ISEE Mathematics Achievement

Question 1

What is the greatest common factor (GCF) of 24 and 36?

Accepted Answer

12

Answer

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?

Accepted Answer

45°

Answer

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?

Accepted Answer

17/12

Answer

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?

Accepted Answer

√89 cm (approximately 9.4 cm)

Answer

Using the Pythagorean theorem: diagonal² = 8² + 5² = 64 + 25 = 89. Diagonal = √89 ≈ 9.4 cm.

Question 5

What is the value of 2³ × 3²?

Accepted Answer

72

Answer

2³ = 2 × 2 × 2 = 8. 3² = 3 × 3 = 9. So 2³ × 3² = 8 × 9 = 72.

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