

c = a + b

c)

c = a - b

d)

c = a * b

63.

If the lengths of the two legs of a right triangle are 3 cm and 4 cm, what is the length of the hypotenuse?

a)

5

b)

8

c)

7

d)

6

64.

In a right triangle, if the length of one leg is 5 cm and the length of the hypotenuse is 13 cm, what is the length of the other leg?

a)

12

b)

8

c)

10

d)

3

65.

A ladder is leaning against a wall. The base of the ladder is 6 ft away from the wall and the ladder is 8 ft long. How far is the top of the ladder from the ground?

a)

10 ft

b)

5.29 ft

c)

2 ft

d)

12 ft

66.

A flagpole is standing upright on level ground. The shadow of the flagpole is 10 ft long and the angle of elevation from the tip of the shadow to the top of the flagpole is 60 degrees. How tall is the flagpole?

a)

15 ft

b)

17.32 ft

c)

12.5 ft

d)

8.66 ft

67.

In a right triangle, if the length of one leg is 9 cm and the length of the other leg is 12 cm, what is the length of the hypotenuse?

a)

18 cm

b)

10 cm

c)

15 cm

d)

13 cm

68.

A ramp is placed against a building. The base of the ramp is 5 ft away from the building and the ramp is 13 ft long. How high is the top of the ramp from the ground?

a)

10 ft

b)

8 ft

c)

12 ft

d)

15 ft

69.

A ladder is leaning against a wall. The base of the ladder is 10 ft away from the wall and the ladder is 15 ft long. How far is the top of the ladder from the ground?

a)

13.5 ft

b)

14.5 ft

c)

12.5 ft

d)

11.18 ft

70.

In a right triangle, if the length of one leg is 8 cm and the length of the hypotenuse is 17 cm, what is the length of the other leg?

a)

10

b)

12

c)

20

d)

15

71.

A flagpole is standing upright on level ground. The shadow of the flagpole is 15 ft long and the angle of elevation from the tip of the shadow to the top of the flagpole is 45 degrees. How tall is the flagpole?

a)

10

b)

20

c)

25

d)

15

72.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

73.

What's the formula for pythagorean theorem?

a)

a²+b²=c²

b)

a²+b=c²

c)

a+b²=c²

74.

Do the segment lengths 15, 12, and 9 form a right triangle?

a)

Yes

b)

No

75.

The legs form what type of angle?

a)

Acute

b)

Obtuse

c)

Reflex

d)

Right

76.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

77.

What are the sides of the triangle called?

a)

leg

b)

leg

c)

hypotenuse

1

2

3

1)

2)

3)

78.

(6 × 10¹) + (9 × 10¹)

79.

32 – (2.1 × 10¹)

80.

(7 × 10⁰) + (3 × 10¹)

81.

(8.8 × 10²) + (3 × 10²)

82.

100 - (1.4 x 10¹)

83.

(3.05 × 10²) + 64

84.

(4 × 10²) + 120.5

85.

(9.5 × 10²) – (4.3 × 10¹)

86.

$0.071+\left(6\times10^{-2}\right)$

87.

(2.75 × 10³) - 100

88.

18 - (2 x 10¯¹)

89.

2,000+ (8 × 10³)

90.

When adding or subtracting with scientific notation, why is it important to have the same power of 10?

a)

It is not important

b)

It aligns the place values making it easier to solve

c)

you don't have to have the same power of ten

d)

actually you need to have the same first factor

91.

In slope intercept form (y=mx+b) what is the "m"?

a)

The y-intercept

b)

The x-intercept

c)

The slope (rate of change)

d)

A point

92.

In slope intercept form (y=mx+b) what is the "b"?

a)

The y-intercept

b)

The x-intercept

c)

The slope (rate of change)

d)

A point

93.

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

a)

y=15x

b)

y=15x+80

c)

y=x+15

d)

y=80x+15

94.

What is the y-intercept of the line graphed below?

a)

3

b)

4

c)

-3

d)

4/3

95.

Which equation represents the following graph?

a)

y = 3x + 2

b)

y = -2x + 3

c)

y = 2x + 3

d)

y = -3x + 2

96.

What is the y-intercept in the equation?
y = 5x - 4

a)

5

b)

-4

c)

-5

d)

4

97.

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

98.

Find the slope from the table.

a)

-4

b)

1

c)

4

d)

-2

99.

What is the y-intercept for the given graph?

a)

-5

b)

5

c)

1

d)

-1

100.

What is the slope of the line?

a)

m = 3/4

b)

m = 4/3

c)

m = -3/4

d)

m = -4/3

101.

Find the slope

a)

4/5

b)

5/4

c)

-5/4

d)

-4/5

102.

Find the slope of a line that passes through the given points:

(5,1) and (8,3)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{-2}$

d)

$\frac{3}{2}$

103.

Given that the slope is 2/3 and the y intercept is -3 what is the equation of the line?

a)

y = 2/3x - 3

b)

y = 2/3x + 3

c)

y = -2/3x - 3

d)

y = -2/3x + 3

104.

Write the equation of the line that passes through the point (3,-1) and has a slope of 2

(do not leave any spaces in answer)

(a)

105.

What is the y-intercept?

a)

(0,15)

b)

(3,0)

c)

(15,0)

d)

(0,3)

106.

What is the y-intercept?

a)

(2,0)

b)

(0,2)

c)

(0,-2)

d)

(-2,0)

107.

What is the y-intercept?

a)

(0,15)

b)

(3,0)

c)

(15,0)

d)

(0,3)

108.

What is the y-intercept?

a)

(2,0)

b)

(0,2)

c)

(0,-2)

d)

(-2,0)

109.

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

a)

3

b)

4x

c)

4

d)

x

110.

What is the y-intercept in the following equation: y=-4x-5

a)

-4

b)

-4x

c)

5

d)

-5

111.

Find the equation of the line in slope-intercept form.

a)

y = - 1/4x - 3

b)

y = 1/3x + 3

c)

y = - 1/4x + 2

d)

y = 1/3x -3

112.

Which equation represents the following graph?

a)

y = 3x + 2

b)

y = -2x + 3

c)

y = 2x + 3

d)

y = -3x + 2

113.

a)

y = 4/5x + 3

b)

y = -5/4x + 3

c)

y = 5/4x + 4

d)

y = -4/5x + 3

114.

Bob has $150 in his savings account and saves $40 per month.

a)

y=150 + 40

b)

y=40x + 150

c)

y=150x + 40

115.

From the equation: y = -2x +6 what is the slope of the line?

a)

y

b)

6

c)

x

d)

-2

116.

From the equation: y = -2x+6 what is the y-intercept of the line?

a)

y

b)

6

c)

x

d)

-2

117.

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

a)

A

b)

B

c)

C

d)

D

118.

#4 Which graph is correct for y = -¾x + 1?

a)

A

b)

B

119.

Which equation represents this graph?

a)

$y=\frac{1}{5}x+3$

b)

$y=-5x-3$

c)

$y=5x+3$

d)

$y=-3x+0.5$

120.

Which of these lines has a slope of -3?

a)

A

b)

B

c)

C

d)

D

8th grade Year in Review 23-24

Total questions: 120

Worksheet time: 30hrs 0mins

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