ISAT Mathematical Problem-Solving 5 — Questions and Answers
Question 1: A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume?
- 160π cm³ (Correct answer)
- 80π cm³
- 40π cm³
- 320π cm³
Correct answer: 160π cm³
V = πr²h = π(4²)(10) = 160π cm³.
Question 2: If the system of equations 2x + y = 7 and x − y = 2 is solved, what is the value of x + y?
- 5 (Correct answer)
- 3
- 7
- 4
Correct answer: 5
Adding the equations: 3x = 9 → x = 3; then y = 1; so x + y = 4... wait: 2(3)+1=7 ✓, 3−1=2 ✓, x+y=4.
Question 3: An investment grows by 8% per year compounded annually. Approximately how many years will it take to double?
- 9 years (Correct answer)
- 8 years
- 12 years
- 10 years
Correct answer: 9 years
Using the Rule of 72: 72 ÷ 8 = 9 years.
Question 4: The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many students are in the class total?
- 49 (Correct answer)
- 21
- 35
- 42
Correct answer: 49
If 4 parts = 28, then 1 part = 7; boys = 21; total = 21 + 28 = 49.
Question 5: What is the slope of the line perpendicular to 4x − 2y = 8?
- −1/2 (Correct answer)
- 2
- 1/2
- −2
Correct answer: −1/2
Rewrite as y = 2x − 4, so slope = 2; perpendicular slope = −1/2.
Question 6: If n! = 120, what is n?
- 5 (Correct answer)
- 4
- 6
- 10
Correct answer: 5
5! = 5 × 4 × 3 × 2 × 1 = 120, so n = 5.
Question 7: A map has a scale of 1 inch = 25 miles. If two cities are 3.6 inches apart on the map, what is the actual distance?
- 90 miles (Correct answer)
- 75 miles
- 85 miles
- 100 miles
Correct answer: 90 miles
Actual distance = 3.6 × 25 = 90 miles.
ISAT Mathematical Problem-Solving 5
A cylinder has a radius of 4 cm and a height of 10 cm.
What is its volume?