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.Write 0.35 as a fraction in its lowest terms.
(a)7/25
(b)35/10
(c)3/10
(d)7/20
2.A circle has centre (0, 0) and equation x² + y² = 3721. The point (11, 60) lies on the circle. One of these is the gradient of the tangent to the circle at (11, 60). Work out which one.
(a)11/60
(b)−60/11
(c)60/11
(d)−11/60
3.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.
(a)510 cm
(b)720 cm
(c)11.25 cm
(d)90 cm
4.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.
(a)40 cm²
(b)120 cm²
(c)24 cm²
(d)15 cm²
5.A two-way table records how 180 students at a school travel: by bus or on foot, split by year group. There are 84 students in Year 11, of whom 38 travel by bus and the rest walk. The rest of the 180 students are in Year 10, and 42 of the Year 10 students travel by bus. Work out the probability that a randomly chosen Year 10 student walks to school. Give your answer as a fraction in its simplest form.
(a)3/10
(b)23/42
(c)9/16
(d)7/16
6.The mean mass of four parcels is 17 kg. Three of the parcels have masses 12 kg, 16 kg and 18 kg. Work out the mass of the fourth parcel.
(a)17 kg
(b)68 kg
(c)22 kg
(d)5 kg
7.Which of these decimals lies between 1/4 and 2/5?
(a)0.45
(b)0.2
(c)0.5
(d)0.3
8.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
9.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.
(a)2.17 litres per minute
(b)130.00 litres per minute
(c)7800.00 litres per minute
(d)2.60 litres per minute
10.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.
(a)100 cm²
(b)260 cm²
(c)120 cm²
(d)240 cm²
11.A factory tests components from a large batch in which 6% are defective. Two components are selected at random, and the batch is large enough that the selections can be treated as independent. Given that at least one of the two components is defective, work out the probability that both are defective.
(a)0.0036
(b)0.0309
(c)0.0600
(d)0.5000
12.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.
(a)5.2
(b)5.1
(c)6.0
(d)5.0
13.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?
(a)It has two whole-number solutions
(b)It has one repeated real solution
(c)It has two different real solutions
(d)It has no real solutions at all
14.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.
(a)5/12
(b)5/7
(c)145/372
(d)7/12
15.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?
(a)Yes - SSS, the three side lengths all match
(b)Yes - SAS, two sides and an angle match
(c)Cannot be determined without the angles
(d)No - the sides are listed in a different order
16.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
17.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.
(a)100 cm²
(b)10000 cm²
(c)1000000 cm²
(d)200 cm²
18.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
(a)(−2, 6)
(b)(−2, −2)
(c)(7, −3)
(d)(8, 6)
19.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?
(a)3x = 12
(b)3x = 10
(c)3x + 2y = 12
(d)x = 12
20.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.
(a)(−2, 6)
(b)(−2, 4)
(c)(2, 6)
(d)(6, 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.