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.Which of these decimals lies between 1/4 and 2/5?
(a)0.45
(b)0.2
(c)0.5
(d)0.3
2.Work out the integer values of x that satisfy x² − 2x − 8 ≤ 0.
(a)−1, 0, 1, 2, 3
(b)−2, −1, 0, 1, 2, 3, 4
(c)−2, −1, 0, 1, 2, 3, 4, 5
(d)−3, −2, −1, 0, 1, 2, 3
3.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
(a)3:1
(b)3:2
(c)2:3
(d)2:1
4.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
(a)sin 30°
(b)tan 0°
(c)cos 45°
(d)sin 90°
5.A survey of 60 readers records: 21 read only fiction, 17 read only non-fiction, 14 read both, and the rest read neither. Work out the probability that a randomly chosen reader reads exactly one of the two types, giving your answer as a fraction in its simplest form.
(a)13/15
(b)19/26
(c)7/30
(d)19/30
6.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.
y = -3x + 74
(a)38, and completely certain, as the line gives exact sales
(b)110, and fairly confident, as 12 °C is inside the range
(c)38, but little confidence, as 12 °C is outside the range
(d)38, and fairly confident, as 12 °C is inside the range
7.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
8.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?
(a)It gets closer to zero but never actually reaches it.
(b)It decreases steadily and reaches zero when x = 60.
(c)It levels off at y = 0.5 as x increases.
(d)It decreases at first, then becomes negative for large x.
9.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
(a)144
(b)18
(c)23
(d)48
10.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?
(a)Yes - SSS, the three side lengths all match
(b)Yes - SAS, two sides and an angle match
(c)Cannot be determined without the angles
(d)No - the sides are listed in a different order
11.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 5 equal sections, numbered 1, 2, 3, 4 and 5. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is 12.
(a)1/10
(b)1/8
(c)1/5
(d)1/20
12.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.
(a)2.5 m
(b)4 m
(c)1.5 m
(d)2.4 m
13.Which expression is equivalent to 7x − 3(2x − 6)?
(a)13x − 18
(b)x − 18
(c)x + 18
(d)x + 6
14.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
15.Triangle S has vertices (2, 2), (5, 2) and (2, 5). It is mapped onto triangle S′ with vertices (2, 5), (5, 5) and (2, 2). Which single composition of two transformations maps S onto S′?
(a)Reflect in the x-axis, then translate by (0, 7).
(b)Reflect in the x-axis, then translate by (7, 0).
(c)Reflect in the y-axis, then translate by (0, 7).
(d)Rotate 180° about the origin, then translate by (0, 7).
16.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.
(a)8
(b)4
(c)2
(d)0
17.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.
(a)2/7
(b)5/12
(c)5/7
(d)7/5
18.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
19.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
(a)An equation, because solving it gives the value of n
(b)An identity, because it is true for many values of n
(c)A formula, because it works out n from 9
(d)An inequality, because ≤ compares the two sides
20.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3

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.