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.Write 0.005 in standard form.
- 2.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
- 3.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 4.Shape T has a vertex at (5, 3). T is enlarged by scale factor −1, centre (2, 1). Work out the coordinates of the image of the vertex (5, 3).
- 5.In a certain town, P(rain on Monday) = 0.3. If it rains on Monday, the probability that it also rains on Tuesday is 0.6. If it does not rain on Monday, the probability that it rains on Tuesday is 0.25. Work out the probability that it rains on Tuesday.
- 6.A council wants to find out what all residents of a town think about a new cycle lane. It posts a survey only on its website and asks people to fill it in online. Give a reason why this sample is likely to be biased.
- 7.Work out ((−3) + 5) × (−4) − (−6) ÷ 2
- 8.Which of these quadratic graphs does NOT cross the x-axis at all?
- 9.y is directly proportional to x², and x is positive. When x = 4, y = 32. Construct the equation connecting x and y, then work out the value of x when y = 200.
- 10.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.
- 11.Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.
- 12.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.
- 13.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.
- 14.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
- 15.Each of these has an exact value. Write down the one whose value is the greatest.
- 16.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?
- 17.A rope of length A is 1.5 times as long as a rope of length B. Write the ratio A : B in its simplest form.
- 18.A shape is reflected in the line y = −x. Which of these points is invariant under this reflection?y = −x
- 19.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
- 20.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?
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.