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.Work out √3 × √12, giving your answer as an integer.
- 2.Write down the expression that means the same as (x + 7) ÷ 4.
- 3.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.
- 4.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.
- 5.A charity raffle has three types of ticket: winning, near-miss and losing, and every ticket is exactly one of these. The probability that a ticket is winning is 1/8 and the probability that it is a near-miss is 1/4. Work out the probability that a ticket is losing.
- 6.A gym draws a histogram of the times, t minutes, that its members spend on one machine. The bar for 0 ≤ t < 10 has a frequency density of 1.8 per minute, the bar for 10 ≤ t < 25 has a frequency density of 3.2 per minute, and the bar for 25 ≤ t < 55 has a frequency density of 0.9 per minute. Members who spend 10 minutes or more on the machine pay an extra charge. Work out the number of members who pay the extra charge.
- 7.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.
- 8.Work out the gradient of the straight line with equation 3y = 12 − 6x.
- 9.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
- 10.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 11.A school buys pens from two suppliers and has 1000 pens in stock. Supplier X provided 70% of the pens and supplier Y provided the other 30%. 2% of supplier X's pens are faulty and 8% of supplier Y's pens are faulty. A pen picked at random from the stock is found to be faulty. Work out the probability that it came from supplier Y. Give your answer as a fraction.
- 12.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.
- 13.By completing the square, find the turning point of the curve y = x² + 8x − 3.y = x² + 8x − 3
- 14.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.
- 15.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.
- 16.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.
- 17.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
- 18.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?
- 19.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?
- 20.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².
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.