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.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.
- 2.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.
- 3.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
- 4.A water tank holds 2.5 m³. Work out this volume in cm³.
- 5.A garden centre recorded 240 plant sales using a frequency tree. The first stage splits the sales into three types: shrubs, bedding plants and trees. 96 sales were shrubs, 114 were bedding plants and the rest were trees. Work out the probability that a sale chosen at random from these 240 was a tree.
- 6.A Year 10 class has 20 boys with a mean height of 150 cm and 10 girls with a mean height of 168 cm. Work out the mean height of all 30 pupils in the class.
- 7.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.
- 8.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).
- 9.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.
- 10.A, B, C and D are points on a circle, with B and D both on the same major arc AC. E lies on the straight line through A and B, beyond B, so that angle CBE = 145°. Work out the size of angle ADC.
- 11.An ordinary fair dice is rolled once. Set A is the set of even scores and set B is the set of scores greater than 4. Work out the probability that the score rolled is in set A or in set B or in both.
- 12.Write 12 as a product of its prime factors.
- 13.A circle has centre (0, 0) and passes through the point (5, 12). Work out the equation of the circle.
- 14.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 15.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?
- 16.Work out the gradient of the straight line with equation 3y = 12 − 6x.
- 17.A textbook is reduced from £60 to £45. Work out the percentage reduction.
- 18.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.
- 19.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.
- 20.A circle has centre (0, 0) and equation x² + y² = 3721. The point (11, 60) lies on the circle. One of these is the gradient of the tangent to the circle at (11, 60). Work out which one.
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.