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%.

CalculatorGCSE Higher

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

New sheet

GCSE Higher sample Paper 2 (calculator)

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

MathsUKwww.geekhero.co.uk

1.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?
(a)1/3
(b)2/3
(c)1/2
(d)7/12
2.The graph of y = sin x is transformed onto the graph of y = sin x + 1. Which statement correctly describes the transformation and the new range of the graph?
y = sin(x)
(a)Reflect in the x-axis; range unchanged, −1 ≤ y ≤ 1
(b)Translate +1 in x; range unchanged, −1 ≤ y ≤ 1
(c)Translate +1 in y; new range 0 ≤ y ≤ 2
(d)Translate +1 in y; new range −2 ≤ y ≤ 0
3.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.
(a)£2,400
(b)£2,000
(c)£3,200
(d)£6,000
4.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector $(- 3 5)$ to a warehouse, then by the vector $(4 - 1)$ to the delivery address. Work out the coordinates of the delivery address.
(a)(7, −2)
(b)(11, −3)
(c)(8, −6)
(d)(6, 2)
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.A Year 10 class has 20 boys with a mean height of 150 cm and 10 girls with a mean height of 168 cm. Work out the mean height of all 30 pupils in the class.
(a)4,680 cm
(b)234 cm
(c)156 cm
(d)159 cm
7.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
8.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
(a)x = 1, y = 3
(b)x = 3, y = 2
(c)x = 3, y = 1
(d)x = 3, y = −1
9.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
10.A drone flies from base station D on a bearing of 065° for 14 km to a checkpoint E. At E it changes course and flies on a bearing of 165° for 20 km to a delivery point F. Work out the direct distance from D to F. Give your answer to 1 decimal place.
(a)23.4 km
(b)498.8 km
(c)22.3 km
(d)26.3 km
11.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.
(a)0.098
(b)0.63
(c)0.532
(d)0.468
12.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.
(a)49 km/h
(b)48.54 km/h
(c)52 km/h
(d)50 km/h
13.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
14.A tangent to a distance–time graph, with distance in kilometres and time in minutes, has gradient 0.78 kilometres per minute at a particular point. Work out the instantaneous rate of change of distance with time, in kilometres per hour.
(a)46.8 km/h
(b)60.78 km/h
(c)0.78 km/h
(d)0.013 km/h
15.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.
(a)11.4 cm
(b)4.8 cm
(c)14.7 cm
(d)58.8 cm
16.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.
y = x² − 3x
(a)2/3
(b)1/2
(c)2
(d)6
17.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
(a)36
(b)0.03
(c)129.5
(d)441
18.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.
(a)31.0°
(b)36.8°
(c)53.1°
(d)36.9°
19.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
20.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.
(a)68
(b)85
(c)80
(d)125

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.