FREE 6th Grade Common Core Math Practice Test

Use these 20 free questions for a short math review, then check the worked answers below. This is an independent mixed practice set, with prerequisite skills and a few extension questions. It does not reproduce a particular state test or cover every Grade 6 Common Core standard.

20 free practice questions

Write your answers on paper before looking at the explanations. You can print this page with your browser’s Print command; it includes both questions and answers. No timer is built into this page. Follow your teacher’s calculator instructions rather than treating this activity as an official test policy.

Questions marked Extension review include angle reasoning, reverse percentages, or signed-number calculations beyond this set’s core Grade 6 review. Question 18 uses the Pythagorean theorem. Skip extension items if your class has not covered them; use the remaining questions to find a useful next lesson.

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

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

A. 5

B. 6

C. 7

D. 8

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

A. 78

B. 90

C. 100

D. 134

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

5- A trapezoid has parallel sides of 8 cm and 10 cm. The perpendicular distance between those parallel sides is 9 cm. What is its area?

A. 198 cm\(^2\)

B. 162 cm\(^2\)

C. 99 cm\(^2\)

D. 81cm\(^2\)

6- Which of the following expressions has the greatest value?

A. \( 3^1+12\)

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

C. \( 3^4-60\)

D. \( 3^5-218\)

7- Alvin has 40 apples. Alfred has 15 more apples than Alvin. Baron has one-fifth as many apples as Alfred. How many apples does Baron have?

A. 5

B. 11

C. 55

D. 275

8- Extension review: In the following triangle, find \(α\).

A. \(100^\circ\)

B. \(90^\circ\)

C. \(60^\circ\)

D. \(30^\circ\)

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

A. $283

B. $430

C. $500

D. $550

10- Find the perimeter of the shape in the following figure? (all angles are right angles)

A. 21

B. 22

C. 24

D. 20

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

12- Which expression equivalent to \(x × 92\)?

A. \((x×90)+2\)

B. \(x×9×2\)

C. \((x×90)+(x×2)\)

D. \((x×90)+2\)

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

14- If point A 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

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

16- Extension review: 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. \(x(-5x-19)=-3\)

17- Complete the prime factorization. Write the missing factor as a power of a prime number.
\(450=2^1×3^2×\underline{\qquad}\)

18- Extension review: 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

19- 65 is what percent of 50?

A. \(50 \%\)

B. \(77 \%\)

C. \(130 \%\)

D. \(140 \%\)

20- Extension review: 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. \((-3) × (-7) + 2\)

Answers and explanations

2- C
\(2205÷315=\frac{2205}{315}=\frac{441}{63}=\frac{147}{21}= 7\)

3- B
\(112=22+x \)
Subtract 22 from both sides of the equation. Then:
\(x=112-22=90\)

4- D
Distance that car B travels \(=1.2 ×\) distance that car A travels
=\(1.2×221.5=265.8 \) km

5- D
Use the average of the parallel side lengths times their perpendicular distance: \(A=\frac{8+10}{2}×9=9×9=81\) square centimeters.

6- D
A. \(3^1+12=3+12=15\)
B. \(3^3-3^2=27-9=18\)
C. \(3^4-60=81-60=21\)
D. \(3^5-218=243-218=25\)

7- B
Alfred has \(x\) apple which is 15 apples more than number of apples Alvin owns. Therefore:
\(x-15=40→x=40+15=55\)
Alfred has 55 apples.
Let \(y\) be the number of apples that Baron has. Then: \(y=\frac{1}{5}×55=11\)

8- A
The 150° exterior angle and β are supplementary: they total 180°. Thus \(β=180°-150°=30°\). The triangle’s interior angles also total 180°, so \(α=180°-30°-50°=100°\).

9- C
A 15% decrease leaves 85% of the original price. Let that price be x. Then \(0.85x=425\), so \(x=425÷0.85=500\). The original price was $500.

10- C
Let \(x\) and \(y\) be two sides of the shape. Then:
\(x+1=1+1+1→x=2\)
\(y+6+2=5+4→y+8=9→y=1\)
Then, the perimeter is:
\(1+5+1+4+1+2+1+6+2+1=24\)

11- B
First, put the numbers in order from least to greatest: \(1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 6\)
The Mode of the set of numbers is: 1 and 3 (the most frequent numbers)
The median is: 3 (the number in the middle)

12- C
\(x×92=x×(90+2)=(x×90)+(x×2)\)

13- C
The ratio of pens to pencils is \(3: 5\). Therefore, there are 3 pens out of all 8 pens and pencils. To find the answer, first divide 96 by 8 then multiply the result by 3.
\(96÷8=12→12×3=36\)
There are 36 pens and 60 pencils \((96-36)\). Therefore, 24 more pens should be put in the box to make the ratio \(1: 1\)

14- D
If the value of point A is greater than the value of point B, then the distance between the two points on the number line is: the value of A- the value of B
A. \(-\frac{24}{3}-(-13)=-8+13=5=5\)
B. \(-3-(-\frac{24}{3})=-3+8=5=5\)
C. \(-2-(-\frac{24}{3})=-2+8=6≠5\)

15- B
Compare decimal values: \(3/13≈0.2308\), \(5/14≈0.3571\), \(4/11≈0.3636\), and \(2/5=0.4\). They increase in the order shown in B.

16- B
Substitute \(x=-4\) into each left-hand side.
A: \((-4)(-13)=52\), not 50.
B: \(5(11-16)=5(-5)=-25\), as required.
C: \(3(8+5)=39\), not 49.
D: \((-4)(20-19)=-4\), not -3.

17- \(5^2\), or 25
The known factors have product \(2×3^2=18\). The missing factor is \(450÷18=25=5^2\), so the complete prime factorization is \(450=2×3^2×5^2\).

18- C
Extension method: use the Pythagorean theorem. The squared hypotenuse is \(6^2+8^2=36+64=100\). Its length is therefore 10 cm. The perimeter is \(6+8+10=24\) cm.

19- C
Divide the part by the whole and multiply by 100: \(65÷50×100=130\). Therefore, 65 is 130% of 50.

20- A
Apply multiplication and division before addition.
A: \((5/2)×(-2)=-5\). Then \(-10-8-5=-23\).
B: \(15-36=-21\).
C: \(48÷(-4)=-12\), so \(-10-12=-22\).
D: \(21+2=23\). Only A equals -23.

Choose your next skill

For each mistake, note whether you misunderstood the question, chose the wrong operation, or made a calculation error. Work through one matching lesson, try a few fresh questions, and explain your method aloud before checking the answer.

Use the Grade 6 math hub to choose a lesson or find more focused practice in the Grade 6 Common Core worksheet collection.

The official Common Core Grade 6 overview describes the five Common Core domains: ratios, the number system, expressions and equations, geometry, and statistics and probability. This short set is a sample, not a standards checklist. Ask your school which state assessment applies and where to find its current timing and calculator rules.

Is this an official Common Core test?

No. Common Core describes learning standards; this is Effortless Math’s independent practice. Your state or school determines the assessment and its rules.

How should I use the score?

Use missed questions to select a lesson, not to predict a state-test result. Keep extension items separate if you have not studied them.

What should I study after this set?

Choose one weak skill, review a worked example, and try a new problem without looking at the solution. Return to mixed practice when you can explain the steps.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to divide fractions
• Order of operations (PEMDAS)
• How to solve one-variable equations
• How to find the area of a triangle
• Rules of exponents

Optional Grade 6 book practice

If you want a longer practice routine, review each book’s product page and available preview. Match its topics and difficulty to the skills your child needs before purchasing.

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