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.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
2.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?
(a)3x/2
(b)−3x/2
(c)3x²/2
(d)3/2
3.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.
(a)27.6 km
(b)1800 km
(c)30 km
(d)19.2 km
4.A triangular plot of land has sides AB = 13 m and AC = 10 m, with angle BAC = 72° between them. Work out the perimeter of the plot. Give your answer to 1 decimal place.
(a)39.7 m
(b)26.7 m
(c)36.7 m
(d)41.7 m
5.A spinner can land on red, blue, green or yellow. The probability that it lands on red is 0.24 and the probability that it lands on yellow is 0.16. The probabilities of landing on blue and on green are equal, and each is called x. Work out the value of x.
(a)0.30
(b)0.15
(c)0.60
(d)0.38
6.The daily high temperatures, in °C, in Leeds over five days were 14, 16, 18, 19 and 23. In York over the same five days they were 15, 17, 17, 18 and 18. Write a sentence comparing Leeds and York using both the median and the range.
(a)Leeds has a higher median and a greater range than York.
(b)York has a higher median but a smaller range than Leeds.
(c)Leeds has a higher median but a smaller range than York.
(d)York has a higher median and a greater range than Leeds.
7.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
8.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.
(a)Tuesday, by 2 km/h
(b)Tuesday, by 8 km/h
(c)Tuesday, by 3 km/h
(d)Monday, by 2 km/h
9.Two mathematically similar cylinders have volumes 64 cm³ and 216 cm³. Work out the ratio of the height of the smaller cylinder to the height of the larger cylinder, in simplest form.
(a)2 : 3
(b)3 : 2
(c)64 : 216
(d)8 : 27
10.Two hikers walk from a campsite A to a lookout B, a distance of 14 km on a bearing of 038°. From B they walk to a shelter C, a distance of 20 km on a bearing of 142°. Work out the direct distance from A to C. Give your answer to 1 decimal place.
(a)34.0 km
(b)21.5 km
(c)23.0 km
(d)27.0 km
11.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
12.Write down the exact decimal value of the fraction 1/6.
(a)0.1666...
(b)0.16
(c)0.17
(d)0.6
13.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?
(a)Third and fourth
(b)First and third
(c)Second and fourth
(d)First and second
14.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.
(a)4 : 1
(b)3 : 12
(c)1 : 4
(d)1 : 1.2
15.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.
(a)44.7 m
(b)34.6 m
(c)50.0 m
(d)60.0 m
16.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?
(a)The object was decelerating
(b)The object was travelling at a constant, non-zero speed
(c)The object was stationary (not moving)
(d)The object was travelling at its maximum speed
17.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
(a)5:3
(b)2:5
(c)2:3
(d)3:2
18.A point is translated twice by the vector $(5 - 3)$ . Write down the single column vector that describes the overall translation.
(a) $(5 - 3)$
(b) $(10 - 6)$
(c) $(5 - 6)$
(d) $(15 - 9)$
19.The graph of y = x² − 4x is translated by the vector (3, 0). Work out the equation of the image, giving your answer in the form y = x² + bx + c.
y = x² − 4xy = x²
(a)y = x² − 7x + 21
(b)y = x² + 2x − 3
(c)y = x² − 4x + 3
(d)y = x² − 10x + 21
20.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6

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.