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)
MathsUKwww.geekhero.co.uk
- 1.Write the mixed number 2 1/4 as an improper fraction.
- 2.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.
- 3.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.
- 4.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
- 5.A fair coin is flipped again and again. After the first 10 flips there have been 7 heads. After 1000 flips there have been 528 heads. Which statement best describes what these results show?
- 6.A vertical line chart shows the number of goals scored by a football team in each of its 20 matches: 0 goals in 4 matches, 1 goal in 7 matches, 2 goals in 6 matches and 3 goals in 3 matches. Write down the modal number of goals.
- 7.Work out 6² − 4².
- 8.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.
- 9.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.
- 10.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 11.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.
- 12.Work out the lowest common multiple of 4 and 6.
- 13.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
- 14.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.
- 15.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?
- 16.A piece of ribbon is 2.4 metres long. Kim cuts 40 cm from it. Work out the length of ribbon left, in millimetres.
- 17.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
- 18.Ravi has 5 pears. He has 4 times as many apples as pears. Write the number of pears as a fraction of the number of apples.
- 19.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.
- 20.Write 350 ml : 1.4 l as a ratio 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.