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

A15
B10
C9
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

A4
B5
C1
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

A2
B4
C3
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) = 6x² − 2x + 3, what is f(3)?

A51
B57
C45
D15
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?

A45%
B35%
C40%
D60%
Explanation
Percent change = (new − old) / old × 100% = (-60) / 150 × 100% = 40%.
Question 6 of 10
Problem-Solving & DataMedium

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

A10%
B85%
C20%
D15%
Explanation
Percent change = (new − old) / old × 100% = (-18) / 120 × 100% = 15%.
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
A11
B10
C9
D12
Explanation
By the Pythagorean theorem: b² = c² − a² = 13² − 5² = 169 − 25 = 144. So b = √144 = 12.
Question 8 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 9 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 10 of 10
Advanced MathMedium

If f(x) = 4x² − 4x + 8, what is f(2)?

A20
B16
C12
D8
Explanation
f(2) = 4(2)² + (-4)(2) + 8 = 16 − 8 + 8 = 16.

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