FREE 6th Grade Common Core Math Practice Test

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Common Core Grade 6 Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Common Core Math Test

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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- The perimeter of the trapezoid below is 38. 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- Alfred has \(x\) apples. Alvin has 40 apples, which is 15 apples less than several apples Alfred owns. If Baron has \(\frac{1}{5}\) times as many apples as Alfred has. How many apples does Baron have?

A. 5

B. 11

C. 55

D. 275

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

A. \(100^\circ\)

B. \(90^\circ\)

C. \(60^\circ\)

D. \(30^\circ\)

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

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- 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- What is the missing prime factor of number 450?
\(450=2^1×3^2×…\) _________

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

19- 65 is what percent of 50?

A. \(50 \%\)

B. \(77 \%\)

C. \(130 \%\)

D. \(140 \%\)

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. \((-3) × (-7) + 2\)

Best 6th Grade Common Core Math Workbook Resource for 2026

Answers:

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
The perimeter of the trapezoid is 38.
Therefore, the missing side (height) is \(= 38 – 8 – 10 – 11 = 9\)
Area of the trapezoid: \(A = \frac{1}{2} h (b_1 + b_2) = \frac{1}{2}1 (9) (8 + 10) = 81\)

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
Complementary angles add up to 180 degrees.
\( β+150^\circ=180^\circ→β=180^\circ-150^\circ=30^\circ\)
The sum of all angles in a triangle is 180 degrees. Then:
\(α+β+50^\circ=180^\circ→α+30^\circ+50^\circ=180^\circ\)
\(→α+80^\circ=180^\circ→α=180^\circ-80^\circ=100^\circ\)

9- C
Let \(x\) be the original price.
If the price of a laptop is decreased by \(15\%\) to $425, then:
\(85 \% \space of \space x=425⇒ 0.85x=425 ⇒ x=425÷0.85=500\)

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 dived 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
\(\frac{3}{13}≅0.23, \frac{5}{14}≅0.357, \frac{4}{11}≅0.36, \frac{2}{5}=0.4\)

16- B
Plug the value of \(x\) in the equations. \(x = -4\), then:
A.\(x(3x-1)=50→-4(3(-4)-1)=-4(-12-1)=-4(-13)=52≠50\)
B. \(5(11-x^2 )=-25→5(11-(-4)^2 )= 5(11-16)=5(-5)=-25\)
C. \(3(-2x+5)=49→3(-2(-4)+5)=3(8+5)=39≠49\)
D. \(x(-5x-19)=-3→-4(-5(-4)-19=-4(20-19)=-4≠-3\)

17- 5
Let \(x\) be the missing prime factor of 450.
\(450= 2 × 3 × 3 × x ⇒ x =\frac{450}{18} ⇒ x = 25=5×5\)

18- C
Use the Pythagorean theorem to find the hypotenuse of the triangle.
\(a^2+b^2=c^2→6^2+8^2=c^2→36+64=c^2→100=c^2→c=10\)
The perimeter of the triangle is: \(6+8+10=24\)

19- C
Use the percent formula:
\(Part = \frac{percent}{100} × whole\)
\(65= \frac{percent}{100} × 50⇒ 65 = \frac{percent ×50}{100}⇒ 65=\frac{percent ×5}{10}\)
Multiply both sides by 10.
\(650 =percent ×5, \space divide \space both \space sides \space by \space 5.\)
130 = percent
The answer is \(130\%\)

20- A
Let’s check the options provided.
A. \(-10+(-8)+ (\frac{5}{2})×(-2)=-10+(-8)+(-5)=-10-13=-23\)
B. \(5×3+(-2)×18=15+(-38)=-21\)
C. \(-10+6×8÷(-4)=-10+48÷(-4)=-10-12=-22\)
D. \((-3)× (-7)+ 2=21+2=23\)

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Recommended EffortlessMath Books

For a workbook your child can use alongside this practice test, the 6th Grade Common Core Math for Beginners walks through every grade-6 CCSS standard with worked examples. For full prep with multiple timed practice tests, see the 6th Grade Common Core Math Test Prep Bundle.

Frequently Asked Questions

What’s on the 6th grade Common Core math test?

Five domains: Ratios and Proportional Relationships (about 18%), The Number System (about 25%), Expressions and Equations (about 30%), Geometry (about 14%), and Statistics and Probability (about 13%). Specific skills include unit rates, dividing fractions, working with negative numbers, evaluating expressions, one-variable equations and inequalities, area of triangles and quadrilaterals, and reading box plots.

How long is the real 6th grade Common Core math test?

That depends on your state. Most state assessments built on Common Core (like Smarter Balanced or PARCC-derived tests) run 2 to 3 hours total across multiple sessions, often spread over two days. This practice test is shorter (20 questions) and works best as a diagnostic, not a full simulation.

Is a calculator allowed on grade 6 Common Core math?

Generally no. Common Core grade 6 expects students to perform arithmetic with fractions, decimals, and integers by hand. Some states allow a basic calculator on a small calculator-permitted section, but most of the test is calculator-free. Check your state’s test portal for the exact policy.

How do I know which Common Core standards my child needs?

The grade 6 Common Core math standards are organized as 6.RP (Ratios), 6.NS (Number System), 6.EE (Expressions and Equations), 6.G (Geometry), and 6.SP (Statistics and Probability). Your state’s department of education site lists the full set of grade 6 standards your child is held to.

How long should we study for the 6th grade Common Core math test?

If your child is on grade level, 3 to 5 weeks of consistent practice (15 to 25 minutes per day) closes most gaps. If math has been a struggle, 8 to 12 weeks works better. Start with this diagnostic, then drill the weakest domain before moving to timed full-length practice.

What’s the hardest topic on the 6th grade Common Core math test?

For most students, dividing fractions by fractions (6.NS.1) and writing/solving one-variable equations from word problems (6.EE.7) are the two biggest stumbling blocks. Ratios and unit rates also trip up students who haven’t seen the topic before grade 6.

How do I help my child review fractions for grade 6?

Make sure your child can: add and subtract fractions with unlike denominators, multiply fractions and mixed numbers, and (the new grade 6 skill) divide fractions by fractions using the rule \(a/b \div c/d = a/b \times d/c\). Work 5 to 10 problems on each operation type, then mix them up.

Does the 6th grade test cover negative numbers?

Yes. Standard 6.NS.5-8 introduces negative numbers, the number line, ordering rational numbers, and working in all four quadrants of the coordinate plane. This is the first grade where students see negatives, so it’s often unfamiliar territory.

What statistics topics show up on the 6th grade Common Core math test?

Mean, median, mode, range, mean absolute deviation, and reading dot plots, histograms, and box plots. The test also asks students to identify whether a question is statistical (one with variability in answers) versus a single-answer math question.

Where can I find more 6th grade Common Core math practice?

EffortlessMath has the 6th Grade Common Core Math for Beginners workbook covering every grade-6 CCSS standard and the 6th Grade Common Core Math Test Prep Bundle with multiple full-length practice tests and answer explanations.

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