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

MathsUKwww.geekhero.co.uk

1.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.
(a)56
(b)336
(c)24
(d)168
2.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
(a)2
(b)3
(c)−6
(d)18
3.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
(a)4 hours
(b)2 hours 40 minutes
(c)3 hours
(d)5 hours 20 minutes
4.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?
(a)22
(b)23
(c)21
(d)24
5.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.
(a)120
(b)180
(c)500
(d)750
6.The times, in seconds, taken by 11 runners to finish a race are given in order: 40, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65. Work out the upper quartile of these times.
(a)52
(b)60
(c)45
(d)58
7.Write 0.36 as a fraction in its simplest form.
(a)36/10
(b)9/25
(c)9/50
(d)3/10
8.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.
(a)9 km
(b)0 km
(c)−9 km
(d)3 km
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.
(a)10
(b)25
(c)100
(d)20
10.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
(a)7 m
(b)5 m
(c)12 m
(d)25 m
11.The probability that a component is faulty is 1/10. Two components are tested independently. Work out the probability that at least one of the two components is faulty.
(a)1/5
(b)1/10
(c)1/100
(d)19/100
12.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.
(a)64π
(b)16π
(c)4π
(d)8π
13.Make x the subject of the formula y = 3(x + 2).
(a)x = (y − 2)/3
(b)x = y/3 − 2
(c)x = 3y − 2
(d)x = y/3 + 2
14.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.
(a)18
(b)12
(c)36
(d)3
15.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?
(a)Yes — two sides and one angle match
(b)No — the angle given is not the included angle
(c)No — SSS needs three equal sides, not two
(d)Yes — SAS allows any equal angle, not just the included one
16.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.
(a)x² + y² = 18
(b)x² + y² = 81
(c)x² − y² = 81
(d)x² + y² = 9
17.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.
(a)25 : 1
(b)1 : 5
(c)1 : 25
(d)1 : 10
18.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
19.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
20.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
(a)No: the 8th term is 50 − 8 × 6 = 2, which is positive.
(b)Yes, but the 8th term is 50 − 8 × 8 = −14.
(c)No: repeated subtraction from 50 can never go negative.
(d)Yes: the 8th term is 50 − 8 × 7 = −6, which is negative.

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.