FREE 6th Grade PARCC Math Practice Test

PARCC reports grade 6 mathematics in four categories: ratios and proportional relationships, the number system, expressions and equations, and geometry with statistics. These twenty practice questions cover all four, with reasoning items alongside straight computation and a worked solution for every one.

Grade 6 PARCC math practice questions

Twenty questions across the four PARCC reporting categories for grade 6: ratios and proportional relationships, the number system, expressions and equations, and geometry with statistics. Several ask for reasoning rather than a single computation, which is how PARCC items are built. Worked explanations follow.

1. A machine fills 8 bottles every 5 seconds. At that rate, how many bottles does it fill in one minute?
   A. 40   B. 64   C. 96   D. 480
2. What is \( \frac{5}{6} \div \frac{10}{3} \) in simplest form?
   A. \( \frac{1}{4} \)   B. \( \frac{25}{9} \)   C. \( \frac{50}{18} \)   D. 4
3. Which number has the greatest absolute value?
   A. \( -12 \)   B. \( 9 \)   C. \( -7.5 \)   D. \( 11 \)
4. A rectangular garden is 14 m long and 9 m wide. A path 1 m wide runs around the outside. What is the area of the path alone?
   A. 46 m²   B. 48 m²   C. 50 m²   D. 126 m²
5. Simplify: \( 4(2x + 3) – 5x \)
   A. \( 3x + 3 \)   B. \( 3x + 12 \)   C. \( 13x + 12 \)   D. \( 8x + 7 \)
6. A jacket is marked down 30% to $63. What was the original price?
   A. $81.90   B. $90   C. $93   D. $210
7. Which point on the coordinate plane is the reflection of \( (-4, 3) \) across the x-axis?
   A. \( (4, 3) \)   B. \( (-4, -3) \)   C. \( (4, -3) \)   D. \( (3, -4) \)
8. The mean of five numbers is 18. Four of them are 12, 20, 15 and 23. What is the fifth?
   A. 17.5   B. 20   C. 22   D. 30
9. A triangular prism has a triangular base with area 15 cm² and a height of 9 cm. What is its volume?
   A. 24 cm³   B. 45 cm³   C. 67.5 cm³   D. 135 cm³
10. Solve for \( n \): \( \frac{n}{6} = \frac{15}{18} \)
    A. 3   B. 5   C. 9   D. 45
11. Which list is ordered from least to greatest?
    A. \( -3, -\frac{1}{2}, 0.4, \frac{3}{4} \)   B. \( -\frac{1}{2}, -3, 0.4, \frac{3}{4} \)   C. \( 0.4, \frac{3}{4}, -\frac{1}{2}, -3 \)   D. \( -3, 0.4, -\frac{1}{2}, \frac{3}{4} \)
12. A store sells 3 notebooks for $7.50. At the same unit price, what do 8 notebooks cost?
    A. $18.75   B. $20.00   C. $22.50   D. $24.00
13. What is the greatest common factor of 48 and 72?
    A. 6   B. 12   C. 24   D. 144
14. A number \( x \) satisfies \( x – 7 \le 12 \). Which statement describes every solution?
    A. \( x \) is at most 19   B. \( x \) is at least 19   C. \( x \) is at most 5   D. \( x \) is exactly 19
15. In a survey of 200 students, 35% chose soccer. How many students chose something else?
    A. 65   B. 70   C. 130   D. 165
16. The dot plot of a class’s test scores is symmetric with a single peak at 82. Which measure of center best summarizes the data?
    A. The mode, because the data is symmetric   B. The mean, because the data is symmetric with no outliers   C. The median, because the data is skewed   D. The range, because it uses every value
17. Evaluate \( 2^3 + 4 \times (9 – 6)^2 \)
    A. 44   B. 36   C. 108   D. 25
18. A recipe needs \( 2\frac{1}{4} \) cups of milk. Maria is making one third of the recipe. How much milk does she need?
    A. \( \frac{3}{4} \) cup   B. \( 1\frac{1}{4} \) cups   C. \( 6\frac{3}{4} \) cups   D. \( \frac{1}{3} \) cup
19. A cube has a surface area of 96 cm². What is the length of one edge? (Write your answer.)
20. Two taxi companies charge differently. Company A charges $3 plus $2 per mile. Company B charges $5 plus $1.50 per mile. For how many miles do the two cost the same?
    A. 2   B. 3   C. 4   D. 8

Answers and explanations

1- C
One minute is 60 seconds, which is \( 60 \div 5 = 12 \) intervals of five seconds. Each interval fills 8 bottles, so \( 12 \times 8 = 96 \).

