FREE 7th Grade MCAS Math Practice Test

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10 Sample 7th Grade MCAS Math Practice Questions

1- What is the slope of a line that is perpendicular to the line \(4x-2y=12\)?

A. \(-2\)

B. 2

C. 4

D. 12

2- Simplify: \(5(x-2y)+(2-x)^2 = (5x-10y)+(4-4x+x^2) = x -10y +4 +x^2\)
When \(x=3\) and \(y=-2\),therefore:
\(x -10y +4 +x^2 =3+20+4+9 =36\)

A. \(-4\)

B. 20

C. 36

D. 50

3- The mean of 50 test scores was calculated as 88. However, it turned out that one of the scores was misread as 94, but it was 69. What is the mean?

A. 85

B. 87

C. 87.5

D. 88.5

4- The width of a box is one-third of its length. The height of the box is one-third of its width. If the length of the box is 27 cm, what is the volume of the box?

A. 81 cm\(^3\)

B. 162 cm\(^3\)

C. 243 cm\(^3\)

D. 729 cm\(^3\)

5- In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km, and 55 km. In the next five hours, it travels at an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours.

A. 425 km

B. 450 km

C. 475 km

D. 500 km

6- The ratio of boys to girls in a school is 2:3. If there are 600 students in a school, how many boys are in the school?____________

7- The perimeter of the trapezoid below is 54 cm. What is its area? _________

8- In 1999, the average worker’s income increased by $2,000 per year starting from a $24,000 annual salary. Which equation represents income greater than average? (\(I =\) income, \(x = \)Number of years after 1999)

A. \(I > 2000 x + 24000\)

B. \(I > -2000 x + 24000\)

C. \(I < -2000 x + 24000\)

D. \(I < 2000 x – 24000\)

9- Which of the following graphs represents the compound inequality?

A. Graph 1

B. Graph 2

C. Graph 3

D. Graph 4

10- A football team had $20,000 to spend on supplies. The team spent $14,000 on new balls. New sports shoes cost $120 each. Which of the following inequalities represents how many new shoes the team can purchase?

A. \( 120x+14,000 ≤20,000 \)

B. \(120x+14,000 ≥20,000\)

C. \(14,000x+12,0 ≤20,000 \)

D. \( 14,000x+12,0 ≥20,000 \)

11- Two dice are thrown simultaneously, what is the probability of getting a sum of 6 or 9?

A. \(\frac{1}{3}\)

B. \(\frac{1}{4}\)

C. \(\frac{1}{6}\)

D. \(\frac{11}{36}\)

12- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool? __________

13- Which graph corresponds to the following inequalities?
\(y≤ x + 4\)
\(2x + y ≤ – 4\)

A.

B.

C.

D.

14- A bank is offering \(4.5\%\) simple interest on a savings account. If you deposit $8,000, how much interest will you earn in five years?

A. $360

B. $720

C. $1800

D. $3600

15- A card is drawn at random from a standard 52, card deck, what is the probability that the card is of Hearts? (The deck includes 13 of each suit: clubs, diamonds, hearts, and spades)

A. \(\frac{1}{3}\)

B. \(\frac{1}{4}\)

C. \(\frac{1}{6}\)

D. \(\frac{1}{52}\)

16- How long does a 420, mile trip take moving at 50 miles per hour (mph)?

A. 4 hours

B. 6 hours and 24 minutes

C. 8 hours and 24 minutes

D. 8 hours and 30 minutes

17- 11 yards 6 feet and 4 inches equals how many inches?

A. 388

B. 468

C. 472

D. 476

18- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) – 200 (0.30)\)

C. \((200) (0.15) – (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

19- Which of the following points lies on the line \(2x + 4y = 10\)

A. \((2, 1)\)

B. \((–1, 3)\)

C. \((–2, 2)\)

D. \((2, 2)\)

20- \(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = \)?

A. \(-30\)

B. \(-20\)

C. \(-10\)

D. 0

Best 7th Grade MCAS Math Workbook Resource for 2026

Answers:

2- C
Simplify: \(5(x-2y)+(2-x)^2 = (5x-10y)+(4-4x+x^2) = x -10y +4 +x^2\)
When \(x=3\) and \(y=-2\),therefore:
\(x -10y +4 +x^2 =3+20+4+9 =36\)

3- C
\(average (mean) = \frac{sum \space of \space terms }{number \space of \space terms}⇒ 88 = \frac{sum \space of \space terms}{50}⇒ sum = 88 × 50 = 4400\)
The difference of 94 and 69 is 25. Therefore, 25 should be subtracted from the sum.
\(4400 – 25 = 4375\)
\(mean =\frac{sum \space of \space terms}{number \space of \space terms}⇒ mean = \frac{4375 }{50}= 87.5\)

4- D
If the length of the box is 27, then the width of the box is one-third of it, 9, and the height of the box is 3 (one-third of the width). The volume of the box is:
\(V = lwh = (27) (9) (3) = 729\)

5- C
Add the first 5 numbers. \(40 + 45 + 50 + 35 + 55 = 225\)
To find the distance traveled in the next 5 hours, multiply the average by the number of hours.
\(Distance = Average × Rate = 50 × 5 = 250\)
Add both numbers.
\(250 + 225 = 475\)

6- 240
The ratio of boys to girls is 2:3. Therefore, there are 2 boys out of 5 students. To find the answer, first divide the total number of students by 5, then multiply the result by 2.
\(600 ÷ 5 = 120 ⇒ 120 × 2 = 240\)

7- 130
The perimeter of the trapezoid is 54 cm.
Therefore, the missing side (high) is \(= 54 – 18 – 12 – 14 = 10\)
Area of a trapezoid:
\( A = \frac{1}{2}h (b_1 + b_2) = \frac{1}{2}(10) (12 + 14) = 130\)

8- A
Let \(x\) be the number of years. Therefore, $2,000 per year equals 2000\(x\).
Starting from $24,000 annual salary means you should add that amount to 2000\(x\).
Income more than that is:
\(I > 2000x + 24000\)

9- D
Solve for \(x\).
\(-2≤2x-4<8 \)⇒ (add 4 all sides)\( -2+4≤2x-4+4<8+4 \)
\(⇒ 2≤2x<12 \)
⇒ (divide all sides by 2)\( 1≤x<6\)
\(x\) is between 1 and 6.

