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.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.
- 2.A circular running track is modelled on a grid whose centre is the origin, where each unit represents 1 metre. A floodlight at the point (30, 40) stands on the edge of the track. A second floodlight stands on the edge of the track at the point (0, k), where k is positive. Work out the value of k.
- 3.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
- 4.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?
- 5.A phone network sends automatic text alerts to customers. On average, 1,500 alerts are sent each day, and the probability that a customer replies 'STOP' to an alert is 0.18. Work out how many replies of 'STOP' the network should expect over a 30-day month.
- 6.A pie chart shows how 180 shoppers at a supermarket paid for their shopping. The sector for card payments has an angle of 90° at the centre. Work out how many of the 180 shoppers paid by card.
- 7.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.
- 8.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
- 9.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
- 10.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 11.At a leisure centre, 50 members are asked which activities they do. 32 do yoga, 24 do pilates, and 11 do both. Work out how many members do yoga only, and not pilates.
- 12.Simplify ⁴√(16a⁸b¹²)
- 13.f(x) = x³ − 3x − 5. Given that f(2.2) = −0.952 and f(2.3) = 0.267, work out what this shows about the equation x³ − 3x − 5 = 0.y = x
- 14.The cost, in pounds, of hiring a minibus is modelled against the number of passengers booked. A tangent to the cost graph at 20 passengers passes through the points (16, 184) and (24, 216). Work out the instantaneous rate at which the cost increases with each extra passenger, at 20 passengers.
- 15.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
- 16.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.y = 3x + 6
- 17.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
- 18.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
- 19.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.
- 20.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
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.