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A-Level MathematicsYear 2023Q1

2   1. Three particles of masses 4m, 2m and km are placed at the points with coordinates (–3, –1), (6, 1) and (–1, 5) respectively. Given that the centre of mass of the three particles is at the point with coordinates (x, y) (a) show that x k k = − + 6 (3) (b) find y in terms of k. (2) Given that the centre of mass of the three particles lies on the line with equation y = 2x + 3 (c) find the value of k. (2) A fourth particle is placed at the point with coordinates (λ, 4). Given that the centre of mass of the four particles also lies on the line with equation y = 2x + 3 (d) find the value of λ. (2) ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 3   Question 1 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________

Paper Source:EASMF3138fm0-26-que-20230520.pdf

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Exam Specification Info

This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.

Syllabus levelAdvanced Level (A-Level)

SubjectMathematics

Official MarksVariable (2–6 marks)