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.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.
(a)8
(b)12
(c)6
(d)2
2.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
3.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
(a)10
(b)15
(c)60
(d)12
4.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?
(a)AAA applies, because both triangles have a right angle
(b)The triangles cannot be proved congruent from this information
(c)RHS applies: the right angle, hypotenuse and one matching side are all equal
(d)SSS applies, because all three sides must be equal in any right-angled triangle
5.At a school fête, a stall invites visitors to spin a fair spinner with 8 equal sections numbered 1 to 8, and separately toss a fair coin. A visitor wins a small prize only if the spinner lands on a multiple of 3 and the coin lands on heads. Work out the probability that a visitor wins a prize, giving your answer as a fraction in its simplest form.
(a)1/2
(b)1/16
(c)1/4
(d)1/8
6.A random sample of 50 pupils at a school were asked whether they prefer sport to music. 30 of the 50 pupils said they prefer sport. The school has 500 pupils altogether. Work out an estimate for the number of the 500 pupils who prefer sport.
(a)150 pupils
(b)200 pupils
(c)60 pupils
(d)300 pupils
7.Find the missing number: 17 × ▢ = 391
(a)23
(b)374
(c)17
(d)6647
8.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.
y = 45x + 60
(a)£315
(b)£108
(c)£135
(d)£195
9.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
(a)3
(b)1.6
(c)13
(d)40
10.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
(a)18 cm
(b)3√3 cm
(c)9√3/2 cm
(d)9√3 cm
11.The probability that Priya's dentist appointment overruns is 0.35. Work out the probability that it does not overrun.
(a)1.35
(b)0.35
(c)0.65
(d)0.75
12.A spinner has 4 colours and a coin has 2 sides. Work out how many different outcomes are possible when the spinner is spun once and the coin is tossed once.
(a)6
(b)4
(c)8
(d)2
13.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
(a)y = −3x − 5
(b)y = 3x − 11
(c)y = −3x + 5
(d)y = −3x + 11
14.A novel has 312 pages. A comic has 48 pages. Write the number of pages in the novel as a fraction of the number of pages in the comic, giving your answer in its simplest form.
(a)11/2
(b)13/2
(c)2/13
(d)13/15
15.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.
(a)segment
(b)arc
(c)sector
(d)radius
16.Two fair six-sided dice are rolled and their scores are added together. By listing the possible totals systematically, work out how many different totals are possible.
(a)11
(b)10
(c)6
(d)36
17.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
18.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.
(a)0.62 miles
(b)1.24 miles
(c)1.61 miles
(d)31.00 miles
19.Write 260,000 in standard form.
(a)2.6 × 10⁶
(b)26 × 10⁴
(c)2.6 × 10⁵
(d)0.26 × 10⁶
20.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

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.