FREE 6th Grade MCAS Math Practice Test

The grade 6 MCAS mathematics test covers ratios and proportional relationships, the number system, expressions and equations, and geometry with statistics. These twenty practice questions cover all four, each with a full worked solution so a missed question points straight at the topic to revise.

Grade 6 MCAS math practice questions

Twenty questions covering the four reporting categories the Massachusetts grade 6 test assesses: ratios and proportional relationships, the number system, expressions and equations, and geometry with statistics. Work them on paper first. Worked explanations follow.

1. What is the value of \( \frac{3}{4} \div \frac{2}{9} \)?
   A. \( \frac{1}{6} \)   B. \( \frac{2}{3} \)   C. \( \frac{27}{8} \)   D. \( \frac{8}{27} \)
2. A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of sugar are needed for 12 cups of flour?
   A. 6   B. 8   C. 18   D. 24
3. Solve for \( x \): \( 112 = 22 + x \)
   A. 80   B. 90   C. 100   D. 134
4. Car A travels 221.5 km. Car B travels 1.2 times as far as car A. How far does car B travel?
   A. 184.6 km   B. 221.5 km   C. 243.7 km   D. 265.8 km
5. A trapezoid has a perimeter of 38. Its two parallel sides measure 8 and 10, and one of its other sides measures 11. The remaining side is perpendicular to the parallel sides. What is the area of the trapezoid?
   A. 45   B. 72   C. 76   D. 81
6. Which of the following has a value of 25?
   A. \( 3^1 + 12 \)   B. \( 3^3 – 3^2 \)   C. \( 3^4 – 60 \)   D. \( 3^5 – 218 \)
7. Alfred has 15 more apples than Alvin, and Alvin has 40 apples. Baron has one fifth as many apples as Alfred. How many apples does Baron have?
   A. 8   B. 11   C. 15   D. 55
8. In the figure, \( \beta \) and an angle of \( 150^\circ \) lie on a straight line. \( \beta \) is one angle of a triangle whose other two angles are \( \alpha \) and \( 50^\circ \). What is \( \alpha \)?
   A. \( 100^\circ \)   B. \( 80^\circ \)   C. \( 50^\circ \)   D. \( 30^\circ \)
9. The price of a laptop is decreased by 15% to $425. What was the original price?
   A. $440   B. $470   C. $500   D. $520
10. A rectangle 7 units long and 5 units wide has a square of side 2 units removed from one corner, leaving a six-sided figure. What is the perimeter of that figure?
    A. 20   B. 22   C. 24   D. 28
11. Find the mode and the median of these numbers: 3, 6, 1, 2, 4, 1, 3, 6, 5, 3, 1
    A. Mode: 3, Median: 1   B. Mode: 1 and 3, Median: 3   C. Mode: 1, Median: 4   D. Mode: 6, Median: 3
12. Which expression is equivalent to \( x \times 92 \)?
    A. \( (x \times 9) + (x \times 2) \)   B. \( (x + 90) \times (x + 2) \)   C. \( (x \times 90) + (x \times 2) \)   D. \( (x \times 90) \times (x \times 2) \)
13. A box holds pens and pencils in the ratio 3 : 5, and there are 96 items in total. How many more pens must be added to make the ratio 1 : 1?
    A. 12   B. 18   C. 24   D. 36
14. On a number line, which pair of points is exactly 5 units apart?
    A. \( -\frac{24}{3} \) and \( -13 \)   B. \( -3 \) and \( -\frac{24}{3} \)   C. \( -2 \) and \( -\frac{24}{3} \)   D. Both A and B
15. Which of these fractions is the second smallest?
    A. \( \frac{3}{13} \)   B. \( \frac{5}{14} \)   C. \( \frac{4}{11} \)   D. \( \frac{2}{5} \)
16. If \( x = -4 \), which equation is true?
    A. \( x(3x – 1) = 50 \)   B. \( 5(11 – x^2) = -25 \)   C. \( 3(-2x + 5) = 49 \)   D. \( x(-5x – 19) = -3 \)
17. The prime factorization of 450 is \( 2 \times 3 \times 3 \times 5 \times \underline{\hspace{1cm}} \). What is the missing prime factor? (Write your answer.)
18. A right triangle has legs of 6 and 8. What is its perimeter?
    A. 14   B. 20   C. 24   D. 48
19. 65 is what percent of 50?
    A. 65%   B. 77%   C. 130%   D. 325%
20. Which expression has the least value?
    A. \( -10 + (-8) + \left(\frac{5}{2}\right) \times (-2) \)   B. \( 5 \times 3 + (-2) \times 18 \)   C. \( -10 + 6 \times 8 \div (-4) \)   D. \( (-3) \times (-7) + 2 \)

Answers and explanations

1- C
Dividing by a fraction means multiplying by its reciprocal: \( \frac{3}{4} \times \frac{9}{2} = \frac{27}{8} \).

2- B
The ratio of flour to sugar is \( 3 : 2 \). Twelve cups of flour is 4 times 3 cups, so the sugar is 4 times 2 cups: 8 cups.

3- B
\(112=22+x \)
Subtract 22 from both sides of the equation. Then:
\(x=112-22=90\) For additional educational resources, visit the U.S. Department of Education website.

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: \(A = \frac{1}{2} h (b_1 + b_2) = \frac{1}{2} (9) (8 + 10) = 81\)

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 the 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
Angles on a straight line are supplementary, so they 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:
\(85 \% \space of \space x=425⇒ 0.85x=425 ⇒ x=425÷0.85=500\)

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10- C
Cutting a square corner out of a rectangle does not change the perimeter: the two removed edges are replaced by two new edges of the same total length. So the perimeter is still \(2(7+5)=24\).

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)
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 of 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. \(5×3+(-2)×18=15+(-36)=-21\)
C. \(-10+6×8÷(-4)=-10+48÷(-4)=-10-12=-22\)
D. \((-3)× (-7)+ 2=21+2=23\)

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