10- A
Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase 120 \(x\).
The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most.
Now, write the inequality:
\(120x+14.000 ≤20.000\)

11- B
For Sum 6: (1 & 5) and (5 & 1), (2 & 4) and (4 & 2), (3 & 3), so we have 5 options.
For sum 9: (3 & 6) and (6 & 3), (4 & 5) and (5 & 4), we have 4 options.
To get a sum of 6 or 9 for two dice: \(5+4=9\)
Since we have \(6 × 6 = 36\) total options, the probability of getting a sum of 6 and 9 is 9 out of 36 or \(\frac{1}{4}\).

12- 8
Use the formula for rectangular prism volume.
\(V = (length) (width) (height) ⇒ 2000 = (25) (10) (height)\)
\( ⇒ height = 2000 ÷ 250 = 8\)

13- A
For each option, choose a point in the solution part and check it on both inequalities.
A. Point \((–4, –4)\) is in the solution section. Let’s check the point in both inequalities.
\(-4 ≤ – 4 + 4, \space It \space works\)
\(2 (–4) + (–4) ≤ –4 ⇒ – 12 ≤ – 4\) it works (this point works in both)
B. Let’s choose this point \((0, 0)\)
\(0 ≤ 0 + 4, \space It \space works\)
\(2 (0) + (0) ≤ –4, \space \space That’s \space not \space true!\)
C. Let’s choose this point \((–5, 0)\)
\(0 ≤ -5 + 4, \space That’s \space not \space true!\)
D. Let’s choose this point \((0, 5)\)
\(5 ≤ 0 + 4, \space That’s \space not \space true!\)

14- C
Use a simple interest formula:
I=prt
(I = interest, p = principal, r = rate, t = time)
\(I=(8000)(0.045)(5)=1800\)

15- B
The probability of choosing a Hearts is \(\frac{13}{52}=\frac{1}{4}\)

16- C
Use the distance formula:
\(Distance = Rate × time ⇒ 420 = 50 × T\)
Divide both sides by 50.
\(\frac{420}{50} = T ⇒ T = 8.4 \space hours\)
Change hours to minutes for the decimal part.
\(0.4 \space hours = 0.4 × 60 = 24 \space minutes\)

17- C
\(11 × 36 + 6 × 12 + 4 = 472\)

18- D
To find the discount, multiply the number by (\(100\% – \)Rate of discount).
Therefore, for the first discount, we get:
\((200) (100\% – 15\%) = (200) (0.85) = 170\)
For the next \(15%\) discount: \((200) (0.85) (0.85)\)

19- B
Input \((-1, 3)\) in the \(2x + 4y = 10\) formula instead of \(x\) and y. So we have:
\( 2(-1) + 4(3) = 10\)
\(-2 + 12 = 10\)

20- A
Use PEMDAS (order of operation):
\(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = 5 + 8 × (–2) – [4 + 110] ÷ 6 = 5 + 8 × (–2) – [114] ÷ 6 = 5 + (–16) – 19 = 5 + (–16) – 19 = –11 – 19 = –30\)

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Recommended EffortlessMath Books

For more structured prep alongside this practice test, the Common Core Mathematics Workbook for Grade 7 covers every MCAS topic with step-by-step worked examples. For practice with the kind of multi-step word problems that appear on the open-response section, see the Mastering Grade 7 Math Word Problems.

Frequently Asked Questions

What grades take the MCAS?

In Massachusetts, students take MCAS English and math every year from grade 3 through grade 8, plus science in grades 5 and 8. In high school, students take the ELA and math tests in grade 10 and a science and technology test, often in grade 9 or 10. So 7th grade MCAS math is one of the last middle school checkpoints before algebra-heavy 8th grade.

Do 9th graders take MCAS?

Many 9th graders do take one MCAS test: the high school science and technology/engineering test, often in biology or introductory physics after finishing that course. The high school ELA and math MCAS tests are usually taken in grade 10. For a 7th grader, that means two more years of middle school math MCAS before the high school tests begin.

How can I help my 7th grader with math?

Ask your 7th grader to explain how they solved a problem, because talking through steps shows exactly where a mistake happens. Practice proportional reasoning with real life, like unit prices at the store, and review negative number rules often. Try a multi-step problem together, such as a box 27 cm long, 9 cm wide and 3 cm high having a volume of 729 cm³.

Are there free grade 7 MCAS math practice exams?

Yes. Massachusetts DESE posts released MCAS questions and online practice tests, and a free 20-question grade 7 practice test with answers adds extra review. Have your child work the set in one sitting, then check each miss. Topics that keep coming up, such as percent change, equations or circle area, are the ones to practice before the spring test.

Related EffortlessMath Lessons

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

• Proportional ratios
• How to add and subtract integers
• How to solve one-step equations
• Percent of change (resource currently unavailable)
• How to find the volume of a prism