GCSE Mathematics Foundation and Higher 2 — Questions and Answers
Question 1: A car travels 150 miles in 2.5 hours. What is its average speed?
- 50 mph
- 55 mph
- 60 mph (Correct answer)
- 65 mph
Correct answer: 60 mph
Average speed = distance ÷ time = 150 ÷ 2.5 = 60 mph. The speed-distance-time triangle is a key tool for these calculations.
Question 2: Factorise the expression x² + 7x + 12.
- (x + 3)(x + 4) (Correct answer)
- (x + 2)(x + 6)
- (x + 1)(x + 12)
- (x + 5)(x + 2)
Correct answer: (x + 3)(x + 4)
Find two numbers that multiply to 12 and add to 7. Those numbers are 3 and 4 (3 × 4 = 12, 3 + 4 = 7). So x² + 7x + 12 = (x + 3)(x + 4).
Question 3: Convert 0.375 to a fraction in its simplest form.
- 3/8 (Correct answer)
- 375/100
- 15/40
- 3/4
Correct answer: 3/8
0.375 = 375/1000. Divide numerator and denominator by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So 0.375 = 3/8.
Question 4: The exterior angle of a regular polygon is 40°. How many sides does the polygon have?
- 8
- 9 (Correct answer)
- 10
- 12
Correct answer: 9
The sum of exterior angles of any polygon is 360°. For a regular polygon, each exterior angle is equal, so the number of sides = 360° ÷ 40° = 9.
Question 5: If y is directly proportional to x and y = 15 when x = 3, what is y when x = 7?
- 25
- 30
- 35 (Correct answer)
- 40
Correct answer: 35
y = kx where k is the constant of proportionality. When y = 15 and x = 3: 15 = 3k, so k = 5. When x = 7: y = 5 × 7 = 35.
Question 6: What is the gradient of the line passing through the points (2, 3) and (6, 11)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Gradient = (y₂ - y₁) ÷ (x₂ - x₁) = (11 - 3) ÷ (6 - 2) = 8 ÷ 4 = 2. The gradient measures the steepness of the line.
GCSE Mathematics Foundation and Higher 2
A car travels 150 miles in 2.5 hours.
What is its average speed?