Mathematics Knowledge Advanced Flashcards

What is 15% of 240?

Answer: 36

15% of 240 = 0.15 × 240 = 36.

Solve for y: 2y/3 + 4 = 10

Answer: y = 9

Subtract 4 from both sides to get 2y/3 = 6, then multiply by 3/2 to get y = 9.

A square has a diagonal of 10. What is the area of the square?

Answer: 50

For a square with diagonal d, area = d²/2 = 100/2 = 50.

Which of the following is a factor of x² − 9?

Answer: (x + 3)

x² − 9 is a difference of squares: (x+3)(x−3), so (x+3) is a factor.

What is the median of the set {7, 3, 11, 9, 5}?

Answer: 7

Ordered: {3, 5, 7, 9, 11}; the middle (3rd) value is 7.

A car travels 180 miles in 3 hours. What is its average speed?

Answer: 60 mph

Speed = distance ÷ time = 180 ÷ 3 = 60 mph.

Simplify: (x² − 4) ÷ (x − 2)

Answer: x + 2

Factor the numerator: (x+2)(x−2) ÷ (x−2) = x+2 (for x ≠ 2).