Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 2 (calculator)
The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
CalculatorGCSE Foundation
GCSE Foundation sample Paper 2 (calculator)
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- 1.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.
- 2.Work out the value of 2x² when x = −3
- 3.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.
- 4.How many edges does a cube have?
- 5.Amir has 3 different coloured pens, red, blue and green, and 2 different types of paper, lined and plain. He wants to choose one pen and one type of paper, and draws a grid to list every combination systematically. Work out how many combinations are in his grid.
- 6.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.
- 7.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.
- 8.Solve x − 4 = −9
- 9.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
- 10.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.
- 11.The probability that it rains in Manchester tomorrow is 1/12. Work out the probability that it does not rain in Manchester tomorrow.
- 12.Round 6.283 to 1 significant figure.
- 13.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.
- 14.Write 250 g : 2 kg as a ratio in its simplest form.
- 15.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.
- 16.Work out 6² − 4².
- 17.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.
- 18.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 19.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.
- 20.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.
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.