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

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

New sheet

GCSE Foundation sample Paper 1 (non-calculator)

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

MathsUKwww.geekhero.co.uk

1.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.
(a)2/5
(b)3/5
(c)2/3
(d)1/2
2.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
3.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.
(a)y = 3x + 4
(b)y = 3/(4x)
(c)y = 4x/3
(d)y = 3x/4
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 small pack contains 5 cards, numbered 1 to 5. One card is drawn at random from the pack, and a fair coin is flipped. Every outcome is listed as a pair, such as (3, H). Work out how many equally likely outcomes there are in total.
(a)5
(b)20
(c)10
(d)7
6.A charity shop in Bath holds 2,000 books. Volunteer A checks a random sample of 50 books and finds 35 paperbacks. Volunteer B checks a different random sample of 50 books and finds 31 paperbacks. Work out the estimate each sample gives for the whole stock, and write down what the shop should do next.
(a)1,400 and 1,240, so combine the samples for one estimate
(b)1,400 and 1,240, so keep 1,400 as the larger estimate
(c)1,400 and 1,240, so one volunteer must have miscounted
(d)1,750 and 1,550, so the larger estimate must be right
7.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.
(a)28.8 km/h
(b)0.48 km/h
(c)2.22 km/h
(d)28 800 km/h
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.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.
(a)500 m
(b)5 m
(c)50 m
(d)0.5 m
10.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?
(a)5 cm by 2 cm
(b)5 cm by 3 cm
(c)3 cm by 2 cm
(d)5 cm by 5 cm
11.The probability that it rains on a given morning is 0.3. If it rains, the probability that Priya's bus is late is 0.8. If it does not rain, the probability that her bus is late is 0.1. Work out the probability that her bus is late.
(a)0.27
(b)0.24
(c)0.31
(d)0.9
12.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.
(a)15
(b)6
(c)30
(d)60
13.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
(a)7n
(b)12n + 7
(c)7n + 12
(d)7n + 5
14.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
(a)50 minutes
(b)20 minutes
(c)15 minutes
(d)25 minutes
15.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?
(a)Yes - SSS, the three side lengths all match
(b)Yes - SAS, two sides and an angle match
(c)Cannot be determined without the angles
(d)No - the sides are listed in a different order
16.A fruit bowl contains apples, pears and plums in the ratio 3 : 4 : 5. What fraction of the fruit are not plums?
(a)5/12
(b)7/24
(c)7/12
(d)7/5
17.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
18.A bag contains red counters and blue counters in the ratio 5:3. There are 56 counters in the bag altogether. Work out how many counters are blue.
(a)35
(b)7
(c)28
(d)21
19.A circle has a radius of 3 cm. Which of these is the exact area of the circle?
(a)28.3 cm²
(b)28.26 cm²
(c)9π cm²
(d)27 cm²
20.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.
(a)12
(b)10
(c)18.75
(d)20

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.