Top 10 Grade 6 Common Core Math Practice Questions

Top 10 Grade 6 Common Core Math Practice Questions

Helping your 6th-grade student prepare for the Common Core Math test? The best way to prepare your student for the Common Core Math test is to work through as many Math practice questions as possible. Here are the top 10 Grade 6 Common Core Math practice questions to help your student reviews the most important Grade 6 Common Core Math concepts. These Grade 6 Common Core Math practice questions are designed to cover mathematics concepts and topics that are found on the actual test. The questions have been fully updated to reflect the latest 2020 Grade 6 Common Core guidelines. Answers and full explanations are provided at the end of the post.

Help your child start his/her Grade 6 Common Core Math test prep journey right now with these sample Grade 6 Common Core Math questions.

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Grade 6 Common Core Math Practice Questions

1- Which expression is equivalent to \(5(12x-16)\)?

☐A. \(-20\)

☐B. \(-20x\)

☐C. \(60x – 16\)

☐D. \(60x – 80\)

2- To produce a special concrete, for every 13 kg of cement, 3 liters of water is required. Which of the following ratios is the same as the ratio of cement to liters of water?

☐A. 91: 21

☐B. 14: 4

☐C. 39: 6

☐D. 9: 39

3- What is the value of \(x\) in the following equation: \(-60=115-x\)

☐A. 175

☐B. \(-175\)

☐C. 55

☐D. \(-55\)

4- Which of the following graphs represents the following inequality?
\(-8≤5x-8≤2\)

☐A.

☐B.

☐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 Grade 6 Common Core Math Prep Resource for 2020

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, therefor, 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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