Straight lines: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 3.1 Straight lines, 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 16 questions on Straight lines, as a list

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, Q2 (5 marks): The line l passes through the points A (–3, 0) and B 5 2 22 , (a) Find the equation of l giving your answer in the form y = mx + c where m and c are constant
June 2024, AS Pure, Q3 (8 marks): Relative to a fixed origin O, • point P has position vector 9i – 8j • point Q has position vector 3i – 5j (a) Find PQ → (2) Given that R is the point such that
June 2024, AS Pure, Q10 (8 marks): C P Q l O y x Figure 4 Figure 4 shows a sketch of the circle C • the point P (–1, k + 8) is the centre of C • the point Q (3, k 2 – 2k) lies on C • k is a posit
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 2023, AS Pure, Q8 (5 marks): O R C l 6 (10, 80) 60 y x Figure 3 Figure 3 shows a sketch of a curve C and a straight line l. Given that • C has equation y x f where f (x) is a quadratic expr
June 2023, AS Pure, Q10 (8 marks): O y x C B A l1 l2 Figure 4 The line l1 has equation y x 3 5 6 The line l2 is perpendicular to l1 and passes through the point B( , ) 8 0 , as shown in the sketc
June 2022, AS Pure, Q11 (8 marks): C O l y x Figure 3 Figure 3 shows the circle C with equation x2 + y2 – 10x – 8y + 32 = 0 and the line l with equation 2y + x + 6 = 0 (a) Find (i) the coordinate
November 2021, AS Pure, Q15 (9 marks): P l O x y N C Figure 4 Figure 4 shows a sketch of a circle C with centre N(7, 4) The line l with equation y = 1 3 x is a tangent to C at the point P. Find (a) t
November 2020, Pure 1, Q7 (5 marks): y x O l C R 25 (−2, 13) Figure 1 Figure 1 shows a sketch of a curve C with equation y = f (x) and a straight line l. The curve C meets l at the points (−2, 13)
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/
November 2020, AS Pure, Q11 (9 marks): (i) A circle C1 has equation x2 + y2 + 18x – 2y + 30 = 0 The line l is the tangent to C1 at the point P(–5, 7). Find an equation of l in the form ax + by + c =
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, Q1 (4 marks): The line l1 has equation 2x + 4y – 3 = 0 The line l2 has equation y = mx + 7, where m is a constant. Given that l1 and l2 are perpendicular, (a) find the value
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 2018, Pure 1, Q6 (10 marks): Not to scale y C A P l O x Figure 3 The circle C has centre A with coordinates (7, 5). The line l, with equation y = 2x + 1, is the tangent to C at the point P,

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