《Pure 历考试真题分类汇编》.docVIP

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《Pure 历考试真题分类汇编》.doc

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《Pure 历考试真题分类汇编》

Section A Coordinates,Points and Lines(Chapter 1) 1 The diagram shows a rectangle ABCD, where A is (3, 2) and B is (1, 6). (i) Find the equation of BC. [4] (02w) Given that the equation of AC is y = x - 1, find (ii) the coordinates of C, [2] (iii) the perimeter of the rectangle ABCD. [3] 2 The line L1 has equation 2x + y = 8. The line L2 passes through the point A(7, 4) and is perpendicular to L1. (03s) (i) Find the equation of L2. [4] (ii) Given that the lines L1 and L2 intersect at the point B, find the length of AB. [4 3 The diagram shows a trapezium ABCD in which BC is parallel to AD and angle BCD = 90?. The coordinates of A, B and D are (2, 0), (4, 6) and (12, 5) respectively. (03w) (i) Find the equations of BC and CD. [5] (ii) Calculate the coordinates of C. [2] 4 The curve y = 9 - and the line y + x = 8 intersect at two points. Find (i) the coordinates of the two points, [4] (04s) (ii) the equation of the perpendicular bisector of the line joining the two points. [4] 5 The equation of a curve is y = x2 ? 4x + 7 and the equation of a line is y + 3x = 9. The curve and the line intersect at the points A and B. (04w) (i) The mid-point of AB is M. Show that the coordinates of M are () [4] (ii) Find the coordinates of the point Q on the curve at which the tangent is parallel to the line y + 3x = 9. [3] (iii) Find the distance MQ. [1] 6 The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD isM. Find, by calculation, the coordinates of each of M, A and C. [6](05s) 7 Three points have coordinates A (2, 6), B (8, 10) and C (6, 0). The perpendicular bisector of AB meets the line BC at D. Find (05w) (i) the equation of the perpendicular bisector of AB in