Sample paper · GCSE Higher · grades 4–9
GCSE Higher sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.
Non-calculatorGCSE Higher
GCSE Higher sample Paper 1 (non-calculator)
MathsUKwww.geekhero.co.uk
- 1.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
- 2.Solve 4(x − 3) = 2x + 6.
- 3.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.
- 4.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?
- 5.A spinner is divided into sectors of 144°, 90° and 126°, coloured purple, orange and grey in that order. The spinner is spun 300 times. Work out how many times you would expect it to land on purple.
- 6.The times, t seconds, taken by 142 competitors to complete a lap are grouped like this: 0 ≤ t < 10, 20 competitors; 10 ≤ t < 25, 12 competitors; 25 ≤ t < 45, 50 competitors; 45 ≤ t < 75, 60 competitors. A histogram is drawn. Write down the class whose bar is the tallest.
- 7.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.
- 8.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
- 9.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
- 10.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?
- 11.A bag contains 5 red counters and 5 green counters. Three counters are taken out one at a time and are not put back. Work out the probability that all three counters are red.
- 12.Work out ∛(−27) + ∛8
- 13.Simplify (x² − 9) ÷ (x² + 5x + 6).
- 14.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
- 15.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
- 16.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.
- 17.Write 45 minutes : 2 hours as a ratio in its simplest form.
- 18.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
- 19.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?
- 20.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.
How the 20 questions are shared out
- Number — 3 questions (15% of the qualification)
- Algebra — 6 questions (30% of the qualification)
- Ratio, proportion and rates of change — 4 questions (20% of the qualification)
- Geometry and measures — 4 questions (20% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.