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.On one night in Manchester the temperature at 3 am was 8 °C below zero and at 9 am it was 3 °C below zero. Write down the warmer of the two readings.
- 2.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.y = x² + 2x − 15
- 3.A jar contains 24 green sweets and 16 orange sweets. Write the ratio of green sweets to orange sweets in its simplest form.
- 4.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
- 5.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.
- 6.On a scatter graph of the arm span and the height of some pupils, the points rise from left to right. Write down the type of correlation this shows.
- 7.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 8.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
- 9.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².
- 10.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?
- 11.Priya and Ben each want to estimate the probability that a coin lands on heads. Priya flips the coin 50 times and works out her relative frequency. Ben flips the same coin 500 times and works out his relative frequency. Whose relative frequency is more likely to be close to the true probability? Give a reason for your answer.
- 12.In a classroom the ratio of boys to girls is 3 : 4. What fraction of the class are boys?
- 13.Which of these is a formula, rather than an expression, an equation, or an identity?
- 14.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
- 15.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
- 16.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
- 17.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.
- 18.Write the ratio 6a : 9a in its simplest form, where a is a positive number.
- 19.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.
- 20.The ratio of two lengths is 0.6 : 1.5. Write this ratio in its simplest whole-number 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.