2- A
Dividing by a fraction means multiplying by its reciprocal: \( \frac{5}{6} \times \frac{3}{10} = \frac{15}{60} = \frac{1}{4} \).

3- A
Absolute value is distance from zero, so the sign is dropped: \( |-12| = 12 \), \( |9| = 9 \), \( |-7.5| = 7.5 \), \( |11| = 11 \). Twelve is the largest.

4- C
The garden is \( 14 \times 9 = 126 \) m². The path adds 1 m on every side, so the outer rectangle is \( 16 \times 11 = 176 \) m². The path alone is \( 176 – 126 = 50 \) m².

5- B
Distribute first: \( 4(2x + 3) = 8x + 12 \). Then \( 8x + 12 – 5x = 3x + 12 \).

6- B
A 30% markdown leaves 70% of the original price. So \( 0.70x = 63 \) and \( x = 63 \div 0.70 = 90 \).

7- B
Reflecting across the x-axis keeps the x-coordinate and changes the sign of the y-coordinate: \( (-4, 3) \) becomes \( (-4, -3) \).

8- B
Five numbers with a mean of 18 have a total of \( 5 \times 18 = 90 \). The four known values total \( 12 + 20 + 15 + 23 = 70 \), so the fifth is \( 90 – 70 = 20 \).

9- D
The volume of any prism is the area of its base times its height: \( 15 \times 9 = 135 \) cm³. The base is already given as an area, so there is no need to halve anything.

10- B
\( \frac{15}{18} \) simplifies to \( \frac{5}{6} \). Since the denominators now match, \( n = 5 \).

11- A
As decimals the values are \( -3, -0.5, 0.4, 0.75 \), which is increasing. Negative numbers come first, and \( -3 \) is further from zero than \( -\frac{1}{2} \), so it is smaller.

12- B
The unit price is \( 7.50 \div 3 = 2.50 \) per notebook, so eight cost \( 8 \times 2.50 = 20.00 \).

13- C
\( 48 = 2^4 \times 3 \) and \( 72 = 2^3 \times 3^2 \). Take the lowest power of each shared prime: \( 2^3 \times 3 = 24 \).

14- A
Adding 7 to both sides gives \( x \le 19 \). The symbol \( \le \) allows 19 itself, so “at most 19” describes every solution.

15- C
35% of 200 is \( 0.35 \times 200 = 70 \) students. The rest is \( 200 – 70 = 130 \). Answering 70 is the common trap: that is the number who chose soccer, not the number who did not.

16- B
The mean is the better summary when a distribution is symmetric and has no outliers, because every value contributes and nothing pulls it off center. The median is preferred for skewed data, and the range measures spread rather than center.

17- A
Work inside the brackets first: \( 9 – 6 = 3 \). Then the exponents: \( 2^3 = 8 \) and \( 3^2 = 9 \). Then multiply: \( 4 \times 9 = 36 \). Finally add: \( 8 + 36 = 44 \).

18- A
One third of \( 2\frac{1}{4} \) is \( \frac{9}{4} \div 3 = \frac{9}{4} \times \frac{1}{3} = \frac{9}{12} = \frac{3}{4} \) cup.

19- 4 cm
A cube has six identical square faces, so \( 6s^2 = 96 \), giving \( s^2 = 16 \) and \( s = 4 \) cm.

20- C
Set the two costs equal: \( 3 + 2m = 5 + 1.5m \). Subtract \( 1.5m \) from both sides to get \( 3 + 0.5m = 5 \), then subtract 3 to get \( 0.5m = 2 \), so \( m = 4 \) miles. At 4 miles both companies charge $11.

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