# FREE 5th Grade ACT Aspire Math Practice Test

Welcome to our FREE 5th Grade ACT Aspire Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help your student succeed on the 5th Grade ACT Aspire Math test. Not only does the test closely match what students will see on the real ACT Aspire, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your student’s ACT Aspire Practice test. Your student will have the chance to try out the most common 5th-grade ACT Aspire Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free 5th Grade ACT Aspire Math practice tests and study resources (updated for 2021) to help your students ace the 5th Grade ACT Aspire Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to practice.

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## 10 Sample **5th Grade ACT Aspire** Math Practice Questions

1- How long is the line segment shown on the number line below?

A. 6

B. 7

C. 8

D. 9

2- If a rectangle is 30 feet by 45 feet, what is its area?

A. 1350

B. 1250

C. 1000

D. 870

3- If a vehicle is driven 32 miles on Monday, 35 miles on Tuesday, and 29 miles on Wednesday, what is the average number of miles driven each day?

A. 32

B. 33

C. 34

D. 35

4- Peter traveled 120 miles in 4 hours and Jason traveled 160 miles in 8 hours. What is the ratio of the average speed of Peter to an average speed of Jason?

A. 3 : 2

B. 2 : 3

C. 5 : 9

D. 5 : 6

5- If \(x=- 8\), which equation is true?

A. \(x(2x-4)=120\)

B. \(8 (4-x)=96\)

C. \(2 (4x+6)=79\)

D. \(6x-2=-46\)

6- A circle has a diameter of 8 inches. What is its approximate circumference?

(\(π = 3.14\))

A. 6.28 inches

B. 25.12 inches

C. 34.85 inches

D. 35.12 inches

7- A woman owns a dog walking business. If 3 workers can walk 9 dogs, how many dogs can 5 workers walk?

A. 13

B. 15

C. 17

D. 19

8- What are the coordinates of the intersection of x–axis and the y–axis on a coordinate plane?

A. \((5, 5)\)

B. \((1, 1)\)

C. \((0, 0)\)

D. \((0, 11)\)

9- Jack added 19 to the product of 16 and 26. What is this sum?

A. 61

B. 330

C. 435

D. 135

10- Joe makes $4.75 per hour at his work. If he works 8 hours, how much money will he earn?

A. $32.00

B. $34.75

C. $36.50

D. $38.00

11- Which of the following is an obtuse angle?

A. 89\(^\circ\)

B. 55\(^\circ\)

C. 143\(^\circ\)

D. 235\(^\circ\)

12- What is the value of \(6 – 3 \frac{4}{9}\)?

A. \(\frac{23}{9}\)

B. \(3\frac{4}{9}\)

C. \(-\frac{1}{9}\)

D. \(\frac{42}{9}\)

13- The bride and groom invited 220 guests to their wedding. 190 guests arrived. What percent of the guest list was not present?

A. \(90\%\)

B. \(20\%\)

C. \(23.32\%\)

D. \(13.64\%\)

14- Frank wants to compare these two measurements.

\(18.023 \space kg \space …….. \space 18,023 \space g\)

Which symbol should he use?

A. \(<\)

B. \(>\)

C. \(≠\)

D. \(=\)

15- Aria was hired to teach three identical 5th-grade math courses, which entailed being present in the classroom for 36 hours altogether. At $25 per class hour, how much did Aria earn for teaching one course?

A. $50

B. $300

C. $600

D. $1400

16- In a classroom of 60 students, 22 are male. What percentage of the class is female?

A. \(51\%\)

B. \(59\%\)

C. \(63\%\)

D. \(73\%\)

17- In a party, 6 soft drinks are required for every 9 guests. If there are 171 guests, how many soft drinks are required?

A. 9

B. 27

C. 114

D. 171

18- While at work, Emma checks her email once every 90 minutes. In 9 hours, how many times does she check her email?

A. 4 Times

B. 5 Times

C. 6 Times

D. 7 Times

19- In a classroom of 44 students, 18 are male. About what percentage of the class is female?

