Top 10 6th Grade NYSE Math Practice Questions
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6th Grade NYSE 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
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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 boys 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 two 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 the 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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