Free GCSE Maths 15-Minute Diagnostic: 12 Quick Questions
A free 15-minute GCSE Maths check-up covering number, algebra, ratio, percentages, geometry and probability.
Instructions
No calculator unless you genuinely need one.
Give yourself 15 minutes.
Show working where possible.
Mark only after all 12 questions.
Questions
1. Calculate 7.2 × 0.4.
2. Write 0.375 as a fraction in simplest form.
3. Increase £80 by 15%.
4. Simplify 3a + 5b − a + 2b.
5. Solve 4x + 7 = 31.
6. Expand 3(x + 4).
7. Flour and sugar are in the ratio 5:2. If 350 g of flour is used, how much sugar is needed?
8. A jacket is reduced from £60 to £45. What percentage reduction is this?
9. The angles in a triangle are 48°, 67° and x°. Find x.
10. A rectangle is 8 cm by 5 cm. Find its area and perimeter.
11. A bag contains 3 red, 5 blue and 2 green counters. What is the probability of choosing green?
12. Sequence: 5, 9, 13, 17, … Write an expression for the nth term.
Answers
1. 2.88
2. 3/8
3. £92
4. 2a + 7b
5. x = 6
6. 3x + 12
7. 140 g
8. 25%
9. 65°
10. Area = 40 cm²; perimeter = 26 cm
11. 1/5
12. 4n + 1
Score guide
10–12 secure: move towards multi-step exam questions and timed practice.
7–9 reasonable foundation: identify the topics behind your errors and practise those first.
4–6 several gaps: focus on core methods before full papers.
0–3 rebuild fundamentals carefully with short targeted practice.
This is a broad skills diagnostic, not a grade predictor.
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