10 Most Common PSAT Math Questions

10 Most Common PSAT Math Questions

Preparing for the PSAT Math test? Want a preview of the most common mathematics questions on the PSAT Math test? If so, then you are in the right place.

The mathematics section of PSAT can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable!

Preparing for the PSAT Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the PSAT can help to reduce those pre-test jitters. Here’s your chance to review the 10 most common PSAT Math questions to help you know what to expect and what to practice most. Try these 10 most common PSAT Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice.

Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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10 Sample PSAT Math Practice Questions

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

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

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

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

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

2- If \(x^2 + 6x – r\) is divisible by \((x – 5)\), what is the value of \(r\)?

A. \(55\)

B. \(56\)

C. \(57\)

D. \(58\)

3- If a parabola with equation \(y=ax^2+5x+10\), where a is constant passes through point \((2, 12)\), what is the value of \(a^2\)?

A. \(-2\)

B. \(2\)

C. \(-4\)

D. \(4\)

4- In the following equation, what is the value of \(y – 3x\)?
\(\frac{y}{4} = x – \frac{2}{5}x + 10\) _________


5- What is the value of \(x\) in the following equation?
\(\frac{x^2-9}{x+3}+2(x+4)=17\) __________


6- If \(x≠0\), what is the value of \(\frac{(10xy^2)^2}{(2xy^2 )^2}\) ? _________



7- What is the slope of a line containing the reflected points of \(A(2,-1)\) and \(B(6,3)\) over the line \(y = x\)? _________


8- If a car has \(80\)-liter petrol and after one hour driving the car use \(6\)-liter petrol, how much petrol will remain after \(x\)-hours driving?

A. \(6x – 80\)

B. \(80 + 6x\)

C. \(80 – 6x\)

D. \(80 – x\)

9- \(5\) less than twice a positive integer is \(83\). What is the integer?

A. \(39\)

B. \(41\)

C. \(42\)

D. \(44\)

10- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks?

A. \(15\)

B. \(14.5\)

C. \(14\)

D. \(13.5\)

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Answers:

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

2- A
If \(r=55→ \frac{x^2+6x-55}{x-5}\) = \(\frac{(x+11)(x-5)}{x-5}\) \(= x + 11\)
For all other options, the numerator expression is not divisible by \((x-5)\).

3- D
Plug in the values of \(x\) and \(y\) in the equation of the parabola. Then:
\(12=a(2)^2+5(2)+10→12=4a+10+10→12=4a+20\)
\(→4a=12-20=-8→a=\frac{-8}{4}=-2→a^2=(-2)^2=4\)

4- 50
\(\frac{y}{4} = x – \frac{2}{5}x + 10 \)
Multiply both sides of the equation by \(5\). Then:
\(5×\frac{y}{4} = 5× (x – \frac{2}{5}x + 10)\)
\(→y=5x-2x+50→y=3x+50\)
Now, subtract \(3x\) from both sides of the equation. Then:
\(y – 3x = 50\)

5- 4
First, factorize the numerator and simplify.
\(\frac{(x-3)(x+3)}{x+3}+2x+8=17\)
\(→x-3+2x+8=15→3x+5=17\)
Subtract \(5\) from both sides of the equation. Then:
\(→3x=17-5→x=\frac{12}{3} x=4\)

6- 25
\(\frac{100x^2 y^4}{4x^2 y^4}\)
Remove \(x^2 y^4\) from both numerator and denominator.
\(\frac{100x^2 y^4}{4x^2 y^4}=\frac{100}{4}=\frac{50}{2}=25\)

7- 1
Remember that, the reflection of the point \((x,y)\) over the line \(y=x\) is the point \((y,x)\). Then:
The reflected point of \(A(2,-1)\), is \((-1,2)\)
The reflected point of \(B(6,3)\) is point \((3,6)\)
Therefore, the slope of the reflected line is:
\(\frac{y_{2} – y_{1}}{x_{2} – x_{1}}=\frac{6-2}{3-(-1)}=\frac{4}{4} \space or\space 1\)

8- C

The amount of petrol consumed after \(x\) hours is: \(6 × x = 6x\)
Petrol remaining after \(x\) hours driving: \(80 – 6x\)

9- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by \(2:\) \(x = 44\)

10- B
\(mean) = \frac{sum \space of \space terms}{number \space of \space terms}=\frac{9+12+15+16+19+16+14.5}{7}=14.5\)

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