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%.

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GCSE Higher sample Paper 1 (non-calculator)

Maths · GCSE Higher · Paper 1 · Non-calculator · 20 questions

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1.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.
(a)2, 3, 4, 5
(b)3, 4, 5
(c)1, 2, 3, 4, 5
(d)2, 3, 4, 5, 6
2.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
3.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.
(a)3/2
(b)2/5
(c)2/3
(d)3/5
4.A, B and C are points on a circle with centre O, and AB is a diameter. Prove that angle ACB = 90°, using the fact that triangle OAC and triangle OBC are both isosceles. In the proof, angle OAC = angle OCA = x and angle OBC = angle OCB = y. Which equation correctly expresses the angle sum of triangle ABC in terms of x and y, and leads to the required proof?
(a)x + y = 180°
(b)2x + 2y = 180°
(c)2x + 2y = 360°
(d)2x + y = 180°
5.A biased six-sided dice is rolled once. The probability that it lands on 6 is 0.25. The other five scores are all equally likely. Work out the probability that it lands on 3.
(a)0.167
(b)0.150
(c)0.125
(d)0.750
6.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
(a)1.5
(b)1
(c)6
(d)2
7.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.
(a)16
(b)30
(c)60
(d)2
8.Solve the simultaneous equations y = x + 1 and x² + y² = 25, giving both pairs of solutions.
y = x + 1
(a)x = 4, y = 5 and x = −3, y = −2
(b)x = −4, y = −3 and x = 3, y = 4
(c)x = 12, y = 13
(d)x = −4, y = −3
9.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
(a)750 g
(b)250 g
(c)20 g
(d)60 g
10.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?
(a)an oval
(b)a rectangle
(c)a triangle
(d)a circle
11.At a school fête, a stall invites visitors to spin a fair spinner with 8 equal sections numbered 1 to 8, and separately toss a fair coin. A visitor wins a small prize only if the spinner lands on a multiple of 3 and the coin lands on heads. Work out the probability that a visitor wins a prize, giving your answer as a fraction in its simplest form.
(a)1/2
(b)1/16
(c)1/4
(d)1/8
12.Write 5,000,000 in standard form.
(a)50 × 10⁵
(b)5 × 10⁷
(c)5 × 10⁶
(d)5 × 10⁻⁶
13.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.
(a)x = 4 ± √13
(b)x = −4 ± √13
(c)x = 8 ± √13
(d)x = 4 ± √19
14.The speed of a car is given by v = d ÷ t. A car travels 180 km in 3 hours. Work out the average speed of the car in km/h.
(a)90 km/h
(b)540 km/h
(c)18 km/h
(d)60 km/h
15.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
16.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
17.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
(a)1/9
(b)1/10
(c)9/10
(d)9/1
18.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
(a)4.2 m
(b)2.8 m
(c)1.4 m
(d)7.84 m
19.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.
(a)(0, 7) and (0, −7)
(b)(7, 0) and (−7, 0)
(c)(7, 0) only
(d)(0, 7) only
20.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?
(a)The rate at which the flow rate changes, in litres/min².
(b)The total volume of water, in litres, that has flowed in.
(c)The average rate of flow, in litres per minute.
(d)The total time taken to fill the tank, in minutes.

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.