GCSE MATH 4 — Questions and Answers
Question 1: Factorise fully: 6x² − 9x
- 3x(2x − 3) (Correct answer)
- 3(2x² − 3x)
- x(6x − 9)
- 2x(3x − 4)
Correct answer: 3x(2x − 3)
The HCF of 6x² and 9x is 3x, giving 3x(2x − 3).
Question 2: In a right-angled triangle, the two shorter sides are 5 cm and 12 cm. What is the hypotenuse?
- 11 cm
- 13 cm (Correct answer)
- 15 cm
- 17 cm
Correct answer: 13 cm
By Pythagoras: c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
Question 3: What is the median of the data set: 7, 3, 9, 1, 5, 8, 4?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
Arranged in order: 1, 3, 4, 5, 7, 8, 9 — the middle value is 5.
Question 4: Write 0.00047 in standard form.
- 4.7 × 10⁻⁴ (Correct answer)
- 4.7 × 10⁻³
- 47 × 10⁻⁵
- 0.47 × 10⁻³
Correct answer: 4.7 × 10⁻⁴
0.00047 = 4.7 × 10⁻⁴ because we move the decimal 4 places to the right.
Question 5: What is the area of a trapezoid with parallel sides 8 cm and 14 cm, and height 6 cm?
- 60 cm²
- 66 cm² (Correct answer)
- 72 cm²
- 84 cm²
Correct answer: 66 cm²
Area = ½ × (a + b) × h = ½ × (8 + 14) × 6 = ½ × 22 × 6 = 66 cm².
Question 6: Solve the simultaneous equations: x + y = 10 and x − y = 4.
- x = 6, y = 4
- x = 7, y = 3 (Correct answer)
- x = 8, y = 2
- x = 5, y = 5
Correct answer: x = 7, y = 3
Adding the equations: 2x = 14, so x = 7; substituting back gives y = 3.
Question 7: What is the value of 2³ × 2⁴?
- 2⁷ (Correct answer)
- 4⁷
- 2¹²
- 8⁷
Correct answer: 2⁷
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2⁷.
