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.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.
(a)30 cm
(b)360 cm
(c)15 cm
(d)10 cm
2.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
3.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.
(a)1 : 18
(b)9 : 5
(c)5 : 9
(d)3 : 5
4.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.
(a)£2.50
(b)£5.00
(c)£325.00
(d)£3.25
5.A basketball player takes two free throws, and the throws are independent. The probability of scoring on each throw is 0.6, and the probability of missing is 0.4. Work out the probability that she scores exactly one of the two throws.
(a)0.48
(b)0.84
(c)0.24
(d)0.36
6.A sports centre in Ipswich has 2,000 members. It wants to know what its members think of its opening hours, so it asks a random sample of 100 of them. Write down what the population is in this survey.
(a)Everybody who lives in Ipswich.
(b)All 2,000 members of the sports centre.
(c)The members who say they are unhappy with the opening hours.
(d)The 100 members who were asked.
7.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.
(a)25
(b)−5
(c)1
(d)−35
8.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
(a)88
(b)39
(c)32
(d)25
9.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
(a)3 cm
(b)300000 cm
(c)0.3 cm
(d)30 cm
10.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6
11.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.
(a)56/125
(b)24/125
(c)3/10
(d)9/25
12.Work out an estimate for 312 × 19, by rounding each number to 1 significant figure.
(a)6200
(b)5928
(c)6000
(d)600
13.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
(a)It does not cross, since the minimum lies below the axis.
(b)It crosses the x-axis, since the minimum is below it.
(c)It touches the x-axis once, at (3, −4).
(d)It is impossible to tell without the full equation.
14.A car travels 150 km in 3 hours at a constant speed. Work out the average speed of the car, in km/h.
(a)450
(b)153
(c)147
(d)50
15.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?
(a)Wrong: multiply by angle ÷ 360, not divide by it.
(b)Wrong: multiply by the angle only, no division.
(c)Wrong: use radius × angle, not circumference.
(d)Correct: dividing by the angle in degrees works.
16.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.
(a)1725 ml
(b)50 ml
(c)2550 ml
(d)1050 ml
17.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.
(a)1.8
(b)72
(c)3.6
(d)6
18.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.
(a)£18.00
(b)£0.01
(c)£8.00
(d)£2.00
19.Work out (3 × 5)²
(a)225
(b)30
(c)75
(d)34
20.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
(a)25:1
(b)1:25
(c)25:8
(d)8:25

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.