Top 10 6th Grade MCAS Math Practice Questions

1- Which of the following is equivalent to \(5(12x-16)\)?

A. \(60x-16\)

B. \(17x-21\)

C. \(12x-80\)

D. \(60x-80\)

2- Which ratio is equivalent to \(91:21\)?

A. \(13:3\)

B. \(9:2\)

C. \(7:3\)

D. \(21:91\)

3- Solve for \(x\) in the equation \(-60=115-x\).

A. \(x=175\)

B. \(x=55\)

C. \(x=-55\)

D. \(x=-175\)

4- Solve the inequality \(-8 \le 5x-8 < 2\).

A. \(-1 \le x < 2\)

B. \(0 \le x < 2\)

C. \(0 < x \le 2\)

D. \(-2 \le x < 0\)

5- The ratio of boys to girls in a school is 4:5. If there are 765 students in the school, how many boys are in the school?

A. 612

B. 510

C. 425

D. 340

6- Martin earns $20 an hour. Which of the following inequalities represents the amount of time Martin needs to work per day to earn at least $100 per day?

A. \(20t≥100\)

B. \(20t≤100\)

C. \(20+t≥100\)

D. \(20+t≤100\)

7- \((55+5)÷12\) is equivalent to …

A. \(60÷3.4\)

B. \( \frac{55}{12}+5\)

C. \((2×2×3×5)÷(3×4)\)

D. \( (2×2×3×5)÷3+4\)

8- What is the value of the expression \(6(2x-3y)+(3-2x)^2\), when \(x=2 \) and \(y=-1\)?

A. \(-23\)

B. 41

C. 43

D. 49

9- Round \(\frac{215}{7}\) to the nearest tenth.

A. 31

B. 30.8

C. 30.7

D. 30

10- A chemical solution contains \(6\%\) alcohol. If there is 45 ml of alcohol, what is the volume of the solution?

A. 270 ml

B. 420 ml

C. 750 ml

D. 1,200 ml

Best 6th Grade MCAS Math Prep Resource for 2026

MCAS Grade 6 Math Full Study Guide Comprehensive Review + Practice Tests + Online Resources

Download

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

Answers:

2- A
\(91: 21 = 13: 3\)
\(13×7=91\)
And \( 3×7=21\)

3- A
\(-60 = 115 – x\)
First, subtract 115 from both sides of the equation. Then:
\(-60 – 115=115 – 115- x→-175 = – x\)
Multiply both sides by \((-1)\):
\(→x = 175\)

4- B
\(-8≤5x-8<2 →\) (add 8 all sides)\(-8+8≤5x-8+8<2+8 →0≤5x<10→\) (divide all sides by 5) \(0≤x<2\)

5- D
The ratio of boys to girls is 4:5. Therefore, there are 4 boys out of 9 students. To find the answer, first, divide the total number of students by 9, then multiply the result by 4.
\(765 ÷ 9 = 85 ⇒ 85 × 4 = 340\)

6- A
For one hour he earns $20, then for t hours he earns $20t. If he wants to earn at least $100, therefore, the number of working hours multiplied by 20 must be equal to 100 or more than 100.
\(20t≥100\)

7- C
\((55+5)÷(12)=(60)÷(12)\)
The prime factorization of 60 is: \(2×2×3×5 \)
The prime factorization of 12 is: \( 3×4 \)
Therefore: \((60)÷(12)=(2×2×3×5)÷(3×4)\)

8- C

Plug in the value of \(x\) and \(y\) and use the order of operations rule.
\(x=2\) and \(y=-1\)
\(6(2x-3y)+(3-2x)^2=6(2(2)-3(-1))+(3-2(2))^2=6(4+3)+(-1)^2 = 42+1=43\)

9- C
\(\frac{215}{7} ≅ 30.71 ≅ 30.7\)

10- C
\(6\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.
Then: \(6\% \space of \space x = 45 \space ml ⇒ 0.06 x = 45 ⇒ x = 45 ÷ 0.06 = 750\)

Looking for the best resource to help you succeed on the Grade 6 MCAS Math test?

