Sample paper · GCSE Higher · grades 4–9

GCSE Higher sample Paper 2 (calculator)

The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.

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GCSE Higher sample Paper 2 (calculator)

Maths · GCSE Higher · Paper 2 · Calculator · 20 questions

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1.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.
(a)0.11 g/cm³
(b)9 g/cm³
(c)480 g/cm³
(d)32400 g/cm³
2.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$
3.5 decorators paint 3 rooms in 6 hours. All the decorators work at the same rate. Work out how long it takes 10 decorators to paint 5 rooms.
(a)3 hours
(b)10 hours
(c)5 hours
(d)6 hours
4.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?
(a)ASA (two angles and the included side)
(b)SAS (two sides and the included angle)
(c)RHS (right angle, hypotenuse, one side)
(d)SSS (three sides)
5.180 people entered a fun run. A frequency tree splits them into 108 adults and the rest children. It then splits each of those groups into those who finished and those who did not. 99 of the adults finished, and 153 of the 180 people finished altogether. Work out how many children did not finish.
(a)9
(b)54
(c)27
(d)18
6.Four pairs of variables are listed below. Write down the pair that you would expect to show negative correlation.
(a)Minutes a candle has burned and length remaining
(b)Letters in a pupil's first name and maths score
(c)A football team's shirt colour and matches won
(d)Age of a primary-school pupil and their shoe size
7.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.
(a)27
(b)12
(c)9
(d)24
8.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
9.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.
(a)273.44 US dollars
(b)4,480.00 US dollars
(c)448.00 US dollars
(d)351.28 US dollars
10.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.
(a)7
(b)3
(c)5
(d)27
11.At a school fête, a tombola stall costs £1.50 to play. The probability of winning is 0.2, and the prize is worth £6. Work out the stall's expected profit, on average, from each game played.
(a)£1.20 profit for the stall
(b)£0.30 profit for the stall
(c)£4.50 loss for the stall
(d)£3.30 loss for the stall
12.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
13.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
14.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.
(a)33 km/h
(b)56.6 km/h
(c)88 km/h
(d)34.38 km/h
15.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).
(a)(−3, 3)
(b)(3, −3)
(c)(3, 3)
(d)(7, 5)
16.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).
(a)A rotation of 180° about the origin
(b)A reflection in the x-axis
(c)A reflection in the y-axis
(d)A reflection in the line y = x
17.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8
18.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.
(a)4 squares
(b)12 squares
(c)6 squares
(d)5 squares
19.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.
(a)4
(b)16
(c)0.25
(d)8
20.Expand and simplify 2(a + 6) − 2(a − 7)
(a)13
(b)4a − 2
(c)−2
(d)26

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.