Free Printable 8th Grade ACAP MATH

1.

The number line shows four points. Which point represents the approximate location of $\sqrt[]{92}$ ?

a)

A

b)

B

c)

C

d)

D

2.

The number line shows four points. Which point represents the approximate location of $\sqrt[]{19}$ ?

a)

A

b)

B

c)

C

d)

D

3.

DON'T USE A CALCULATOR!!! MAKE YOURSELF BETTER!!!!

Turn .33333... into a fraction. Remember this is repeating.

a)

1/3

b)

5/9

c)

7/9

d)

2/11

4.

DON'T USE A CALCULATOR!!! MAKE YOURSELF BETTER!!!!

Turn .7777... into a fraction. Remember this is repeating

a)

1/3

b)

5/9

c)

7/9

d)

2/11

5.

DON'T USE A CALCULATOR!!! MAKE YOURSELF BETTER!!!!

Turn .181818... into a fraction.

a)

1/3

b)

5/9

c)

7/9

d)

2/11

6.

a)

y=3x

b)

y=x

c)

y=-x

d)

y=5x+1

7.

Dreanna opened a new health club in January. The graph shows the membership in her club since she started it.If the membership continues to grow at the same rate, what will the membership number be in August?

a)

350

b)

400

c)

450

d)

500

8.

The table shows the results of a survey on the preferred flavor of ice cream. Based on this survey, what is the probability that the person who prefers chocolate ice cream is an adult?

a)

15/70

b)

55/107

c)

55/101

d)

15/77

9.

3x - 2x + 4 = 5x - 4x - 8

a)

3

b)

6

c)

-3

d)

no solution

10.

Troy made two deliverers for his boss. The graph shows Troy's drive from his home to make the deliveries and then returning home. Which intervals show Troy's distance from home constant?

a)

A and C

b)

B and D

c)

C and E

d)

B, D, and E

11.

A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Formulate a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.

a)

f(x) = 15x + 25; f(2) = 60

b)

f(x) = 25x + 15; f(3) = 90

c)

f(x) = 25x + 15; f(1) = 40

d)

f(x) = 15x + 25; f(3) = 70

12.

A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Formulate a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, and blow dry.

a)

f(x) = 15x + 25; f(2) = 55

b)

f(x) = 25x + 15; f(3) = 90

c)

f(x) = 25x + 15; f(1) = 40

d)

f(x) = 15x + 25; f(2) = 50

13.

Find f(-10) f(x) = 7x - 5

a)

90

b)

-75

c)

-65

d)

65

14.

Identify the unit rate in the graph.

a)

60

b)

120

c)

1

d)

240

15.

The graph shows the number of copies a copier can make. What is the unit rate?

a)

6

b)

1/25

c)

15

d)

25

16.

What is the perimeter of a square with an area of 324 cm²?

a)

18 cm

b)

36 cm

c)

72 cm

d)

144 cm

17.

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

18.

When using scientific notation, a positive exponent means ...

a)

the standard number is greater than one

b)

the standard number is less than one

c)

the negative sign doesn't have a meaning

d)

None of the above

19.

Convert this number to standard notation: 1.4 x 10^-2

(a)

20.

Convert this number into scientific notation: 950,000

a)

9.5 x 10⁵

b)

9.5 x 10^-9

c)

9.5 x 10²

d)

None of the above

21.

Which value is the greatest

a)

5.0 x 10^-9

b)

5.0 x 10^-4

c)

5.0 x 10⁶

d)

5.0 x 10⁸

22.

3.2 x 10²+ 2.2 x 10²

a)

5.7 x 10²

b)

57 x 10²

c)

5.7 x 10⁴

d)

5.4 x 10²

23.

Add withing scientific notation
(5.2 x 10⁷) + (3.01 x 10⁴)

a)

5.20301 x 10¹¹

b)

.520301 x 10⁷

c)

5.20301 x 10⁷

d)

5.20301 x 10⁸

24.

(2.8 x 10⁸)+(5.4 x 10⁹)

a)

5.68 x 10⁹

b)

5.69 x 10⁹

c)

5.67 x 10⁹

d)

5.70 x 10⁹

25.

Solve:

(8.0 x 10¹³) - (7.5 x 10¹²)

a)

1.55 x 10¹²

b)

0.5 x 10⁰

c)

5.0 x 10¹¹

d)

7.25 x 10¹³

26.

