PSAT 8/9 Math — Semester A
Free Practice · 10 Questions · 20 min
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Question 1 of 10
AlgebraEasy

Solve for x:

5x + 1 = 51

A10
B9
C15
D11
Explanation
Subtract 1 from both sides: 5x = 50. Then divide both sides by 5: x = 10.
Question 2 of 10
AlgebraEasy

Solve for x:

6x + 12 = 42

A1
B5
C4
D9
Explanation
Subtract 12 from both sides: 6x = 30. Then divide both sides by 6: x = 5.
Question 3 of 10
AlgebraEasy

Solve for x:

8x + 15 = 39

A4
B0
C3
D2
Explanation
Subtract 15 from both sides: 8x = 24. Then divide both sides by 8: x = 3.
Question 4 of 10
Advanced MathMedium

If f(x) = 6x² − 2x + 3, what is f(3)?

A51
B57
C15
D45
Explanation
f(3) = 6(3)² + (-2)(3) + 3 = 54 − 6 + 3 = 51.
Question 5 of 10
Problem-Solving & DataMedium

A product's price decreased from $150 to $90. What is the percent decrease?

A60%
B35%
C45%
D40%
Explanation
Percent change = (new − old) / old × 100% = (-60) / 150 × 100% = 40%.
Question 6 of 10
Advanced MathMedium

If f(x) = 2x² − 3x + 8, what is f(4)?

A4
B30
C26
D28
Explanation
f(4) = 2(4)² + (-3)(4) + 8 = 32 − 12 + 8 = 28.
Question 7 of 10
Geometry & TrigMedium Diagram

In the right triangle shown, the hypotenuse has length 50 and one leg has length 14. What is the length of the other leg?

14?50
A48
B44
C47
D46
Explanation
By the Pythagorean theorem: b² = c² − a² = 50² − 14² = 2500 − 196 = 2304. So b = √2304 = 48.
Question 8 of 10
Advanced MathMedium

If f(x) = 4x² − 4x + 8, what is f(2)?

A12
B20
C8
D16
Explanation
f(2) = 4(2)² + (-4)(2) + 8 = 16 − 8 + 8 = 16.
Question 9 of 10
Problem-Solving & DataMedium

A product's price decreased from $120 to $102. What is the percent decrease?

A20%
B15%
C10%
D85%
Explanation
Percent change = (new − old) / old × 100% = (-18) / 120 × 100% = 15%.
Question 10 of 10
Geometry & TrigMedium Diagram

In the right triangle shown, the hypotenuse has length 13 and one leg has length 5. What is the length of the other leg?

5?13
A9
B10
C12
D11
Explanation
By the Pythagorean theorem: b² = c² − a² = 13² − 5² = 169 − 25 = 144. So b = √144 = 12.

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