Mathematics Achievement Flashcards

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

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.

A triangle has angles measuring 45° and 90°. What is the measure of the third angle?

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.

What is 3/4 + 2/3?

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).

If a rectangle has a length of 8 cm and a width of 5 cm, what is the length of its diagonal?

Answer: √89 cm (approximately 9.4 cm)

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

What is the value of 2³ × 3²?

Answer: 72

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

A shirt originally priced at $60 is on sale for 30% off. If sales tax is 8%, what is the total cost?

Answer: $45.36

Sale price: $60 × 0.70 = $42. Tax: $42 × 0.08 = $3.36. Total: $42 + $3.36 = $45.36.