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

Solve for x:

5x + 19 = 39

A0
B6
C-1
D4
Explanation
Subtract 19 from both sides: 5x = 20. Then divide both sides by 5: x = 4.
Question 2 of 10
AlgebraEasy

Solve for x:

4x + 19 = 67

A13
B9
C12
D17
Explanation
Subtract 19 from both sides: 4x = 48. Then divide both sides by 4: x = 12.
Question 3 of 10
AlgebraEasy

Solve for x:

3x + 3 = 12

A7
B2
C-2
D3
Explanation
Subtract 3 from both sides: 3x = 9. Then divide both sides by 3: x = 3.
Question 4 of 10
Advanced MathMedium

What are the solutions to the equation x² + 4x − 5 = 0?

Ax = 2 and x = -4
Bx = 1 and x = -3
Cx = -1 and x = 5
Dx = 1 and x = -5
Explanation
Factor: (x − 1)(x − -5) = 0. Setting each factor to zero gives x = 1 or x = -5.
Question 5 of 10
Advanced MathMedium

What are the solutions to the equation x² − 6x + 5 = 0?

Ax = 2 and x = 6
Bx = 1 and x = 5
Cx = -1 and x = -5
Dx = 1 and x = 7
Explanation
Factor: (x − 1)(x − 5) = 0. Setting each factor to zero gives x = 1 or x = 5.
Question 6 of 10
Problem-Solving & DataMedium

A product's price increased from $250 to $287. What is the percent increase?

A15%
B20%
C114%
D10%
Explanation
Percent change = (new − old) / old × 100% = (37) / 250 × 100% = 15%.
Question 7 of 10
Problem-Solving & DataMedium

A product's price increased from $100 to $115. What is the percent increase?

A20%
B10%
C115%
D15%
Explanation
Percent change = (new − old) / old × 100% = (15) / 100 × 100% = 15%.
Question 8 of 10
Advanced MathMedium

What are the solutions to the equation x² − 3x + 2 = 0?

Ax = 2 and x = 1
Bx = -2 and x = -1
Cx = 2 and x = 3
Dx = 3 and x = 2
Explanation
Factor: (x − 2)(x − 1) = 0. Setting each factor to zero gives x = 2 or x = 1.
Question 9 of 10
Geometry & TrigHard Diagram
In the right triangle shown, θ is the angle opposite the side of length 8. What is sin(θ)? 15817θ
A15/17
B8/15
C17/8
D8/17
Explanation
sin(θ) = opposite/hypotenuse = 8/17 = 8/17 in simplest form.
Question 10 of 10
Geometry & TrigHard Diagram
In the right triangle shown, θ is the angle opposite the side of length 9. What is sin(θ)? 40941θ
A40/41
B9/41
C9/40
D41/9
Explanation
sin(θ) = opposite/hypotenuse = 9/41 = 9/41 in simplest form.

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