FREE 6th Grade ACT Aspire Math Practice Test

Is Grade 6 ACT Aspire still a current test?

Check your school’s current assessment before choosing exam preparation. The Arizona Department of Education reports that ACT Aspire has been discontinued nationally; Arizona continues its Early High School assessment for its Grade 9 cohort under an existing contract. This older Grade 6 practice set remains available for math review. It is not an official ACT assessment or a simulation of a current Grade 6 state test.

Use the questions to choose your next lesson

Try the questions on paper before reading the answers. Show your steps and mark anything you have not learned yet. There is no official time limit or scaled score for this set. Ask your teacher which calculator rules and test format apply to your current assessment.

This is a mixed review, not a complete Grade 6 curriculum checklist. Questions 8 and 18 use triangle-angle relationships and the Pythagorean theorem as extension work. Skip those until you have studied those ideas. Grade 6 core study also includes fraction division, rational numbers, ratios, expressions, statistics, area and volume; see the Grade 6 standards overview.

20 free math practice questions

Question 1

A baker needs to pack 143 chocolate cookies and 55 vanilla cookies into boxes so that each box has the same number of cookies and only one type of cookie per box. What is the largest number of cookies that can be put in each box?

A. 5

B. 7

C. 9

D. 11

Question 2

What is the value of \(2{,}205 \div 315\)?

A. 5

B. 6

C. 7

D. 8

Question 3

If \(112=22+x\), what is the value of \(x\)?

A. 78

B. 90

C. 100

D. 134

Question 4

Car A travels 221.5 km. Car B travels 1.2 times the distance of Car A. How far does Car B travel?

A. 184.6 km

B. 221.5 km

C. 242.8 km

D. 265.8 km

Question 5

A trapezoid has parallel bases of 8 cm and 10 cm and a perpendicular height of 9 cm. What is its area?

A. 198 cm\(^2\)

B. 162 cm\(^2\)

C. 99 cm\(^2\)

D. 81 cm\(^2\)

Question 6

Which of the following expressions has the greatest value?

A. \( 3^1+12\)

B. \( 3^3-3^2\)

C. \( 3^4-60\)

D. \( 3^5-218\)

Question 7

Alfred has \(x\) apples. Alvin has 40 apples, which is 15 apples less than the number of apples Alfred owns. Baron has \(\frac{1}{5}\) as many apples as Alfred. How many apples does Baron have?

A. 5

B. 11

C. 55

D. 275

Question 8

In the following triangle find \(α\).

A. \(100^\circ\)

B. \(90^\circ\)

C. \(60^\circ\)

D. \(30^\circ\)

Question 9

The price of a laptop is decreased by \(15\%\) to $425. What is its original price?

A. $283

B. $430

C. $500

D. $550

Question 10

Find the perimeter of the shape in the following figure. (all angles are right angles)

A. 21

B. 22

C. 24

D. 20

Question 11

What are the values of mode and median in the following set of numbers?
\(1,3,3,6,6,5,4,3,1,1,2\)

A. Mode: 1, 2, Median: 2

B. Mode: 1, 3, Median: 3

C. Mode: 2, 3, Median: 2

D. Mode: 1, 3, Median: 2.5

Question 12

Which expression is equivalent to \(x × 92\)?

A. \((x×90)+2\)

B. \(x×9×2\)

C. \((x×90)+(x×2)\)

D. \(x×(90×2)\)

Question 13

The ratio of pens to pencils in a box is 3 to 5. If there are 96 pens and pencils in the box altogether, how many more pens should be put in the box to make the ratio of pens to pencils 1: 1?

A. 22

B. 23

C. 24

D. 25

Question 14

If point A is placed at \(-\frac{24}{3}\) on a number line, which of the following points has a distance equal to 5 from point A?

A. \(-13\)

B. \(-3\)

C. \(-2\)

D. A and B

Question 15

Which of the following shows the numbers in increasing order?

A. \(\frac{3}{13}, \frac{4}{11}, \frac{5}{14}, \frac{2}{5}\)

B. \(\frac{3}{13}, \frac{5}{14}, \frac{4}{11}, \frac{2}{5}\)

C. \(\frac{3}{13}, \frac{5}{14}, \frac{2}{5}, \frac{4}{11}\)

D. \(\frac{5}{14}, \frac{3}{13}, \frac{2}{5}, \frac{4}{11}\)

Question 16

If \(x=- 4\), which of the following equations is true?

A. \(x(3x-1)=50\)

B. \(5(11-x^2 )=-25\)

C. \(3(-2x+5)=49\)

D. \(x(-5x-19)=-3\)

Question 17

Complete the prime factorization of 450. Write the missing power of 5: 450 = 2¹ × 3² × ______.

