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 quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.
(a)(12 + 12π) cm
(b)3π cm
(c)(12 + 3π) cm
(d)(6 + 3π) cm
2.Which expression means 'y squared, multiplied by 3'?
(a)3y²
(b)y³
(c)(3y)²
(d)3 + y²
3.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.
(a)32 cm
(b)24 cm
(c)16 cm
(d)14 cm
4.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(2, 3)
(c)(5, 4)
(d)(6, 3)
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.For each of 30 fires in one county, the number of fire engines sent and the cost of the damage were recorded. The scatter graph of the data shows strong positive correlation. A newspaper prints the headline "Sending more fire engines causes more damage". Is the newspaper right? Give a reason for your answer.
(a)No, the size of the fire affects both of the quantities
(b)Yes, the points lie close to the line of best fit
(c)Yes, strong positive correlation shows one causes the other
(d)No, the correlation on the scatter graph is negative
7.Work out 2/3 × 3/4 exactly, giving your answer in its simplest form.
(a)17/12
(b)1/2
(c)8/9
(d)2
8.Which expression means 'add 3 to n, then multiply the result by 4'?
(a)4n + 3
(b)3(n + 4)
(c)4(n + 3)
(d)n + 3 × 4
9.Two mathematically similar containers have a volume scale factor of 64 (the larger container's volume is 64 times the smaller container's volume). Work out the length scale factor between the two containers.
(a)4
(b)8
(c)64
(d)32
10.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?
(a)No — hexagons can't be regular
(b)Yes — six equal sides means regular
(c)Yes — all sides are equal
(d)No — angles must be equal too
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.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.
(a)6 × 10² metres
(b)6 × 10¹⁴ metres
(c)6 × 10⁻⁴⁸ metres
(d)5 × 10² metres
13.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.
(a)Tuesday, by 2 km/h
(b)Tuesday, by 8 km/h
(c)Tuesday, by 3 km/h
(d)Monday, by 2 km/h
14.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
(a)3 cm
(b)300000 cm
(c)0.3 cm
(d)30 cm
15.Which of these correctly compares a 'line' with a 'line segment'?
(a)A line has two endpoints; a segment has none
(b)A line segment is always curved
(c)A line has no endpoints; a segment has two
(d)A line segment is a closed shape
16.Write down a prime number between 30 and 40.
(a)33
(b)31
(c)36
(d)34
17.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
18.Divide 84 in the ratio 3:4. Work out the smaller share.
(a)42
(b)48
(c)36
(d)28
19.In a photo album the ratio of colour photos to black-and-white photos is 9 : 4. Work out the number of black-and-white photos as a fraction of the number of colour photos.
(a)4/9
(b)4/13
(c)9/13
(d)9/4
20.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.
(a)7:5
(b)15:7
(c)1:2
(d)7:15

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.