Level 2

(2 x 10⁹)(4 x 10^-4)

a)

8 x 10¹³

b)

8 x 10³⁶

c)

8 x 10⁵

d)

8 x 10^-36

27.

Level 3

(9.4 x 10⁶) (3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹⁰

c)

3.008 x 10¹²

d)

1.26 x 10³⁰

28.

Level 4

(1.5 x 10³) ²

a)

1.5 x 10⁶

b)

1.5 x 10⁵

c)

2.25 x 10⁶

d)

2.25 x 10⁵

e)

None of these

29.

If you add to your exponent of 10, you move your decimal...

a)

Left

b)

Right

c)

Up

d)

Down

30.

If you subtract from your exponent of 10, you move your decimal to the ....

a)

Right

b)

Left

c)

North

d)

South

31.

What is the simplified version of

a)

3.9 x 10⁶

b)

4 x 10²⁰

c)

4 x 10⁶

d)

3.9 x 10²⁰

32.

(9.6×10^-8)÷(2×10^-15)

a)

-4.8×10⁷

b)

4.8×10⁷

c)

4.8×10^-7

d)

-4.8×10^-7

33.

3. In the year 2000, the United States public debt was about 5.6 x 10¹² dollars. The population of the United States in that year was about 2.8 x 10⁸ people. What was the average debt per person?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

34.

2. On average, Mercury is about 57,000,000 km from the sun, whereas Neptune is about 4.5 x 10^9 km from the sun. What is the difference between Neptune’s and Mercury’s distances from the sun?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

35.

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)

Add

b)

Subtract

c)

Multiply

d)

Divide

36.

There are approximately 3.1 x 10⁸ people in the United States. If each person has 4.1 x 10¹ coins, how many coins are there altogether?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

37.

The mass of he sun is 1.989 x 10³⁰ kilograms. The mass of the earth is 5.98 x 10²⁴ kilograms. How many times bigger is the sun than the earth?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

38.

A factory can make 3 × 10⁴ t-shirts per day, how many t-shirts will it make in 2.5 ×10² days?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

39.

In 2012, New York City (NYC) and Los Angeles (LA) has the highest populations of any cities in the United States. NYC’s population was about 8.1 × 10⁶ and LA’s population was about 3.8 × 10⁶. What is the population of these two cities combined?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

40.

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

41.

What is the BASE in the power below?
4³

a)

4

b)

3

c)

4³

d)

64

42.

What is the Exponent in the following example?
-2⁵

a)

-2

b)

2

c)

5

d)

-2⁵

43.

Write each product using an exponent.
4 x 4 x 4 x 4 x 4

a)

4⁵

b)

5⁴

c)

4⁶

d)

4⁶

44.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

45.

$3^7\cdot3^7$

a)

$9^{49}$

b)

$3^{14}$

c)

$3^{49}$

d)

$9^{14}$

46.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

47.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

48.

Simplify: $\frac{2^9}{2^6}$

a)

$1^3$

b)

$0^3$

c)

$2^3$

d)

$2^{15}$

49.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

50.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

51.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

52.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

53.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

54.

Simplify: $\left(-x^3\right)\left(-5x\right)$

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

55.

Simplify: $\frac{k^3}{5k}$

a)

$5k^2$

b)

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

c)

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

d)

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

56.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

57.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

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

d)

$\frac{64}{2d^2}$

58.

Simplify: $\frac{-15x^9}{10x^{17}}$

a)

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

b)

$\frac{-3x^8}{2}$

c)

$\frac{-3x^{-8}}{2}$

d)

$\frac{-3}{2x^8}$

59.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

60.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

61.

Is 8.27 rational or irrational?

a)

Rational

b)

Irrational

c)

Both

d)

None of the above

62.

Based on the chart, how many subsets are within the integers set?

a)

1

b)

2

c)

3

d)

none

63.

Zero is a ___________.

a)

whole number

b)

natural number

c)

whole number, integer, and rational

d)

irrational

64.

A fraction is which type of number?

a)

Rational

b)

Irrational

65.

A non-terminating decimal is which type of number?

a)

Rational

b)

Irrational

66.

A repeating decimal is what type of number?

a)

Rational

b)

Irrational

67.

Is √2 Irrational?

a)

Yes

b)

No

68.

The square root of 57 is ...

a)

rational

b)

irrational

69.

