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.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
2.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
(a)12 km/h
(b)9 km/h
(c)8 km/h
(d)0.2 km/h
3.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2
4.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.
(a)20 litres
(b)20000 litres
(c)0.02 litres
(d)30 litres
5.A box contains counters that are silver, bronze or copper only. The probability that a counter taken at random is silver is 1/2 and the probability that it is bronze is 1/8. The box contains 64 counters in total. Work out the number of copper counters.
(a)8
(b)40
(c)24
(d)32
6.The times, t minutes, taken by 80 people to travel to work are grouped like this: 0 ≤ t < 10, 6 people; 10 ≤ t < 20, 14 people; 20 ≤ t < 30, 25 people; 30 ≤ t < 40, 20 people; 40 ≤ t < 50, 15 people. Work out the cumulative frequency for t < 30.
(a)25
(b)35
(c)65
(d)45
7.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2
(a)1/2, 3/5, 2/3, 5/6
(b)5/6, 2/3, 3/5, 1/2
(c)1/2, 3/5, 5/6, 2/3
(d)1/2, 2/3, 3/5, 5/6
8.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.
(a)500 m
(b)300 m
(c)200 m
(d)400 m
9.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.
(a)72 cm
(b)9 cm
(c)36 cm
(d)23 cm
10.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?
(a)y
(b)z
(c)x
(d)X
11.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.
(a)3/4
(b)9/16
(c)3/16
(d)1/2
12.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?
(a)9/10
(b)3/5
(c)4/15
(d)2/5
13.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7
14.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.
(a)£102
(b)£68
(c)£136
(d)£170
15.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.
(a)Isosceles trapezium
(b)Kite
(c)Parallelogram
(d)Rhombus
16.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
17.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.
(a)1.3
(b)−1.3
(c)7.7
(d)14.4
18.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
(a)44
(b)22
(c)10
(d)5.5
19.Which of these pairs of lines are perpendicular to each other?
(a)y = 2x and y = 2x + 1
(b)y = 2x and y = −(1/2)x + 1
(c)y = 2x and y = −2x + 1
(d)y = 2x and y = (1/2)x + 1
20.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².
(a)0.625 m/s²
(b)1.6 m/s²
(c)8 m/s²
(d)2.2 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.