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.Work out −4.5 + 2.8.
(a)1.7
(b)−7.3
(c)−2.3
(d)−1.7
2.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).
(a)y = (x − 3)(x − 5)
(b)y = (x − 3)(x + 5)
(c)y = (x + 3)(x + 5)
(d)y = (x + 3)(x − 5)
3.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.
(a)4/5
(b)5/6
(c)5/9
(d)5/4
4.Triangle E has vertices (1, 2), (4, 2) and (1, 5). It is rotated 90° anticlockwise about the origin, and the image is then reflected in the line y = x. Work out the coordinates of the image of (4, 2).
y = x
(a)(−2, 4)
(b)(4, 2)
(c)(−4, 2)
(d)(4, −2)
5.Two pupils each flip the same coin to estimate the probability of heads. Leah flips it 40 times and gets 24 heads. Ben flips it 60 times and gets 33 heads. By combining both pupils' results, work out the relative frequency of heads, giving your answer as a fraction in its simplest form.
(a)3/5
(b)57/100
(c)11/20
(d)23/40
6.A shop compares customer waiting times, in minutes, at two branches over one week. Branch A had a median of 12 minutes and an interquartile range of 5 minutes. Branch B had a median of 9 minutes and an interquartile range of 11 minutes. Compare the waiting times at the two branches.
(a)Branch A waits longer, and Branch B is more consistent
(b)Branch B waits longer, and Branch B is more consistent
(c)Branch A waits longer, and Branch A is more consistent
(d)Branch B waits longer, and Branch A is more consistent
7.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?
(a)3/13
(b)4/39
(c)1/3
(d)9/13
8.The diagram shows the graph of a function. Which equation could it represent?
(a) $y = x^{3} + 4 x$
(b) $y = x^{3} - 4 x$
(c) $y = - x^{3} + 4 x$
(d) $y = x^{2} - 4 x$
9.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
10.Point Q has coordinates (3, 5). It is translated by the vector (1, −2), and the image is then enlarged by scale factor 3, centre the origin. Work out the coordinates of the final image of Q.
(a)(9, 15)
(b)(12, 9)
(c)(6, 21)
(d)(10, 13)
11.Two fair coins are thrown together 400 times. Work out how many of the 400 throws you would expect to give one head and one tail.
(a)100
(b)200
(c)133
(d)300
12.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?
(a)They cannot both be describing the same path
(b)Jon's measurement must be wrong
(c)Mia's measurement must be wrong
(d)They must both be describing the same path
13.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
14.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.
(a)20 people/year
(b)84 people/year
(c)80 people/year
(d)−20 people/year
15.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?
(a)Its rotational symmetry order is always 4
(b)Its diagonals cross at right angles
(c)Its diagonals are always equal in length
(d)It always has four right angles
16.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?
(a)x = 4
(b)x = −4
(c)x = 0
(d)x = 8
17.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
(a)2 hours
(b)1.5 hours
(c)3 hours
(d)1 hour 20 minutes
18.At a cycling event, a circular track has centre O. Two flags, F and M, are fixed on the track. A course marker P is also on the track, positioned so that angle FOP = 55° and angle POM = 43°, with P between F and M as seen from O. A spectator S stands on the major arc FM, on the opposite side of the track from P. The event programme needs angle FSM. Work out angle FSM.
(a)196°
(b)27.5°
(c)82°
(d)49°
19.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.
(a)7n − 2
(b)n² + 4n
(c)2n² + 4n
(d)n²
20.The table shows the speed, in m/s, of a car at times, in seconds, all 2 seconds apart: 0 at t = 0, 3 at t = 2, 8 at t = 4, 15 at t = 6, 24 at t = 8. A student uses the trapezium rule with these five readings to estimate the distance the car travels. By finding the second differences of the speed values, decide whether this trapezium estimate is an overestimate or an underestimate of the true distance.
(a)Underestimate — second differences are constant.
(b)Overestimate — the speed values are increasing.
(c)Underestimate — the curve bends upward (convex).
(d)Overestimate — the curve bends upward (convex).

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.