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%.

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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.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?
(a)2/3
(b)4/9
(c)2/5
(d)1/3
2.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.
3.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.
(a)A straight line with a negative gradient
(b)A straight line crossing the vertical axis above zero
(c)A straight line through the origin
(d)A falling curve that never touches either axis
4.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?
(a)(3, 9)
(b)(6, 2)
(c)(2, 3)
(d)(−2, 6)
5.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.
(a)56/125
(b)24/125
(c)3/10
(d)9/25
6.An estate agent in Leeds lists the prices of the five houses sold on one street last year: £170,000, £150,000, £580,000, £140,000 and £160,000. A newspaper wants to print one figure for a typical price on this street. Work out the mean and the median, and write down which figure the newspaper should print.
(a)The mean, £240,000, as a median ignores three of the prices
(b)The median, £580,000, the middle value of the list given
(c)The median, £160,000, as one very high price lifts the mean
(d)The mean, £155,000, found after the top price is dropped
7.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.
(a)1725 ml
(b)50 ml
(c)2550 ml
(d)1050 ml
8.y = 5x − 1. Work out the value of y when x = 3.
y = 5x − 1
(a)14
(b)16
(c)15
(d)10
9.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.
(a)3200 × 0.64
(b)3200 × 0.12³
(c)3200 × 0.88 × 3
(d)3200 × 0.88³
10.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.
(a)9
(b)4.5
(c)18
(d)90
11.Two fair five-sided dice, numbered 1 to 5, are rolled. Work out the probability that the two scores differ by at least 2.
(a)6/25
(b)12/25
(c)10/25
(d)13/25
12.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
13.Make b the subject of the formula a = 5b.
(a)b = 5/a
(b)b = a/5
(c)b = 5a
(d)b = a − 5
14.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.
(a)7/4
(b)3/7
(c)4/11
(d)4/7
15.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?
(a)the single point exactly halfway along AB
(b)points as far from A as the length AB
(c)points twice as far from A as from B
(d)points the same distance from A as from B
16.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.
(a)31/50
(b)25/4
(c)5/8
(d)8/5
17.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
(a)720
(b)184
(c)176
(d)45
18.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
19.Work out an estimate for 6.8 × 41, by rounding each number to 1 significant figure.
(a)28
(b)240
(c)280
(d)350
20.Two scale plans of the same football pitch are drawn: Plan A has a scale of 1 : 1000 and Plan B has a scale of 1 : 200. A pitch length is 8 cm on Plan A. Work out the length of the same pitch on Plan B, in centimetres.
(a)4 cm
(b)1.6 cm
(c)40 cm
(d)8 cm

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.