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 square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.
(a)144√2
(b)24√2
(c)6√2
(d)12√2
2.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
3.A cup of tea is cooling. Its temperature, in °C, is plotted against time, in minutes, since it was poured. At t = 4 minutes, the gradient of the tangent to the graph is −3.2. What does this tell you about the tea at t = 4 minutes?
(a)Temperature is 3.2°C
(b)Rising at 3.2°C per minute
(c)Falling at 3.2°C per minute
(d)Fallen 3.2°C in total so far
4.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
(a)22
(b)28
(c)35
(d)63
5.A spinner lands on one of four colours: amber, black, cyan or damson. The probability it lands on amber is 0.18, on black is 0.22 and on cyan is 0.24. Work out the probability that it lands on amber or damson.
(a)0.54
(b)0.36
(c)0.82
(d)0.64
6.A histogram is drawn for the masses, m grams, of 200 letters. The bar for 0 ≤ m < 50 has a frequency density of 1.2 per gram and the bar for 50 ≤ m < 100 has a frequency density of 1.8 per gram. All the remaining letters lie in the class 100 ≤ m < 200. Work out the frequency density of the bar for 100 ≤ m < 200.
(a)1.4 per gram
(b)2 per gram
(c)0.5 per gram
(d)0.25 per gram
7.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.
(a)Yes — Priya's jump could have been up to 3.9 m
(b)No — their possible jump lengths do not overlap
(c)Yes — both jumps could have been 3.85 m
(d)No — a recorded jump is exactly the length jumped
8.Simplify (x² − 9) ÷ (x² + 5x + 6).
(a)(x + 3)/(x + 2)
(b)(x − 3)/(x + 2)
(c)x − 3
(d)−9/(5x + 6)
9.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
(a)4
(b)36
(c)84
(d)9
10.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.
(a)16 cm
(b)10 cm
(c)9 cm
(d)4 cm
11.An archer hits the bullseye with probability 0.24 on any one shot. She wants to know how many shots she must take to expect to hit the bullseye 12 times. Work out how many shots this is.
(a)50
(b)16
(c)3
(d)48
12.Work out 35% of 180.
(a)45
(b)63
(c)145
(d)126
13.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
(a)7.4
(b)1.25
(c)5
(d)4
14.The density of a type of wood is 0.8 g/cm³. Work out the mass of a piece of this wood with a volume of 150 cm³.
(a)149.2 g
(b)187.5 g
(c)1200 g
(d)120 g
15.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.
(a)3 cm²
(b)24 cm²
(c)12 cm²
(d)768 cm²
16.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.
(a)x = 14, y = −4
(b)x = 7, y = 3
(c)x = 5, y = 5
(d)x = 7, y = 4
17.A cyclist's speed, in metres per second, is plotted against time, in seconds, since she sets off. Which statement correctly pairs the gradient of a tangent to this graph, and the area between the graph and the time-axis, with what each one represents?
(a)Gradient = distance travelled; area = acceleration.
(b)Gradient = speed itself; area = distance travelled.
(c)Gradient = acceleration; area = acceleration too.
(d)Gradient = acceleration; area = distance travelled.
18.Vector A is $(- 5 2)$ and vector B is $(5 - 2)$ . Write down how vector B compares to vector A.
(a)B is the same as A
(b)B is unrelated to A in direction
(c)B is twice A
(d)B is the reverse of A
19.Which expression means 'triple c, then add double d'?
(a)6cd
(b)2c + 3d
(c)3c + 2d
(d)5(c + d)
20.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.
(a)£50
(b)£120
(c)£60
(d)£40

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.