Sample paper · GCSE Higher · grades 4–9
GCSE Higher 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 Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.
Non-calculatorGCSE Higher
GCSE Higher sample Paper 1 (non-calculator)
MathsUKwww.geekhero.co.uk
- 1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
- 2.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
- 3.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.
- 4.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.
- 5.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.
- 6.The 120 pupils in Year 11 at a school sat a maths test. Their marks m are grouped into classes of unequal width: 0 ≤ m < 40, 12 pupils; 40 ≤ m < 60, 24 pupils; 60 ≤ m < 70, 36 pupils; 70 ≤ m ≤ 100, 48 pupils. A histogram is drawn for these data. Work out the frequency density of the class 40 ≤ m < 60.
- 7.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.
- 8.Solve x² − 5x + 6 = 0 by factorising.
- 9.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
- 10.A tank holds 3.2 m³ of water. Work out this volume in litres.
- 11.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.
- 12.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2
- 13.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?
- 14.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
- 15.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?
- 16.Which of these statements is an identity?
- 17.Simplify the ratio 12 : 18 : 30 to its simplest form.
- 18.Point Q has coordinates (3, 5). It is translated by the vector (1, −2), and the image is then enlarged by scale factor 3, centre the origin. Work out the coordinates of the final image of Q.
- 19.Make x the subject of the formula y = 5x + 3.y = 5x + 3
- 20.When a number is added to its square the result is 30. Work out the possible values of the number.
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.