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 train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.
(a)42.5 ≤ t < 47.5
(b)40 ≤ t < 50
(c)42.5 ≤ t ≤ 47.5
(d)44.5 ≤ t < 45.5
2.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.
(a)6
(b)9
(c)18
(d)12
3.A recipe requires flour and butter in the ratio 3 : 2. Write down which of these amounts could be used in the recipe.
(a)180 g flour and 120 g butter
(b)120 g flour and 180 g butter
(c)180 g flour and 90 g butter
(d)180 g flour and 140 g butter
4.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.
(a)15.7 cm
(b)31.4 cm
(c)62.8 cm
(d)78.5 cm
5.A garden centre recorded 240 plant sales using a frequency tree. The first stage splits the sales into three types: shrubs, bedding plants and trees. 96 sales were shrubs, 114 were bedding plants and the rest were trees. Work out the probability that a sale chosen at random from these 240 was a tree.
(a)2/5
(b)1/8
(c)19/40
(d)3/40
6.A netball team scored 50, 83 and 68 points in three matches. Work out the mean number of points scored.
(a)68
(b)33
(c)67
(d)100.5
7.Work out (−2)³ + (−3)² − (−4)
(a)5
(b)−13
(c)−3
(d)21
8.Work out the equation of the straight line through the points (−2, 1) and (0, 7).
(a)y = −3x + 7
(b)y = 3x + 1
(c)y = 3x + 7
(d)y = (1/3)x + 7
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.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.
(a)20 litres
(b)20000 litres
(c)0.02 litres
(d)30 litres
11.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.
(a)50/3
(b)3/47
(c)1/10
(d)3/50
12.Work out (5 + 2) × 3²
(a)147
(b)63
(c)23
(d)441
13.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
14.In a box of pens, 3/7 of the pens are blue and the rest are black. Write down the ratio of the number of blue pens to the number of black pens, in its simplest form.
(a)4 : 3
(b)4 : 7
(c)3 : 4
(d)3 : 7
15.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.
(a)62.8 cm
(b)125.6 cm
(c)251.2 cm
(d)31.4 cm
16.Work out the lowest common multiple of 4 and 6.
(a)12
(b)2
(c)6
(d)24
17.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.
(a)1.5
(b)8
(c)3
(d)12
18.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
19.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
(a)28.3 cm²
(b)28.26 cm²
(c)9π cm²
(d)27 cm²
20.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
(a)600 litres
(b)6 litres
(c)0.6 litres
(d)60 litres

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.