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.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
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.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
(a)7.8 kg/m³
(b)78000 kg/m³
(c)7800 kg/m³
(d)780 kg/m³
4.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.
(a)19
(b)10
(c)20
(d)14
5.A biased six-sided dice is rolled once. The probability that it lands on 6 is 0.25. The other five scores are all equally likely. Work out the probability that it lands on 3.
(a)0.167
(b)0.150
(c)0.125
(d)0.750
6.A bus company runs two routes into the centre of Exeter. On ten weekdays the journey time on Route 1 was, in minutes: 22, 23, 24, 24, 25, 25, 26, 26, 27 and 28. On Route 2 it was: 18, 19, 20, 20, 21, 22, 26, 30, 36 and 38. A commuter must reach the centre on time every day. Work out the mean and the range for each route, and write down which route she should take.
(a)Route 2, as its mean time is lower than Route 1's mean
(b)Route 2, as its fastest journey took only 18 minutes
(c)Either route, as both have a mean time of 25 minutes
(d)Route 1, as its times vary by 6 minutes rather than 20
7.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.
(a)1,500 ≤ m < 2,500
(b)1,000 ≤ m < 3,000
(c)1,950 ≤ m < 2,050
(d)1,500 < m ≤ 2,500
8.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.
(a)s = t / d
(b)s = d / t
(c)s = d − t
(d)s = dt
9.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.
(a)500 m
(b)50 m
(c)5 m
(d)0.05 m
10.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
11.A drawer contains 4 red socks and 2 blue socks. Two socks are taken out at random, one after the other, without the first being put back. Work out the probability that both socks are the same colour.
(a)7/18
(b)2/5
(c)5/9
(d)7/15
12.Work out an estimate for 89 + 52, by rounding each number to the nearest 10.
(a)141
(b)130
(c)150
(d)140
13.Work out the value of 3a − 2b when a = 5 and b = 4
(a)52
(b)−7
(c)23
(d)7
14.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.
(a)26
(b)5.6
(c)28
(d)35
15.A polygon has 9 sides. What is the name of this polygon?
(a)Octagon
(b)Nonagon
(c)Heptagon
(d)Decagon
16.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
17.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
18.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.
(a)1:2
(b)1:200000
(c)1:2000
(d)1:20000
19.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.
(a)25
(b)−5
(c)1
(d)−35
20.A fruit bowl contains 9 apples and 21 oranges. Write down the ratio of apples to oranges in its simplest form.
(a)9 : 12
(b)9 : 21
(c)7 : 3
(d)3 : 7

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.