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.Simplify x⁶ ÷ x²
- 2.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.
- 3.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.
- 4.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
- 5.A table shows how two Year 10 classes did in a spelling test. In class A, 18 out of 24 pupils passed. In class B, 21 out of 30 pupils passed. Which class had the greater proportion of pupils passing?
- 6.A line graph shows the temperature in a greenhouse at the end of each of six hours. The six readings were 10 °C, 14 °C, 18 °C, 22 °C, 26 °C and 30 °C. Describe the trend shown by the line graph.
- 7.Estimate the value of √45, giving your answer to the nearest whole number.
- 8.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
- 9.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.
- 10.Work out the exact value of cos 0° − sin 30°.
- 11.A bag contains 5 yellow marbles and 3 blue marbles. Noah takes a marble at random, notes its colour and puts it back in the bag. He then takes a second marble at random. Work out the probability that the first marble is yellow and the second marble is blue.
- 12.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.
- 13.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.y = 2x + 4
- 14.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.
- 15.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.
- 16.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
- 17.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.
- 18.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.
- 19.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.
- 20.x is 2/3 of y. Write the ratio x : y 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.