Given the following radical, decide if it is rational or irrational:
√121

a)

Rational

b)

Irrational

70.

A repeating decimal and a terminating decimal which of the following in common.

a)

both are whole numbers

b)

both are irrational

c)

both are rational

d)

they have nothing in common

71.

List all the classifications of numbers that apply to the real number.
436

a)

Irrational

b)

Rational, Integer, Whole

c)

Natural, Whole, Integer, Rational

d)

Rational, Integer

72.

List all the classifications of numbers that apply to the real number.
436

a)

Irrational

b)

Rational, Integer, Whole

c)

Natural, Whole, Integer, Rational

d)

Rational, Integer

73.

Choose the number(s) that apply to these sets: Real, Rational, Integer

a)

-27

b)

2/3

c)

0

d)

1/4

e)

2.75

74.

The 3 in 3xy is called the _______

a)

constant

b)

index

c)

expression

d)

coefficient

75.

Which expressions are equivalent to 3(4x + 5)

a)

12x + 5

b)

12x + 15

c)

3x + 4x + 5x + 10 + 5

d)

5x + 7 + 7x + 8

e)

7x + 8

76.

Determine how to translate triangle ABC to triangle A'B'C'.

a)

right two, down five

b)

right two, down 9

c)

left two, up 9

d)

left two, down 5

77.

Determine where X' would be if you translated X 3 units to the left and 9 units down.

a)

(-4, 4)

b)

(-10, 2)

c)

(-4, -5)

d)

(-1, 5)

78.

What does a translation do to an image?

a)

Turns it 90* clockwise

b)

Mirrors it

c)

Shrinks it

d)

Slides it

79.

Which answer shows a reflection across the y-axis?

a)

a

b)

b

c)

c

d)

d

80.

Reflections over the x-axis change the sign of the ____-__________.

a)

y-coordinate

b)

x-coordinate

c)

y-axis

d)

x-axis

81.

Reflecting over the y-axis changes the sign of the ____-_____________.

a)

x-axis

b)

x-coordinate

c)

y-coordinate

d)

none of the above

82.

How many degrees was the figure rotated?

a)

90 degrees counterclockwise

b)

180 degrees

c)

270 counterclockwise

83.

A type of transformation where a figure is “flipped” over a line of symmetry. A reflection produces a mirror image of a figure.

a)

rotation

b)

translation

c)

dilation

d)

reflection

84.

A transformation that “turns” a figure about a fixed point at a given angle and a given direction.

a)

rotation

b)

translation

c)

reflection

d)

dilation

85.

Point (-5,2) is reflected over the y axis. Where is the new point located?

a)

(5,2)

b)

(-5,-2)

c)

(-5,2)

d)

(5,-2)

86.

Identify the transformation from ABC to A'B'C'.

a)

(x+8, y+4)

b)

(x-8, y-4)

c)

(x+4, y+8)

d)

(x-4, y-8)

87.

What is Dilation?

a)

Dilation means to enlarge or reduce

b)

Dilation means to reflect on something

c)

Dilation means to like something

d)

Dilation means to make something different by making it smaller

88.

Does the image show a Dilation?

a)

Yes

b)

No

89.

Dilate Point A by a scale factor of 1/2

a)

(-4,-4)

b)

(-1,-4)

c)

(-1,-1)

d)

(-2,-2)

90.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

91.

What is the solution?

a)

(6, 3)

b)

(3, 6)

c)

(-6, 3)

d)

No solution

92.

How many solutions?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

93.

What is the solution?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

94.

A system of equations with no solution will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

95.

A system of equations with infinitely many solutions will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

96.

The graph above represents the allowance that Stefin and Daniel receive every week. If the x-axis represents the number of weeks and the y-axis represents the earnings ($), what is the amount of earnings that both boys will have the same?

a)

$4

b)

$2

c)

$6

d)

$8

97.

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

a)

(3,-9)

b)

(-3,-9)

c)

(-3,9)

d)

(0,1)

98.

Solve the system of equations.
x + 5y = -27
-2x - 5y = 24

a)

(3, 6)

b)

(-3, -6)

c)

(-3, -4)

d)

(3, -6)

99.

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

a)

0

b)

Undefined

c)

-1

d)

1

100.

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

8th Grade ACAP MATH

Total questions: 100

Worksheet time: 3hrs 28mins

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