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)
MathsUKwww.geekhero.co.uk
- 1.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
- 2.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
- 3.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
- 4.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.
- 5.A drawing pin is dropped many times and lands either point up or point down. The relative frequency of landing point up is recorded as the experiment goes on: after 50 drops it is 0.720, after 200 drops it is 0.665, and after 1000 drops it is 0.638. The pin is to be dropped a further 2000 times. Work out the best estimate of the number of times it will land point up.
- 6.A histogram shows the ages, in years, of 250 members of a running club. The bar for the class 10 ≤ age < 20 has a frequency density of 4.5 members per year, the bar for 20 ≤ age < 35 has a frequency density of 6 members per year, and the bar for 50 ≤ age < 70 has a frequency density of 2.75 members per year. Work out the frequency of the remaining class, 35 ≤ age < 50.
- 7.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
- 8.Factorise fully 5x + 5y − 5
- 9.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.
- 10.A footpath is 3750 m long. Work out this distance in kilometres.
- 11.A bag contains 3 red beads and 7 blue beads. A bead is taken out at random and not put back. A second bead is then taken out at random. Work out the probability that the first bead is red and the second bead is also red.
- 12.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.
- 13.Solve x² − x − 12 = 0.
- 14.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
- 15.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.
- 16.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?
- 17.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.
- 18.Line l1 has equation x = 2, and line l2 has equation y = x − 1. They intersect at a single point. A shape is reflected in l1, and the image is then reflected in l2. Which point is invariant under this combined transformation?y = x − 1
- 19.Which of these is a factor of 15x + 20?
- 20.Expand and simplify (x − 3)²
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.