Sample paper · GCSE Foundation · grades 1–5

GCSE Foundation 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 Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.

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GCSE Foundation sample Paper 2 (calculator)

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

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1.Write 0.325 as a fraction in its simplest form.
(a)13/40
(b)3/8
(c)8/25
(d)13/4
2.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
(a)3n − 1
(b)2n + 3
(c)3n − 2
(d)3n + 2
3.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.
(a)20 litres per minute
(b)20 minutes for each litre
(c)0.05 litres per minute
(d)25 litres per minute
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.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.
(a)4 times as likely
(b)3 times as likely
(c)12 times as likely
(d)6 times as likely
6.The times taken, in minutes, by 30 runners in a Portsmouth fun run are grouped in this table: 0 < t ≤ 20 — 5 runners, 20 < t ≤ 40 — 10 runners, 40 < t ≤ 60 — 10 runners, 60 < t ≤ 80 — 5 runners. Work out an estimate for the mean time, in minutes.
(a)7.5 minutes
(b)50 minutes
(c)40 minutes
(d)1200 minutes
7.Work out ((−3) + 5) × (−4) − (−6) ÷ 2
(a)−11
(b)−1
(c)−5
(d)11
8.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
9.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.
(a)£14224
(b)£13600
(c)£14200
(d)£18224
10.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?
(a)Join the two crossing points with a straight line.
(b)Draw wider arcs from each crossing point, meeting above.
(c)Draw an arc centred at P through only one crossing point.
(d)Draw a circle centred at P through both crossing points.
11.A fair spinner has 6 equal sections, and 2 of the sections are coloured purple. The spinner is spun 180 times. Work out how many times you would expect it to land on purple.
(a)30
(b)60
(c)120
(d)90
12.In a fruit crate the ratio of oranges to lemons is 5 : 6. What fraction of the fruit in the crate are lemons?
(a)6/11
(b)5/6
(c)5/11
(d)6/5
13.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.
(a)P = 100I / (RT)
(b)P = 100I/R
(c)P = 100RT/I
(d)P = IRT/100
14.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.
(a)1 : 2 000 000
(b)1 : 200 000
(c)1 : 12 000 000
(d)1 : 20 000
15.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.
(a)π cm
(b)4π cm
(c)10π cm
(d)2π cm
16.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
17.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
18.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.
(a)675 ml
(b)300 ml
(c)450 ml
(d)900 ml
19.Work out the value of √(16 + 9)
(a)5
(b)12
(c)7
(d)−5
20.Write the ratio 18:22 in its simplest form.
(a)9:11
(b)9:22
(c)11:9
(d)9:13

How the 20 questions are shared out

Number — 5 questions (25% of the qualification)
Algebra — 4 questions (20% of the qualification)
Ratio, proportion and rates of change — 5 questions (25% of the qualification)
Geometry and measures — 3 questions (15% 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.