Modelling with functions: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 2.12 Modelling with functions, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 14 questions on Modelling with functions, as a list

June 2025, Pure 1, Q6 (7 marks): A scientist is monitoring the flight of sea birds after they leave their nests on a cliff. The height above the sea, h metres, of one of the birds is modelled b
June 2025, Pure 2, Q11 (11 marks): A company is trying to determine the most profitable selling price for a new toy. Given that • if the selling price of each toy is £30, the company expects to s
June 2025, AS Pure, Q7 (10 marks): P x O Figure 3 A company makes a particular type of chair. The annual profit made by the company is modelled by the equation P = –x 2 + 260x – 16 450 where P is
June 2024, Pure 2, Q9 (7 marks): O B(20, 0.8) A(0, 2) H (m) x (m) Figure 3 The graph in Figure 3 shows the path of a small ball. The ball travels in a vertical plane above horizontal ground. Th
June 2023, Pure 1, Q13 (7 marks): On a roller coaster ride, passengers travel in carriages around a track. On the ride, carriages complete multiple circuits of the track such that • the maximum
June 2023, Pure 2, Q12 (10 marks): O 5 t N NA NB Figure 2 The number of subscribers to two different music streaming companies is being monitored. The number of subscribers, NA , in thousands, to
June 2023, AS Pure, Q7 (8 marks): The distance a particular car can travel in a journey starting with a full tank of fuel was investigated. • From a full tank of fuel, 40 litres remained in the
June 2022, Pure 1, Q5 (6 marks): The height, h metres, of a tree, t years after being planted, is modelled by the equation h 2 = at + b 0  t < 25 where a and b are constants. Given that • the
November 2021, Pure 1, Q12 (9 marks): H x O 3 Figure 3 Figure 3 is a graph of the trajectory of a golf ball after the ball has been hit until it first hits the ground. The vertical height, H metres,
November 2020, AS Pure, Q4 (6 marks): In 1997 the average CO2 emissions of new cars in the UK was 190 g/km. In 2005 the average CO2 emissions of new cars in the UK had fallen to 169 g/km. Given A g/
June 2019, Pure 2, Q7 (7 marks): A small factory makes bars of soap. On any day, the total cost to the factory, £y, of making x bars of soap is modelled to be the sum of two separate elements:
June 2019, AS Pure, Q4 (5 marks): A tree was planted in the ground. Its height, H metres, was measured t years after planting. Exactly 3 years after planting, the height of the tree was 2.35 met
June 2019, AS Pure, Q9 (6 marks): A company started mining tin in Riverdale on 1st January 2019. A model to find the total mass of tin that will be mined by the company in Riverdale is given by
June 2018, Pure 2, Q8 (7 marks): H x O Figure 1 Figure 1 is a graph showing the trajectory of a rugby ball. The height of the ball above the ground, H metres, has been plotted against the horiz

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