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 grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.
(a)1 × 10³
(b)0.1 × 10⁻²
(c)1 × 10⁻⁴
(d)1 × 10⁻³
2.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
3.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
(a)750 g
(b)250 g
(c)20 g
(d)60 g
4.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.
(a)2π cm²
(b)9π cm²
(c)81π cm²
(d)18π cm²
5.A two-way table records 200 members of a gym. 80 of the members are women and the rest are men. 60 of the women attend yoga classes. Work out the percentage of the women who attend yoga classes.
(a)75%
(b)30%
(c)25%
(d)50%
6.A scatter graph shows the height, x cm, and the mass, y kg, of 20 pupils in Year 10. The heights on the graph run from 150 cm to 180 cm, and the line of best fit is y = 0.9x − 85. Nadia puts x = 90 into this equation to estimate the mass of a two-year-old child who is 90 cm tall. Is her estimate reliable? Give a reason for your answer.
y = 0.9x − 85
(a)Yes, the line passes through all 20 of the points
(b)Yes, the equation works for any value put into it
(c)No, 90 cm is far outside the heights on the graph
(d)No, a line of best fit cannot be used to predict at all
7.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.
(a)£600
(b)£400
(c)£561
(d)£570
8.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.
y = 3x − 2
(a)−1/3
(b)1/3
(c)3
(d)−3
9.The exchange rate is £1 = €1.15. Convert £200 to euros.
(a)€30.00
(b)€230.00
(c)€2300.00
(d)€201.15
10.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
(a)1000 kg
(b)0.254 kg
(c)0.0625 kg
(d)1 kg
11.A charity raffle sells 250 tickets. A group of friends buy 40 of the tickets between them. Three prizes are awarded, each to a different randomly drawn ticket, and no ticket can win more than one prize. Work out the expected number of prizes won by the group. Give your answer as a fraction in its simplest form.
(a)64/15625
(b)4/25
(c)4/75
(d)12/25
12.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
(a)36
(b)6
(c)108
(d)216
13.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.
(a)k = −9
(b)k = 9
(c)k = 3
(d)k = 36
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 circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.
(a)38.47 m²
(b)18.84 m²
(c)3.14 m²
(d)34.54 m²
16.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
17.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.
(a)1:13
(b)1:12
(c)12:144
(d)12:1
18.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
(a)(3, −4)
(b)(3, −1)
(c)(3, −5)
(d)(−3, 5)
19.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11
20.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?
y = x − 2y = x² − 4x + 2
(a)Right — x² − 3x + 4 = 0 is correct.
(b)Right — subtracting is the same as adding.
(c)Wrong — the correct equation is x² − 5x + 4 = 0.
(d)Wrong — it should be x² − 5x − 4 = 0.

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.