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.Which one of these statements about negative numbers is true?
(a)−3 > 0
(b)0 > −1
(c)0 < −1
(d)−5 > −3
2.Solve 2x − 2 = 2
(a)x = 2
(b)x = 8
(c)x = 0
(d)x = 4
3.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
4.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
(a) $(2 - 5)$
(b) $(8 9)$
(c) $(- 2 5)$
(d) $(2 5)$
5.At a fête, a game costs £3 to play. The probability of winning is 0.1, and each win pays out £20. 150 people play the game. Work out the fête's expected profit from the game.
(a)£150
(b)£450
(c)£300
(d)£1
6.Seven pupils were asked how many books they had read last month. Their answers were 3, 5, 5, 7, 8, 5, 3. Write down the mode.
(a)7
(b)8
(c)5
(d)3
7.Work out ((−3) + 5) × (−4) − (−6) ÷ 2
(a)−11
(b)−1
(c)−5
(d)11
8.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
9.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
(a)2 hours
(b)1.5 hours
(c)3 hours
(d)1 hour 20 minutes
10.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
(a)45 m
(b)4500 m
(c)450 m
(d)0.45 m
11.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.
(a)1/6
(b)6/11
(c)1/7
(d)7/36
12.Work out 0.6 × 0.04.
(a)2.4
(b)0.24
(c)0.024
(d)0.0024
13.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.
(a)x = −2 and x = −5
(b)x = 2 and x = −5
(c)x = −2 and x = 5
(d)x = 2 and x = 5
14.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.
(a)160 g
(b)10 g
(c)200 g
(d)8 g
15.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).
(a)(9, 8)
(b)(5, −2)
(c)(5, 2)
(d)(−5, 2)
16.Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.
(a)7/8
(b)1/8
(c)6/8
(d)5/8
17.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
18.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
19.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
(a)x⁶
(b)x⁴
(c)6x
(d)x¹⁰
20.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².
(a)0.03 N/m²
(b)35 N/m²
(c)201.6 N/m²
(d)81.6 N/m²

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.