ISEE Mathematics Achievement 1 — Questions and Answers
Question 1: What is the greatest common factor (GCF) of 24 and 36?
- 12 (Correct answer)
- 6
- 8
- 4
Correct answer: 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest common factor is 12.
Question 2: A triangle has angles measuring 45° and 90°. What is the measure of the third angle?
- 45° (Correct answer)
- 90°
- 60°
- 30°
Correct answer: 45°
The sum of angles in a triangle is 180°. Third angle = 180° - 45° - 90° = 45°. This is a 45-45-90 right triangle.
Question 3: What is 3/4 + 2/3?
- 17/12 (Correct answer)
- 5/7
- 5/12
- 1/2
Correct answer: 17/12
Find a common denominator: 3/4 = 9/12 and 2/3 = 8/12. Then 9/12 + 8/12 = 17/12 (or 1 5/12).
Question 4: If a rectangle has a length of 8 cm and a width of 5 cm, what is the length of its diagonal?
- √89 cm (approximately 9.4 cm) (Correct answer)
- 13 cm
- 40 cm
- 6.5 cm
Correct answer: √89 cm (approximately 9.4 cm)
Using the Pythagorean theorem: diagonal² = 8² + 5² = 64 + 25 = 89. Diagonal = √89 ≈ 9.4 cm.
Question 5: What is the value of 2³ × 3²?
- 72 (Correct answer)
- 36
- 48
- 54
Correct answer: 72
2³ = 2 × 2 × 2 = 8. 3² = 3 × 3 = 9. So 2³ × 3² = 8 × 9 = 72.
Question 6: A shirt originally priced at $60 is on sale for 30% off. If sales tax is 8%, what is the total cost?
- $45.36 (Correct answer)
- $42.00
- $46.80
- $43.20
Correct answer: $45.36
Sale price: $60 × 0.70 = $42. Tax: $42 × 0.08 = $3.36. Total: $42 + $3.36 = $45.36.
ISEE Mathematics Achievement 1
What is the greatest common factor (GCF) of 24 and 36?