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.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.
(a)−3
(b)4
(c)3
(d)2
2.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$
3.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.
(a)The distance the cyclist travels in 18 hours
(b)The total distance the cyclist travels, in kilometres
(c)The time the cyclist takes, in hours
(d)The cyclist's speed, in kilometres per hour
4.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
(a)62°
(b)59°
(c)90°
(d)118°
5.A fair coin is flipped again and again. After the first 10 flips there have been 7 heads. After 1000 flips there have been 528 heads. Which statement best describes what these results show?
(a)The counts of heads and tails are levelling out
(b)The relative frequency is settling near 0.5
(c)The next flip is more likely to be a tail
(d)The coin is biased, as 528 is more than 500
6.Two classes sat the same test. The 30 pupils in Class A had a mean mark of 72. The 20 pupils in Class B had a mean mark of 82. Work out the mean mark of all 50 pupils.
(a)3800 marks
(b)78 marks
(c)76 marks
(d)77 marks
7.In a car park the ratio of vans to cars is 2 : 7. Work out the number of vans as a fraction of the number of cars.
(a)7/9
(b)2/7
(c)7/2
(d)2/9
8.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?
(a)y = 2x + 1
(b)y = 1/x
(c)y = x²
(d)y = x³
9.Square P has sides of length 3 cm. Square Q has sides of length 12 cm. Write the ratio of the area of square P to the area of square Q in its simplest form.
(a)1 : 64
(b)16 : 1
(c)1 : 16
(d)1 : 4
10.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
(a)(5, 2)
(b)(−5, −2)
(c)(−5, 2)
(d)(2, 5)
11.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.
(a)1/2
(b)1/6
(c)1/3
(d)1/5
12.Work out the lowest common multiple of 4 and 6.
(a)12
(b)2
(c)6
(d)24
13.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
14.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
(a)2 hours
(b)1.5 hours
(c)3 hours
(d)1 hour 20 minutes
15.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
(a)(5, 7)
(b)(2, 2)
(c)(4, 8)
(d)(6, 10)
16.Work out the value of 2⁻²
(a)4
(b)−4
(c)1/4
(d)−1/4
17.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.
(a)(−4, −7)
(b)(7, −4)
(c)(−4, 7)
(d)(4, 7)
18.A ribbon of length 90 cm is cut into two pieces in the ratio 4:5. Work out the length of the shorter piece.
(a)50 cm
(b)10 cm
(c)40 cm
(d)45 cm
19.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.
(a)11
(b)8
(c)12
(d)9
20.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).
(a)3/4
(b)4/3
(c)3/7
(d)4/7

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.