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.Work out √225 ÷ 3.
- 2.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?
- 3.An online shop's total number of orders received is recorded at the end of each day for five consecutive days: Day 1, 1,284 orders; Day 2, 1,509 orders; Day 3, 1,830 orders; Day 4, 2,296 orders; Day 5, 2,510 orders. Work out between which two consecutive days the average rate of increase in orders was greatest.
- 4.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.
- 5.In Manchester the probability of rain on any day in November is taken to be 0.3, and whether it rains on one day is independent of whether it rains on the next. Work out the probability that it rains on both the 10th and the 11th of November.
- 6.The masses, m kg, of 60 parcels are grouped like this: 0 ≤ m < 5, 22 parcels; 5 ≤ m < 10, 20 parcels; 10 ≤ m < 20, 9 parcels; 20 ≤ m < 30, 5 parcels; 30 ≤ m < 50, 4 parcels. Write down the class interval that contains the median mass.
- 7.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.
- 8.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.
- 9.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.
- 10.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.
- 11.The probability that a seed fails to germinate is 1/5. Three seeds are planted independently. Work out the probability that at least one of the three seeds germinates.
- 12.Work out the value of .
- 13.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.
- 14.A curve has equation y = 2x² + 5. Work out an estimate for the gradient of the curve at x = 3, using a chord between the points where x = 2 and x = 4.y = 2x² + 5
- 15.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?
- 16.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.
- 17.The height of a ball, in metres, above the ground is plotted against time, in seconds, after it is thrown. The tangent to the graph at t = 1.5 seconds has gradient 2. Which of these four statements about the ball at t = 1.5 seconds is correct?
- 18.Work out the exact value of cos 0° − sin 30°.
- 19.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?
- 20.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.
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.