Question 18

What is the perimeter of the following shape? (it’s a right triangle)

A. 14 cm

B. 18 cm

C. 24 cm

D. 32 cm

Question 19

65 is what percent of 50?

A. \(50 \%\)

B. \(77 \%\)

C. \(130 \%\)

D. \(140 \%\)

Question 20

Which of the following expressions has a value of \(-23\)?

A. \(-10+(-8)+ \frac{5}{2}×(-2)\)

B. \(5×3+(-2)×18\)

C. \(-10+6×8÷(-4)\)

D. \((-3) × (-7) + 2\)

Answer key and explanations

Answer 1 — D — 11 cookies per box

The greatest common factor of 143 and 55 is 11: 143 = 11 × 13 and 55 = 11 × 5. That gives 13 chocolate-cookie boxes and 5 vanilla-cookie boxes, or 18 boxes in total. The question asks for cookies per box.

Answer 2 — C — 7

315 × 7 = 2,205, so 2,205 ÷ 315 = 7.

Answer 3 — B — 90

Subtract 22 from both sides: x = 112 − 22 = 90.

Answer 4 — D — 265.8 km

Multiply the distance by 1.2: 221.5 × 1.2 = 265.8.

Answer 5 — D — 81 cm²

Area is half the sum of the parallel bases times the perpendicular height: (8 + 10) ÷ 2 × 9 = 81 cm².

Answer 6 — D — 25

Evaluate powers first. The four values are 15, 18, 21 and 25, respectively.

Answer 7 — B — 11

Alfred has 40 + 15 = 55 apples. Baron has one fifth of 55, so 55 ÷ 5 = 11.

Answer 8 — A — 100°

The 150° exterior angle and beta are supplementary: beta = 180° − 150° = 30°. The triangle angles total 180°, so alpha = 180° − 30° − 50° = 100°.

Answer 9 — C — $500

After a 15% decrease, 85% of the original price remains. Divide $425 by 0.85 to get $500. Check: $500 − $75 = $425.

Answer 10 — C — 24

The unlabeled left vertical edge is 2, because 1 + 2 = 1 + 1 + 1. The unlabeled left horizontal edge is 1, because 5 + 4 = 6 + 2 + 1. Add all ten boundary lengths: 6 + 1 + 2 + 1 + 4 + 1 + 5 + 1 + 1 + 2 = 24.

Answer 11 — B — modes 1 and 3; median 3

In order: 1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 6. Both 1 and 3 occur three times. The sixth value, 3, is the median.

Answer 12 — C

Use the distributive property: x × 92 = x × (90 + 2) = (x × 90) + (x × 2).

Answer 13 — C — 24 more pens

There are 8 ratio parts. Each part is 96 ÷ 8 = 12. That means 36 pens and 60 pencils, so add 60 − 36 = 24 pens.

Answer 14 — D — both −13 and −3

Point A is −24 ÷ 3 = −8. Moving 5 units left gives −13; moving 5 units right gives −3. The point −2 is 6 units away.

Answer 15 — B

Compare decimals: \(\frac{3}{13}\approx0.2308\), \(\frac{5}{14}\approx0.3571\), \(\frac{4}{11}\approx0.3636\), and \(\frac{2}{5}=0.4\).

Answer 16 — B

Substitute x = −4. The left sides of A, B, C and D become 52, −25, 39 and −4. Only B matches its right side: 5 × (11 − 16) = −25.

Answer 17 — 5², or 25

Divide 450 by 2 × 3² = 18 to get 25 = 5². The complete prime factorization is 450 = 2 × 3² × 5². A single factor of 5 would give only 90.

Answer 18 — C — 24 cm

For this extension question, use the Pythagorean theorem: the hypotenuse is the square root of (6² + 8²) = 10 cm. The perimeter is 6 + 8 + 10 = 24 cm.

Answer 19 — C — 130%

Divide the part by the whole and multiply by 100: (65 ÷ 50) × 100 = 130%. A part larger than the whole gives a percentage above 100%.

Answer 20 — A — −23

Calculate multiplication and division before addition. A gives −10 − 8 − 5 = −23. B gives 15 − 36 = −21; C gives −10 − 12 = −22; D gives 21 + 2 = 23.

Choose a focused Grade 6 review

Use a missed question to choose one skill, then solve a few more problems on that skill. For printable practice, browse the free Grade 6 math worksheets. For lessons and a broader study path, start at the Grade 6 Math Online Center.

Review common factors after Question 1, expressions after Questions 6 and 12, ratios after Question 13, and comparing fractions after Question 15. Explain why an answer works before trying another mixed set.

Optional books for continued study

If you want a book to use alongside free practice, open the product pages below and review the description, available preview and format before choosing. These are general study options; this page does not establish alignment with your school’s current assessment.

The Ultimate Middle School Math Bundle Grades 6-8

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.