ICAS Mathematics 4 — Questions and Answers
Question 1: What is the prime factorization of 36?
- 2 × 18
- 4 × 9
- 2² × 3² (Correct answer)
- 6²
Correct answer: 2² × 3²
36 = 4 × 9 = 2² × 3², which is its prime factorization.
Question 2: If y = 3x − 5 and x = 4, what is y?
- 7 (Correct answer)
- 12
- 17
- 2
Correct answer: 7
y = 3(4) − 5 = 12 − 5 = 7.
Question 3: A clock shows 3:45. What is the angle between the hour and minute hands?
- 157.5° (Correct answer)
- 172.5°
- 135°
- 150°
Correct answer: 157.5°
At 3:45, the minute hand is at 270° and the hour hand is at 112.5°, giving a difference of 157.5°.
Question 4: What is 0.375 written as a fraction in simplest form?
- 3/8 (Correct answer)
- 375/100
- 1/3
- 3/10
Correct answer: 3/8
0.375 = 375/1000 = 3/8 after dividing numerator and denominator by 125.
Question 5: A cylinder has a radius of 5 cm and a height of 10 cm. Using π ≈ 3.14, what is its volume?
- 785 cm³ (Correct answer)
- 314 cm³
- 1570 cm³
- 250 cm³
Correct answer: 785 cm³
Volume = π × r² × h = 3.14 × 25 × 10 = 785 cm³.
Question 6: In a class of 30 students, 40% play soccer. How many students play soccer?
- 40
- 10
- 15
- 12 (Correct answer)
Correct answer: 12
40% of 30 = 0.40 × 30 = 12 students.
Question 7: What is the greatest common factor (GCF) of 48 and 72?
- 12
- 24 (Correct answer)
- 6
- 8
Correct answer: 24
The factors of 48 include 24, and 72 ÷ 24 = 3, so GCF(48, 72) = 24.
ICAS Mathematics 4
What is the prime factorization of 36?