A. \(63\%\)

B. \(51\%\)

C. \(59\%\)

D. \(53\%\)

20- A florist has 516 flowers. How many full bouquets of 12 flowers can he make?

A. 40

B. 41

C. 43

D. 45

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## Answers:

1- **D**

The line segment is from 1 to\( -8\). Therefore, the line is 9 units.

\(1 –(-8)= 1+8=9\)

2- **A**

Use the area of the rectangle formula.

Area \(=\) length \(×\) width \(⇒ A = 30 × 45 ⇒ A = 1,350\)

3-** A**

\(average (mean) = \frac{sum \space of \space terms}{number \space of \space terms}⇒ average= \frac{32+35+29}{3}⇒ average = 32\)

4- **A**

Peter’s speed \(= \frac{120}{4}= 30\)

Jason’s speed \(= \frac{160}{8}=20\)

\(\frac{The \space average \space speed \space of \space peter}{The \space average \space speed \space of \space Jason}=\frac{30}{20}\)

equals to: \(\frac{3}{2}\)or 3 : 2

5- **B**

Plug in \(x=- 8\) in each equation.

\(x(2x-4)=120→(-8)(2(-8)-4)=(-8)×(-16-4)=160\)

\(8 (4-x)=96→8(4-(-8)=8(12)=96\)

\(2 (4x+6)=79→2(4(-8)+6)=2(-32+6)=-52\)

\(6x-2=-46→6(-8)-2=-48-2=-50\)

Only option B is correct.

6- **B**

The diameter of the circle is 8 inches. Therefore, the radius of the circle is 4 inches.

Use the circumference of the circle formula.

\(C = 2πr ⇒ C = 2 × 3.14 × 4 ⇒ C = 25.12\)

7- **B**

3 workers can walk 9 dogs ⇒ 1 worker can walk 3 dogs.

5 workers can walk \((5 × 3) 15\) dogs.

8- **C**

The horizontal axis in the coordinate plane is called the \(x\)-axis. The vertical axis is called the \(y\)-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the \(x\)-axis and 0 on the \(y\)-axis.

9- **C**

\(19 + (16 × 26) = 19 + 416 = 435\)

10- **D**

1 hour: \($4.75\)

8 hours: \(8 × $4.75 = $38\)

11- C

An obtuse angle is an angle of greater than 90\(^\circ\) and less than 180\(^\circ\). From the options provided, only option C (143 degrees) is an obtuse angle.

12- **A**

\(6 – 3\frac{4}{9}=\frac{54}{9}-\frac{31}{9}=\frac{23}{9}\)

13- **D**

The number of guests that are not present are \((220 – 190) 30\) out of \(220 =\frac{30}{220}\)

Change the fraction to percent:

\(\frac{30}{220}×100\%=13.64\%\)

14- **D**

Each kilogram is 1,000 grams.

18,023 grams \(= (\frac{18,023}{1,000}) =18.023\) kilograms.

Therefore, the two amounts provided are equal.

15- **B**Aria teaches 36 hours for three identical courses. Therefore, she teaches 12 hours for each course. Aria earns $25 per hour. Therefore, she earned $300 (\(12 × 25\)) for each course.

16- **C**

The number of female students in the class is \((60 – 22) 38\) out of \(60 = \frac{38}{60}\)

Change the fraction to percent:

\(\frac{38}{60} ×100\%=63\%\)

17- **C**

Write a proportion and solve.

\(\frac{6 \space soft \space drinks}{9 \space guests}=\frac{x}{171 \space guests}\)

\(x =\frac{171×6}{9}⇒x=114\)

18- **C**

Every 90 minutes Emma checks her email.

In 9 hours (540 minutes), Emma checks her email \((540 ÷ 90) 6\) times.

19- **C**

There are 44 students in the class. 18 of them are male and 26 of them are female.

26 out of 44 are female. Then:

\(\frac{26}{44}=\frac{x}{100}→2,600=44x→x=2,600÷44≈59\%\)

20- **C**

Divide the number flowers by \(12: 516 ÷ 12 = 43\)

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