The Most Comprehensive Review for 6th-Grade Students

Recommended EffortlessMath Books

For a workbook that pairs with this page, Mastering Grade 6 Math walks your sixth grader through every grade-6 topic with worked examples and plenty of practice. For more story-problem reps, Mastering Grade 6 Math Word Problems is the matching word-problem book.

Frequently Asked Questions

What’s on the MCAS Grade 6 math test?

Five domains: Ratios and Proportional Relationships, The Number System (including fraction division), Expressions and Equations, Geometry (area, surface area, volume), and Statistics and Probability. Massachusetts uses a Common Core-aligned framework, so the content is similar to most state tests but with slightly stronger emphasis on writing about reasoning.

How long is the MCAS Grade 6 math test?

Two sessions, untimed within a reasonable window – roughly 90 minutes each. About 40 questions total: multiple choice, multi-select, drag-and-drop, equation editor, and short open-response items. Most sixth graders finish each session in 45-60 minutes.

Is MCAS the same as Common Core?

Very close. Massachusetts has its own framework, but it’s built on the Common Core State Standards with extra clarifications. Common Core practice books transfer almost perfectly. The main MCAS-specific feature is a couple of constructed-response questions that ask your child to explain reasoning in writing – practice this with longer answers.

How do I work with ratios at grade 6?

Three forms: \(3:4\), \(3 \text{ to } 4\), and \(\dfrac{3}{4}\). To find an equivalent ratio, multiply or divide both parts by the same number: \(3:4 = 6:8 = 9:12\). Word problems often ask you to scale up or down – if 2 cups of flour serve 4 people, then 5 cups serve 10 people (multiply both by 2.5).

How do I divide a fraction by a fraction?

Multiply by the reciprocal. \(\dfrac{3}{4} \div \dfrac{2}{5} = \dfrac{3}{4} \times \dfrac{5}{2} = \dfrac{15}{8} = 1\dfrac{7}{8}\). MCAS likes to ask “how many \(\dfrac{1}{4}\)-cups are in \(\dfrac{3}{4}\) cup?” The answer is \(\dfrac{3}{4} \div \dfrac{1}{4} = 3\) – three quarter-cups fit in three-quarters of a cup.

What expressions and equations show up at grade 6?

Writing and evaluating expressions like \(3x + 5\), solving one-step equations like \(x + 7 = 12\), and translating word problems into equations. Example: “Five more than twice a number is 17” becomes \(2x + 5 = 17\), so \(x = 6\). Practice writing the equation FROM the words – that’s where points are won.

How do you find the area of polygons on the coordinate plane?

Plot the points, connect them, and use the familiar formulas. For a triangle with vertices \((0,0)\), \((4,0)\), \((0,3)\): the base is 4, height is 3, area is \(\dfrac{1}{2} \times 4 \times 3 = 6\) square units. For weird shapes, break them into rectangles and triangles.

How do I find the volume of a rectangular prism?

Multiply length times width times height: \(V = l \times w \times h\). For a box with dimensions \(2 \times 3 \times 4\), volume is \(24\) cubic units. MCAS grade 6 also asks about prisms with fractional edges – \(V = \dfrac{1}{2} \times 2 \times 3 = 3\) cubic units works the same way.

How should we use these 10 questions for practice?

First, your child works each one without help. Then read the solutions together, focusing on the reasoning. Two days later, redo any missed question from scratch – if it sticks, you’re good. If not, click into the related lesson first. Spaced practice teaches more than long cram sessions.

Where can we get more MCAS Grade 6 practice?

EffortlessMath has MCAS Grade 6 full-length practice tests, the Mastering Grade 6 Math workbook, and a focused Grade 6 Math Word Problems book. The Related Lessons section below links to step-by-step explanations of the biggest sixth-grade skills.

Related EffortlessMath Lessons

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

• How to find the percent of a number
• How to solve percent of change
• How to add and subtract fractions
• How to multiply fractions
• How to solve multi-step word problems