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

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GCSE Foundation sample Paper 1 (non-calculator)

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

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1.Work out how many factors 36 has.
(a)5
(b)10
(c)8
(d)9
2.Solve x² − x − 12 = 0.
(a)x = 4 or x = −3
(b)x = −4 or x = 3
(c)x = 12 or x = −1
(d)x = 4 or x = 3
3.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.
(a)64
(b)45
(c)25
(d)35
4.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).
(a)(5, 2)
(b)(3, 10)
(c)(0, 11)
(d)(1, 7)
5.A bag contains 5 letter tiles spelling the word MATHS, with one letter on each tile. Two tiles are drawn at random, one after the other, without the first tile being put back. Work out the probability that both tiles drawn are consonants.
(a)3/4
(b)4/5
(c)16/25
(d)3/5
6.Noah wrote down the numbers 9, 3, 7, 1, 5 and said, “The median is 7, because 7 is in the middle of my list.” Is Noah right? Give a reason for your answer.
(a)Yes — the mean of the five numbers is 7, so the median is 7 as well.
(b)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 5.
(c)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 3.
(d)Yes — 7 is the third of the five numbers he wrote, so it is the median.
7.Write down the symbol that makes this statement true: 3/10 ___ 0.3
(a)=
(b)<
(c)≠
(d)>
8.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
(a)30
(b)27
(c)28
(d)20
9.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
(a)1/5
(b)5/9
(c)4/5
(d)6/5
10.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?
(a)2.40m
(b)m/2.40
(c)m − 2.40
(d)2.40 + m
11.The probability that the Hughes family go away during the summer holidays is 3/7. Work out the probability that they do not go away during the summer holidays.
(a)4/7
(b)1/7
(c)3/7
(d)1/2
12.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.
(a)£27.00
(b)£15.00
(c)£9.00
(d)£33.00
13.Solve the inequality 2(3x − 1) ≥ 4x + 8.
(a)x ≥ 4.5
(b)x ≥ 5
(c)x ≥ 1
(d)x ≥ 20
14.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
15.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
(a)40 cm²
(b)80 cm²
(c)20 cm²
(d)13 cm²
16.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
17.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
(a)38
(b)40
(c)32
(d)39
18.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.
(a)£7
(b)£28
(c)£21
(d)£33
19.Work out the total cost of 3 pens at 45p each and one notebook at £2.35. Give your answer in pounds.
(a)£2.80
(b)£3.70
(c)£8.40
(d)£15.85
20.The table shows values of x and y. x: 3, 5, 8. y: 12, 20, 32. Which statement correctly describes the relationship between x and y?
(a)y is always 4 times x.
(b)y is always double x, plus 6.
(c)y is always x plus 9.
(d)x is always 4 times y.

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.