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
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 2.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
- 3.Two mathematically similar oil drums have a length scale factor of 3 from the smaller drum to the larger drum. Work out the volume scale factor from the smaller drum to the larger drum.
- 4.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?
- 5.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.
- 6.A timetable shows the departure times of a bus from Leeds to Harrogate: 08:15, 08:50, 09:25, 10:05, 10:40. Chloe arrives at the bus stop at 09:30. Work out how many minutes she has to wait for the next bus.
- 7.Work out ((−3) + 5) × (−4) − (−6) ÷ 2
- 8.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.
- 9.Divide 84 in the ratio 3:4. Work out the smaller share.
- 10.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.
- 11.A bag contains 5 red counters and 3 blue counters. A counter is taken at random, its colour is noted, and it is put back in the bag before a second counter is taken at random. Work out the probability that both counters are the same colour.
- 12.Round 0.006852 to 2 significant figures.
- 13.Expand and simplify 2(a + 6) − 2(a − 7)
- 14.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
- 15.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.
- 16.Write 0.0038 in standard form.
- 17.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.
- 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.
- 19.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?
- 20.A jar contains 24 green sweets and 16 orange sweets. Write the ratio of green sweets to orange sweets in its simplest form.
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.