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 down the decimal that is equal to 3/5.
(a)1.67
(b)0.6
(c)0.35
(d)0.53
2.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.
(a)y = 2
(b)y = 2.2
(c)y = 3
(d)y = 10
3.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
4.Triangle ABC has AB = 8 cm, BC = 10 cm and CA = 6 cm. Triangle LMN has LM = 10 cm, MN = 6 cm and NL = 8 cm. The two triangles are congruent by SSS. Which of the following correctly matches the corresponding vertices?
(a)A↔L, B↔M, C↔N (ABC≅LMN)
(b)A↔N, B↔M, C↔L (ABC≅NML)
(c)A↔N, B↔L, C↔M (ABC≅NLM)
(d)A↔M, B↔N, C↔L (ABC≅MNL)
5.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.
(a)1/2
(b)1/6
(c)1/3
(d)1/5
6.A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.
(a)3
(b)9
(c)4
(d)6
7.A fruit bowl contains apples, pears and plums in the ratio 3 : 4 : 5. What fraction of the fruit are not plums?
(a)5/12
(b)7/24
(c)7/12
(d)7/5
8.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.
(a)6.4
(b)4
(c)5.2
(d)3.5
9.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.
(a)£334.80
(b)£338.68
(c)£338.69
(d)£302.40
10.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.
(a)50 m
(b)201 m
(c)25 m
(d)13 m
11.A school surveys 60 pupils. 32 say they walk to school, 24 say they cycle to school, and 12 say they do both, on different days. The rest travel only by car. One of the 60 pupils is chosen at random. Work out the probability that this pupil travels only by car.
(a)4/15
(b)4/5
(c)1/5
(d)7/15
12.Work out (5 + 2) × 3²
(a)147
(b)63
(c)23
(d)441
13.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.
(a)It touches the x-axis once, only at x = 4.
(b)It never touches the x-axis at all.
(c)It crosses twice, at x = 4 and x = −4.
(d)It crosses twice, at x = 2 and x = −2.
14.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.
(a)£120.00
(b)£580.00
(c)£480.00
(d)£720.00
15.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.
(a)94.2 cm³
(b)90 cm³
(c)282.6 cm³
(d)1130.4 cm³
16.Freya types 4² + 3² into her calculator and writes down 49. Work out the correct value of 4² + 3².
(a)14
(b)25
(c)49
(d)12
17.Which expression is equivalent to 6x − (2x − 5)?
(a)8x + 5
(b)8x − 5
(c)4x − 5
(d)4x + 5
18.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
19.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
20.A factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.
(a)48 minutes
(b)120 minutes
(c)108 minutes
(d)1,350 minutes

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.