Praxis Mathematics (5165) Secrets Study Guide.

Praxis Mathematics (5165) Secrets Study Guide




Praxis Mathematics 5165 — Questions 1–20

I. Number Sense & Operations

1. Which of the following is a rational number?
A) √2
B) ⅗
C) π
D) e
✔ Correct Answer: B — ⅗
Rationale: Rational numbers can be expressed as a ratio of two integers; ⅗ meets this definition.

2. What is the prime factorization of 84?
A) 2² × 3 × 7
B) 2 × 3² × 7
C) 2³ × 3 × 5
D) 2 × 3 × 7²
✔ Correct Answer: A — 2² × 3 × 7
Rationale: Dividing 84: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7; prime factors: 2² × 3 × 7.

3. Which property justifies that a + b = b + a?
A) Associative
B) Commutative
C) Distributive
D) Identity
✔ Correct Answer: B — Commutative
Rationale: The commutative property allows numbers to be added in any order.

4. What is the least common multiple (LCM) of 6 and 8?
A) 12
B) 24
C) 48
D) 36
✔ Correct Answer: B — 24
Rationale: Multiples of 6: 6,12,18,24…; multiples of 8: 8,16,24…; first common: 24.

5. If 5x = 35, what is x?
A) 5
B) 6
C) 7
D) 8

, ✔ Correct Answer: C — 7
Rationale: Divide both sides by 5: x = 35 ÷ 5 = 7.



II. Algebra & Functions

6. Simplify: 3x + 5x – 7
A) 8x – 7
B) 8x + 7
C) 15x – 7
D) 8x – 12
✔ Correct Answer: A — 8x – 7
Rationale: Combine like terms: 3x + 5x = 8x; constant –7 remains.

7. Solve for y: 2y – 7 = 13
A) 5
B) 10
C) 20
D) 7
✔ Correct Answer: B — 10
Rationale: 2y = 13 + 7 → 2y = 20 → y = 10.

8. Which function is linear?
A) y = 3x + 2
B) y = x² + 1
C) y = √x
D) y = 2^x
✔ Correct Answer: A — y = 3x + 2
Rationale: Linear functions have the form y = mx + b with constant rate of change.

9. If f(x) = 2x – 1, what is f(4)?
A) 7
B) 8
C) 6
D) 9
✔ Correct Answer: A — 7
Rationale: f(4) = 2(4) – 1 = 8 – 1 = 7.

10. Which property allows a(b + c) = ab + ac?
A) Commutative
B) Associative
C) Distributive
D) Identity
✔ Correct Answer: C — Distributive
Rationale: The distributive property multiplies a term across a sum or difference.



III. Geometry & Measurement