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.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.
- 2.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.
- 3.A coach travels 210 miles at an average speed of 70 mph. Work out how long the journey takes.
- 4.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.
- 5.A garage tested 200 cars in one week. 70% of the cars were more than 3 years old and the rest were 3 years old or less. Of the cars more than 3 years old, 1 in 4 failed the test. 12 of the cars that were 3 years old or less failed the test. Work out how many of the 200 cars failed the test altogether.
- 6.A shop records the colour of every car that uses its car park one Tuesday. Its frequency table reads: black 44, silver 37, blue 26, red 18, white 12. Write down the frequency of black cars.
- 7.Work out the total cost of 3 pens at 45p each and one notebook at £2.35. Give your answer in pounds.
- 8.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
- 9.Divide 84 in the ratio 3:4. Work out the smaller share.
- 10.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 11.A weather station records whether it rains each day for 40 days: it rains on 9 of the days and does not rain on the rest. A local forecaster claims that the probability of rain on any day is 0.3. Work out the relative frequency of rain from the recorded data.
- 12.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 13.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
- 14.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.
- 15.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.
- 16.Work out the value of √49 + ∛27
- 17.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
- 18.y is directly proportional to x, and y = 7x. Work out the value of x when y = 35.y = 7x
- 19.In a fruit basket the ratio of bananas to oranges is 2 : 5. What fraction of the fruit are oranges?
- 20.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
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.