Preparing for the PSAT Math test? Try these free PSAT Math Practice questions. Reviewing practice questions is the best way to brush up your Math skills. Here, we walk you through solving 10 common PSAT Math practice problems covering the most important math concepts on the PSAT Math test.

These PSAT Math practice questions are designed to be similar to those found on the real PSAT Math test. They will assess your level of preparation and will give you a better idea of what to study on your exam.

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## 10 Sample **PSAT** Math Practice Questions

1- The area of a circle is \(64π\). What is the circumference of the circle?

A. \(8π\)

B. \(16π\)

C. \(32π\)

D. \(64π\)

2- Which of the following values for \(x\) and \(y\) satisfy the following system of equations?

\(x+4y=10\)

\(5x+10y=20\)

A. \(x=3,y=2\)

B. \(x=2,y=-3\)

C. \(x=-2,y=3\)

D. \(x=3,y=-2\)

3- If \(a ≠ 0\) and \(6b=5a\sqrt{3}\), then what is the value of \(\frac{2b \sqrt{3}}{4a}\) ?

A. \(\frac{5}{4}\)

B. \(\frac{5}{4}a\)

C. \(2a\)

D. \(2a\sqrt{3}\)

4- If a gas tank can hold 25 gallons, how many gallons does it contain when it is \( \frac{2}{5} \) full?

A. 50

B. 125

C. 62.5

D. 10

5- In the \(xy\)-plane, the point \((4,3)\) and \((3,2)\) are on line \(A\). Which of the following equations of lines is parallel to line \(A\)?

A. \(y = 3x\)

B. \(y = \frac{x}{2}\)

C. \(y = 2x\)

D. \(y = x\)

6- In the following graph, which of the data point is farthest from the line of best fit (not shown)?

A. (6,1)

B. (5,4)

C. (3,3)

D. (2,2)

7- A football team won exactly \(80\%\) of the games it played during the last session. Which of the following could be the total number of games the team played last season?

A. 49

B. 35

C. 12

D. 32

8- If \(x\) is greater than 0 and less than 1, which of the following is true?

A. \(x<\sqrt {(x^2+1)}<\sqrt{(x^2 )}+1\)

B. \(x<\sqrt {(x^2 )}+1<\sqrt {(x^2+1)}\)

C. \((\sqrt {(x^{2} + 1)}< x <\sqrt {(x^{2} ) }+ 1\)

D. \(\sqrt {(x^{2} )}+1< \sqrt{(x^{2}+1) }< x\)

9- If \(x\) is directly proportional to the square of \(y\), and \(y=2\) when \(x=12\), then when \(x=75 y=\) ?

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

B. 1

C. 5

D. 12

10- Jack earns $616 for his first 44 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs $826 to pay his rent, bills, and other expenses. How many hours must he work to make enough money this week?

A. 40

B. 48

C. 53

D. 54

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## Answers:

1- **B**

Use the formula of areas of circles.

Area of a circle = \(πr^2→64 π=πr^2→64=r^2→r=8\)

The radius of the circle is 8. Now, use the circumference formula:

Circumference \(= 2πr = 2π (8) = 16π\)

2- **C**

\(x+4y=10\)

\(5x+10y=20\)

Multiply the top equation by -5 then,

\(-5x-20y=-50\)

\(5x+10y=20\)

\(Add \space two \space equations\)

\(-10y=-30→y=3 \) plug in the value of y into the first equation

\(x+4y=10→x+4(3)=10→x+12=10\)

Subtract 12 from both sides of the equation. Then:

\(x+12=10→x=-2\)

3-** A**

\(6b=5a\sqrt3→b= \frac{5a\sqrt3}{6}\)

\(Therefore:\)

\(\frac{2b\sqrt3}{4a}=\frac{2× \frac{5a\sqrt3}{6}×\sqrt3}{4a}=\frac{2×5a×3}{4×6a}=\frac{5}{4}\)

4- **D**\( \frac{2}{5} ×25= \frac{50}{5} =10\)

5- **D**

The slop of line A is:

\(\frac{y_{2} – y_{1}}{x_{2} – x_{1}} = \frac{3-2}{4-3}=1 \)

Parallel lines have the same slope and only choice \(D (y=x)\) has slope of 1.

6- **A**

Line AB is the best fit line.

Then, point (6,1) is the farthest from line AB.

7- **B**

Choices \(A, C\) and \(D\) are incorrect because \(80\%\) of each of the numbers is non-whole number.

\(49, 80 \% \ of \ 49 = 0.80×49=39.2\)

\(35, 80 \% \ of \ 35=0.80×35=28\)

\(12, 80 \% \ of \ 12=0.80×12=9.6\)

\(32, 80 \% \ of \ 32=0.80×32=25.6\)

8- **A**

Let \(x\) be equal to 0.5, then: \(x = 0.5\)

\(\sqrt{(x^2+1)}=\sqrt{(0.5^2+1)}=\sqrt{1.25}≈1.12\)

\(\sqrt{(x^2 )+1}=\sqrt{(0.5^2 )}+1=0.5+1=1.5\)

Then, option A is correct.

\(x<\sqrt{(x^2+1)}<\sqrt{(x^2 )}+1\)

9- **C**

\(x\) is directly proportional to the square of \(y\). Then:

\(x=cy^2\)

\(12=c(2)^2→12=4c→c=\frac{12}{4}=3\)

The relationship between \(x\) and y is:

\(x=3y^2\)

\(x=75\)

\(75= 3y^2 →y^2 = \frac{75}{3} = 25→y=5\)

10- **D**

The amount of money that jack earns for one hour:

\(\frac{$616}{44} =$14\)

Number of additional hours that he work to make enough money is:

\(\frac{$826-$616}{1.5×$14}=10\)Number of total hours is: \(44 + 10 = 54\)

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