Sample paper · GCSE Foundation · grades 1–5

GCSE Foundation sample Paper 1 (non-calculator)

The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-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 no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.

Non-calculatorGCSE Foundation

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

New sheet

GCSE Foundation sample Paper 1 (non-calculator)

Maths · GCSE Foundation · Paper 1 · Non-calculator · 20 questions

MathsUKwww.geekhero.co.uk

1.Round 24,681 to the nearest 1,000.
(a)24,700
(b)24,000
(c)20,000
(d)25,000
2.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
3.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.
(a)1:13
(b)1:12
(c)12:144
(d)12:1
4.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?
(a)0
(b)2
(c)4
(d)1
5.A weather station records whether it rains each day for 40 days: it rains on 9 of the days and does not rain on the rest. A local forecaster claims that the probability of rain on any day is 0.3. Work out the relative frequency of rain from the recorded data.
(a)0.29
(b)0.225
(c)0.09
(d)0.3
6.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.
(a)Children, as most of them are at home at that time
(b)Unemployed people, as most of them are out at that time
(c)Retired people, as most of them are at work then
(d)Full-time workers, as most are at work at that time
7.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.
(a)22 mm
(b)242 mm
(c)60.5 mm
(d)11 mm
8.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.
(a)No — it has never happened and never will
(b)Yes — when Harry is 20
(c)No — that moment has already passed
(d)Yes — when Harry is 16
9.Write 0.25 as a percentage.
(a)2.5%
(b)0.25%
(c)250%
(d)25%
10.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.
(a)(3, 2)
(b)(3, −2)
(c)(−3, 2)
(d)(−2, −3)
11.A bag contains 45 sweets. 18 of the sweets are lemon flavour and the rest are orange. A sweet is taken at random, its flavour is recorded, and it is put back in the bag. This is repeated 200 times. Work out how many times you would expect an orange sweet to be taken.
(a)80
(b)27
(c)120
(d)182
12.A jug holds 1.25 litres of water. Ella pours in another 400 ml. Work out the total volume, in litres.
(a)5.25 litres
(b)401.25 litres
(c)0.85 litres
(d)1.65 litres
13.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.
(a)52
(b)67
(c)39
(d)17
14.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.
(a)3/4
(b)1/4
(c)4/3
(d)3/7
15.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?
(a)1
(b)8
(c)2
(d)4
16.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.
(a)6 × 10¹
(b)6 × 10¹²
(c)5 × 10⁷
(d)6 × 10⁷
17.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
(a)10
(b)16
(c)12
(d)13
18.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
19.Is 120 divisible by 5? Give a reason for your answer.
(a)Yes, because 120 ends in 0
(b)No, because 1 + 2 + 0 = 3 is not a multiple of 5
(c)Yes, because 120 is even
(d)No, because 5 does not divide into 12
20.A taxi journey of m miles costs C pounds, where C = 2.5m + 3. A driver says the ratio C : m is the same for every journey. Is the driver correct? Give a reason for your answer.
(a)The driver is correct — the ratio C : m is the same for every journey.
(b)The ratio C : m is not constant because the formula includes a fixed charge of £3 as well as the charge per mile.
(c)The ratio C : m is not constant because the charge per mile, £2.50, is not a whole number.
(d)The ratio C : m is not constant because C increases as m increases.

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.