Sample paper · GCSE Higher · grades 4–9
GCSE Higher sample Paper 2 (calculator)
The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.
CalculatorGCSE Higher
GCSE Higher sample Paper 2 (calculator)
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- 1.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.
- 2.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
- 3.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.
- 4.Points P and Q have coordinates P(0, 0, 0) and Q(5, 7, 9) in a three-dimensional coordinate system, with all lengths in centimetres. Work out the distance PQ. Give your answer correct to 1 decimal place.
- 5.In a class of 32 pupils, 19 study geography and 15 study history. 8 study both subjects. Work out n(G ∪ H), the number of pupils who study geography or history or both.
- 6.The masses, m kg, of 150 boxes are summarised by these cumulative frequencies: m < 5, 18 boxes; m < 10, 52 boxes; m < 20, 96 boxes; m < 35, 130 boxes; m < 60, 150 boxes. Work out the number of boxes with a mass in the class 10 ≤ m < 20.
- 7.Simplify x⁷ × x⁴, giving your answer as a single power of x.
- 8.A square tile has an area of 144 cm². Work out the side length of the tile.
- 9.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
- 10.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.
- 11.A bag contains 4 red sweets and 6 yellow sweets. Two sweets are taken at random, one after the other, and are not put back. The first sweet taken is red. Work out the probability that the second sweet taken is also red.
- 12.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
- 13.The iterative formula xₙ₊₁ = 12 ÷ (xₙ + 2) is used repeatedly, starting from x₀ = 1. Work out the value that xₙ approaches, correct to 2 decimal places.
- 14.6 identical taps fill a paddling pool in 20 minutes. Each tap fills at the same steady rate. Work out how long 3 of these taps would take to fill the same pool.
- 15.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?
- 16.By completing the square, find the turning point of the curve y = x² − 4x + 9.y = x² − 4x + 9
- 17.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.
- 18.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?
- 19.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
- 20.Solve 5(x + 3) = 40
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.