GCSE Mathematics Foundation and Higher — Questions and Answers
Question 1: A shop reduces the price of a jacket from £80 to £60. What is the percentage decrease?
- 20%
- 25% (Correct answer)
- 30%
- 15%
Correct answer: 25%
The decrease is £80 - £60 = £20. Percentage decrease = (20 ÷ 80) × 100 = 25%. Always divide the change by the original value, not the new value.
Question 2: Simplify the expression 3x + 5y - 2x + 4y.
- x + 9y (Correct answer)
- 5x + y
- 5x + 9y
- x + y
Correct answer: x + 9y
Collect like terms: 3x - 2x = x, and 5y + 4y = 9y. So the simplified expression is x + 9y.
Question 3: What is the area of a triangle with a base of 12 cm and a height of 8 cm?
- 96 cm²
- 48 cm² (Correct answer)
- 20 cm²
- 60 cm²
Correct answer: 48 cm²
The area of a triangle is ½ × base × height = ½ × 12 × 8 = 48 cm². This formula works because a triangle is exactly half of a rectangle with the same base and height.
Question 4: Solve the equation 4x - 7 = 13.
- x = 3
- x = 5 (Correct answer)
- x = 4
- x = 6
Correct answer: x = 5
Add 7 to both sides: 4x = 20. Then divide both sides by 4: x = 5. You can check by substituting back: 4(5) - 7 = 20 - 7 = 13 ✓
Question 5: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?
- 3/10
- 1/2 (Correct answer)
- 2/5
- 5/10
Correct answer: 1/2
Total marbles = 3 + 5 + 2 = 10. Probability of blue = 5/10 = 1/2. Probability is always favourable outcomes divided by total outcomes.
Question 6: What is the value of 2³ × 2⁴?
- 2⁷ (Correct answer)
- 2¹²
- 4⁷
- 2¹
Correct answer: 2⁷
When multiplying powers with the same base, add the indices: 2³ × 2⁴ = 2^(3+4) = 2⁷ = 128. This is one of the fundamental index laws.
GCSE Mathematics Foundation and Higher
A shop reduces the price of a jacket from £80 to £60.
What is the percentage decrease?