Top 10 PSAT/NMSQT Math Practice Questions

Top 10 PSAT/NMSQT Math Practice Questions

Preparing students for the PSAT/NMSQT Math test? The best way to prepare for the PSAT Math test is to work through as many PSAT Math practice questions as possible. Here are the top 10 PSAT Math practice questions to help your students review the most important PSAT Math concepts. These PSAT 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 2022 PSAT guidelines. Answers and full explanations are provided at the end of the post.

Help your students start their PSAT Math test prep journey right now with these sample PSAT Math questions.

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PSAT Math Practice Questions

1- A taxi driver earns $9 per 1-hour work. If he works 10 hours a day and in 1 hour he uses 2-liters petrol with price $1 for 1-liter. How much money does he earn in one day?

A. $90

B. $88

C. $70

D. $60

2- Five years ago, Amy was three times as old as Mike was. If Mike is 10 years old now, how old is Amy?

A. 4

B. 8

C. 12

D. 20

3- What is the solution of the following system of equations?
\(\begin{cases}\frac{-x}{2}+ \frac{y}{4} = 1 \\ \frac{-5y}{6}+2x = 4 & \end{cases}\)

A. \(x=48,y=22\)

B. \(x=50,y=20\)

C. \(x=20,y=50\)

D. \(x=22,y=48\)

4- What is the length of AB in the following figure if AE=4, CD=6, and AC=12?

A. 3.8

B. 4.8

C. 7.2

D. 24

5- If a and b are solutions of the following equation, which of the following is the ratio \(\frac{a}{b}\)? \((a > b)\)
\(2x^2-11x+8=-3x+18\)

A. \(\frac{1}{5}\)

B. 5

C. \(-\frac{1}{5}\)

D. \(-5\)

6- How many tiles of 8 cm\(^2\) is needed to cover a floor of dimension 6 cm by 24 cm?

A. 6

B. 12

C. 18

D. 24

7- Which of the following is the solution to the following inequality?
\(2x+4>11x-12.5-3.5x\)

A. \(x<3\)

B. \(x>3\)

C. \(x≤4\)

D. \(x≥4\)

8- If a, b and c are positive integers and \(3a = 4b = 5c\), then the value of \(a + 2b + 15c\) is how many times the value of a?

A. 11.5

B. 12

C. 12.5

D. 15

9- A company pays its employer $7000 plus \(2\%\) of all sales profit. If \(x\) is the number of all sales profit, which of the following represents the employer’s revenue?

A. \(0.02x\)

B. \(0.98x-7000\)

C. \(0.02x+7000\)

D. \(0.98x+7000\)

10- \(\frac{5x^2+75x-80}{x^2-1} = \)?

A. \(\frac{5x+75}{ x-1} \)

B. \(\frac{x+16}{ x+1} \)

C. \(\frac{5x+80}{ x+1} \)

D. \(\frac{x+15}{ x-1} \)

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Answers:

1- C
\( $9×10=$90\)
Petrol use: \(10×2=20\) liters
Petrol cost: \(20×$1=$20\)
Money earned: \($90-$20=$70\)

2- D
Five years ago, Amy was three times as old as Mike. Mike is \(10\) years now. Therefore, \(5\) years ago Mike was \(5\) years.
Five years ago, Amy was: \(A=3×5=15 \)
Now Amy is \(20\) years old: \(15 + 5 = 20\)

3- D
\(\begin{cases}\frac{-x}{2}+ \frac{y}{4} = 1 \\ \frac{-5y}{6}+2x = 4 & \end{cases}\)
Multiply the top equation by \(4\). then:
\(-2x+y=4\)
\(\frac{-5y}{6} + 2x = 4\)
Add two equations.
\( \frac{1}{6}y=8→y=48 \)
plug in the value of \(y\) into the first equation \(→(x=22)\)

4- B
Two triangles ∆BAE and ∆BCD are similar. Then:
\(\frac{AE}{CD} = \frac{AB}{BC}\)
\(\frac{4}{6} = \frac{x}{12}\)
then:
\(48-4x=6x→10x=48→x=4.8\)

5- D
\(2x^2-11x+8=-3x+18→2x^2-11x+3x+8-18=0→2x^2-8x-10=0\)
\(→2(x^2-4x-5)=0→\) Divide both sides by \(2\). Then:
\(x^2-4x-5=0\), Find the factors of the quadratic equation.
\(→(x-5)(x+1)=0→x=5\) or \( x=-1\)
\(a>b\), then: \(a=5\) and \(b=-1\)
\(\frac{a}{b} = \frac{5}{-1}= -5 \)

6- C
The area of the floor is: \(6 cm × 24 cm = 144 cm\)
The number is tiles needed \(= 144 ÷ 8 = 18\)

7- A
\(2x+4>11x-12.5-3.5x→\) Combine like terms:
\(2x+4>7.5x-12.5$→\) Subtract \(2x\) from both sides: \(4>5.5x-12.5\)
Add \(12.5\) both sides of the inequality.
\(16.5>5.5x\)
Divide both sides by \(5.5\).
\(\frac{16.5}{5.5}>x→x<3\)

8- A
\(3a=4b→b=\frac{3a}{4}\) and \( 3a=5c→c= \frac{3a}{5}\)
\(a+2b+15c=a+ (2× \frac{3a}{4})+(15× \frac{3a}{5})=a+1.5a+9a=11.5a\)

9- C
\(x\) is the number of all sales profit and \(2\%\) of it is:
\(2\%×x=0.02x\)
Employer’s revenue: \(0.2x+7000\)

10- C
First, find the factors of numerator and denominator of the expression. Then simplify.
\(\frac{5x^2+75x-80}{x^2-1}=\frac{5(x^2+15x-16)}{(x-1)(x+1)}\)
\(\frac{5(x+16)(x-1)}{ (x-1)(x+1)}=\frac{5(x+16)}{ (x+1)} \)
\(=\frac{(5x+80)}{ (x+1)}\)

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