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

Solve for x:

8x + 15 = 39

A3
B2
C4
D0
Explanation
Subtract 15 from both sides: 8x = 24. Then divide both sides by 8: x = 3.
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:

5x + 1 = 51

A10
B15
C11
D9
Explanation
Subtract 1 from both sides: 5x = 50. Then divide both sides by 5: x = 10.
Question 4 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
A11
B9
C10
D12
Explanation
By the Pythagorean theorem: b² = c² − a² = 13² − 5² = 169 − 25 = 144. So b = √144 = 12.
Question 5 of 10
Advanced MathMedium

If f(x) = 2x² − 3x + 8, what is f(4)?

A4
B26
C28
D30
Explanation
f(4) = 2(4)² + (-3)(4) + 8 = 32 − 12 + 8 = 28.
Question 6 of 10
Advanced MathMedium

If f(x) = 4x² − 4x + 8, what is f(2)?

A8
B12
C20
D16
Explanation
f(2) = 4(2)² + (-4)(2) + 8 = 16 − 8 + 8 = 16.
Question 7 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 8 of 10
Advanced MathMedium

If f(x) = 6x² − 2x + 3, what is f(3)?

A45
B51
C15
D57
Explanation
f(3) = 6(3)² + (-2)(3) + 3 = 54 − 6 + 3 = 51.
Question 9 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
B46
C47
D44
Explanation
By the Pythagorean theorem: b² = c² − a² = 50² − 14² = 2500 − 196 = 2304. So b = √2304 = 48.
Question 10 of 10
Problem-Solving & DataMedium

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

A20%
B85%
C10%
D15%
Explanation
Percent change = (new − old) / old × 100% = (-18) / 120 × 100% = 15%.

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