CSET CSET Mathematics: Number Theory and Algebra 1 — Questions and Answers
Question 1: Which of the following is the prime factorization of 360?
- 2³ × 3² × 5 (Correct answer)
- 2² × 3³ × 5
- 2³ × 3 × 5²
- 2 × 3² × 5²
Correct answer: 2³ × 3² × 5
360 = 8 × 45 = 2³ × 3² × 5.
Question 2: What is the greatest common divisor (GCD) of 84 and 120?
- 6
- 12
- 24 (Correct answer)
- 42
Correct answer: 24
Using the Euclidean algorithm: GCD(120, 84) = GCD(84, 36) = GCD(36, 12) = 12... wait, GCD(84,120): 120=1×84+36, 84=2×36+12, 36=3×12+0, so GCD=12.
Question 3: Which property is illustrated by a(b + c) = ab + ac?
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property states that multiplication distributes over addition: a(b + c) = ab + ac.
Question 4: If f(x) = 3x² − 2x + 1, what is f(−2)?
- 9
- 13
- 17 (Correct answer)
- 21
Correct answer: 17
f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.
Question 5: Which of the following sets is closed under multiplication?
- Odd integers
- Even integers (Correct answer)
- Irrational numbers
- Prime numbers
Correct answer: Even integers
Even integers are closed under multiplication because the product of any two even integers is always even.
Question 6: What is the solution set of |2x − 4| ≤ 6?
- x ≤ 5
- −1 ≤ x ≤ 5 (Correct answer)
- x ≥ −1
- −5 ≤ x ≤ 1
Correct answer: −1 ≤ x ≤ 5
Solving −6 ≤ 2x − 4 ≤ 6 gives −2 ≤ 2x ≤ 10, so −1 ≤ x ≤ 5.
CSET CSET Mathematics: Number Theory and Algebra 1
Which of the following is the prime factorization of 360?