Sample paper · GCSE Higher · grades 4–9
GCSE Higher 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 Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.
CalculatorGCSE Higher
GCSE Higher sample Paper 2 (calculator)
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- 1.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.
- 2.Which expression means 'add 3 to n, then multiply the result by 4'?
- 3.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.
- 4.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?
- 5.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
- 6.A teacher records the number of pets owned by each of 25 pupils in a class; each pupil owns 0, 1, 2, 3 or 4 pets. The teacher wants to show how many pupils own each number of pets. Write down the most suitable type of chart for this data, and give a reason for your answer.
- 7.Work out −(−3)⁴ + (−3)³
- 8.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
- 9.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.y = 3x
- 10.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.
- 11.A call centre finds that 40% of its calls are about billing. 35% of the calls about billing are dealt with in under five minutes. The centre takes 500 calls on Monday. Work out how many of Monday's calls you would expect to be about billing and dealt with in under five minutes.
- 12.Which of these statements about −0.7 and −0.25 is true?
- 13.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.
- 14.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
- 15.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.
- 16.Work out the period of the graph of y = cos x, in degrees.y = cos(x)
- 17.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.
- 18.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?
- 19.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.
- 20.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.
How the 20 questions are shared out
- Number — 3 questions (15% of the qualification)
- Algebra — 6 questions (30% of the qualification)
- Ratio, proportion and rates of change — 4 questions (20% of the qualification)
- Geometry and measures — 4 questions (20% 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.