The points and have coordinates (3k 4, and (1, + 1) respectively, where is a 8. A B k k − −2) constant. Given that the gradient of is , AB − (a) show that = 3, k (2) (b) find an equation of the line through and A B, (3) (c) find an equation of the perpendicular bisector of and Leave your answer in the form A B. where and are integers. ax + by + c = 0 a, b c (4) (Total 9 marks) ___________________________________________________________________________ 9. A stone is thrown from the top of a cliff. The height in metres, of the stone above the ground level after seconds is modelled by the h, t function h(t) = 115 + 12.25t 4.9t 2. – (a) Give a physical interpretation of the meaning of the constant term 115 in the model. (1) (b) Write in the form where and are constants to be found. h(t) A B(t C)2, A, B C – – (3) (c) Using your answer to part (b), or otherwise, find, with justification the time taken after the stone is thrown for it to reach ground level, (3) (ii) the maximum height of the stone above the ground and the time after which this maximum height is reached. (2) (Total 9 marks) ___________________________________________________________________________ 10. The diagram shows with = 8x 3, = 4x 1, = 120 and = 15. ABC AC – BC – ABC ACB
8. The points A and B have coordinates (3k − 4, −2) and (1, k + 1) respectively, where k is a constant. Given that the gradient of AB is − , (a) show that k = 3, (2) (b) find an equation of the line through A and B, (3) (c) find an equation of the perpendicular bisector of A and B. Leave your answer in the form ax + by + c = 0 where a, b and c are integers. (4) (Total 9 marks) ___________________________________________________________________________ 9. A stone is thrown from the top of a cliff. The height h, in metres, of the stone above the ground level after t seconds is modelled by the function h(t) = 115 + 12.25t – 4.9t 2. (a) Give a physical interpretation of the meaning of the constant term 115 in the model. (1) (b) Write h(t) in the form A – B(t – C)2, where A, B and C are constants to be found. (3) (c) Using your answer to part (b), or otherwise, find, with justification the time taken after the stone is thrown for it to reach ground level, (3) (ii) the maximum height of the stone above the ground and the time after which this maximum height is reached. (2) (Total 9 marks) ___________________________________________________________________________ 10. The diagram shows ABC with AC = 8x – 3, BC = 4x – 1, ABC = 120 and ACB = 15.
19728_05_as_pure_mathematics_practice_paper_c.docx