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
B11
C9
D15
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

A4
B9
C1
D5
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

A3
B4
C2
D0
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) = 4x² − 4x + 8, what is f(2)?

A16
B20
C12
D8
Explanation
f(2) = 4(2)² + (-4)(2) + 8 = 16 − 8 + 8 = 16.
Question 5 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
A46
B48
C47
D44
Explanation
By the Pythagorean theorem: b² = c² − a² = 50² − 14² = 2500 − 196 = 2304. So b = √2304 = 48.
Question 6 of 10
Advanced MathMedium

If f(x) = 6x² − 2x + 3, what is f(3)?

A45
B57
C51
D15
Explanation
f(3) = 6(3)² + (-2)(3) + 3 = 54 − 6 + 3 = 51.
Question 7 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
A10
B9
C11
D12
Explanation
By the Pythagorean theorem: b² = c² − a² = 13² − 5² = 169 − 25 = 144. So b = √144 = 12.
Question 8 of 10
Problem-Solving & DataMedium

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

A85%
B15%
C20%
D10%
Explanation
Percent change = (new − old) / old × 100% = (-18) / 120 × 100% = 15%.
Question 9 of 10
Problem-Solving & DataMedium

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

A60%
B35%
C40%
D45%
Explanation
Percent change = (new − old) / old × 100% = (-60) / 150 × 100% = 40%.
Question 10 of 10
Advanced MathMedium

If f(x) = 2x² − 3x + 8, what is f(4)?

A26
B28
C30
D4
Explanation
f(4) = 2(4)² + (-3)(4) + 8 = 32 − 12 + 8 = 28.

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