GCSE GCSE Mathematics 1 — Questions and Answers
Question 1: Solve for x: 3x + 7 = 22
- x = 3
- x = 4
- x = 5 (Correct answer)
- x = 6
Correct answer: x = 5
Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Always perform the same operation to both sides to keep the equation balanced.
Question 2: What is the gradient of the line y = 4x − 3?
- −3
- 3
- 4 (Correct answer)
- −4
Correct answer: 4
In the equation y = mx + c, m is the gradient and c is the y-intercept. For y = 4x − 3, the gradient m = 4 and the y-intercept c = −3.
Question 3: Factorise: x² + 5x + 6
- (x + 1)(x + 6)
- (x + 2)(x + 3) (Correct answer)
- (x + 3)(x + 2)
- (x + 5)(x + 1)
Correct answer: (x + 2)(x + 3)
Find two numbers that multiply to 6 and add to 5: 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3). Note that answers B and C are the same, so (x + 2)(x + 3) is correct.
Question 4: A circle has a radius of 5 cm. What is its area? (Use π ≈ 3.14)
- 31.4 cm²
- 78.5 cm² (Correct answer)
- 15.7 cm²
- 25 cm²
Correct answer: 78.5 cm²
Area of a circle = πr² = π × 5² = π × 25 ≈ 3.14 × 25 = 78.5 cm². Remember to square the radius, not the diameter.
Question 5: What is the probability of rolling a 4 on a fair six-sided die?
- 1/4
- 4/6
- 1/6 (Correct answer)
- 2/3
Correct answer: 1/6
A fair die has 6 equally likely outcomes (1, 2, 3, 4, 5, 6). There is one way to roll a 4, so the probability = 1/6 ≈ 0.167.
Question 6: Expand and simplify: 2(x + 3) + 3(x − 1)
- 5x + 9
- 5x + 3 (Correct answer)
- 5x + 7
- 5x − 3
Correct answer: 5x + 3
2(x + 3) = 2x + 6 and 3(x − 1) = 3x − 3. Adding: 2x + 6 + 3x − 3 = 5x + 3.
GCSE GCSE Mathematics 1
Solve for x: 3x + 7 = 22