Straight lines: OCR MEI A‑Level Maths questions

OCR MEI A-Level Maths past-paper questions on 3.1 Straight lines, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 18 questions on Straight lines, as a list

June 2025, Paper 3, Q3 (10 marks): The straight line with equation x 2 y 6 crosses the x‑axis at A and the y‑axis at B. + = (a) Draw the line with equation x 2 y 6 on the grid in the Printed Answ
June 2025, AS Paper 1, Q3 (4 marks): In this question you must show detailed reasoning. The graph below shows the line y 3 x - and the line through P and Q where P is (–1, 3) and Q 4 = is (5, 0). y
June 2024, Paper 1, Q15 (9 marks): 2 15 The circle x y 2 x 14 y 25 0 has its centre at the point C. The line y 7 x 25 intersects + + - + = = + the circle at points A and B. Prove that triangle AB
June 2024, Paper 2, Q1 (2 marks): Calculate the exact distance between the points (2, 1 - ) and (6, 1). Give your answer in the form a b, where a and b are prime numbers. [2]
June 2024, AS Paper 2, Q6 (4 marks): Determine the equation of the line which passes through the point (4, ‒1) and is perpendicular to the line with equation x 2 3 y 6 . + = Give your answer in the
June 2023, Paper 1, Q7 (7 marks): Determine the exact distance between the two points at which the line through (4, 5) and (6, -1) 2 meets the curve y 2 x 7 x + . 1 [7] = -
June 2023, Paper 3, Q6 (10 marks): (a) Quadrilateral KLMN has vertices K ( - , 1), L (5, 1 4 - ), M (6, 2) and N (2, 5), as shown in Fig. 6.1. Fig. 6.1 y N (2, 5) R S M (6, 2) K (−4, 1) Q x O P L
June 2023, AS Paper 2, Q5 (3 marks): Show that the distance between the points (5, 2) and (11, ‒1) is a b, where a and b are integers to be determined. [3]
June 2022, Paper 3, Q8 (16 marks): 3 8 The curves y h ( ) x and y h - ( ) x , where ( ) h x x - , are shown below. 8 = = = The curve y h ( ) x crosses the x-axis at B and the y-axis at A. = 1 The
June 2022, AS Paper 1, Q10 (9 marks): A triangle has vertices A ( , ), 1 4 B ( , ) 7 0 and C - ( 4 , 1 ). - (a) Show that the equation of the line AC is y x 3 . [2] = + M is the midpoint of AB. The
November 2021, AS Paper 1, Q1 (2 marks): Find the coordinates of the point of intersection of the lines y 3 x - and 2 x 2 y 10 . [2] = + =
November 2021, AS Paper 2, Q10 (6 marks): In this question you must show detailed reasoning. The points P, Q and R have coordinates (‒ 3, 7), (11, 5) and (9, ‒ 9) respectively. (a) Show that PQ is perpe
November 2020, AS Paper 1, Q8 (7 marks): The point A has coordinates (-1, -2) and the point B has coordinates (7, 4). The perpendicular bisector of AB intersects the line y 2 x k at P. + = Determine th
June 2019, Paper 1, Q2 (3 marks): Show that the line which passes through the points ( , 2 4 ) and ( 1 5 , ) does not intersect the line - - 3 x y 10 . [3] + =
June 2019, Paper 1, Q12 (6 marks): t4 2 12 Fig. 12 shows a curve C with parametric equations x , y t4 . The point P, with parameter t, = = is a general point on the curve. Q is the point on the l
June 2019, Paper 3, Q12 (2 marks): Show that the equation of the line in Fig. C2 is ry hx hr , as given in line 24. [2] + =
June 2018, Paper 1, Q12 (14 marks): 2 12 Fig. 12 shows the circle ( x 1 ) ( y 1 ) 25 , the line y 4 3 x 32 and the tangent to the circle at the - + + = = - point A (5, 2). D is the point of inters
June 2018, AS Paper 2, Q8 (7 marks): In this question you must show detailed reasoning. The centre of a circle C is at the point (−1, 3) and C passes through the point (1, −1). The straight line L

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