Top 10 6th Grade Common Core Math Practice Questions
C.
D.
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 Common Core Math Prep Resource for 2026
Answers:
1- D
\(5(12x-16)=(5×12x)-(5×16)=(5×12)x-(5×16)=60x-80\)
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 boy 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 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: \(6\% \space of \space x = 45 \space ml ⇒ 0.06 x = 45 ⇒ x = 45 ÷ 0.06 = 750\)
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