8. Figure 1 Figure 1 shows a rectangle ABCD. The point lies on the and the points and lie on the as shown in Figure 1. A y-axis B D x-axis Given that the straight line through the points and has equation 5y + 2x = 10, A B (a) show that the straight line through the points and has equation 2y = 4, A D − 5x (4) (b) find the area of the rectangle ABCD. (3) (Total for Question 8 is 7 marks) ___________________________________________________________________________ 9. Given that is constant and A = 2A2, show that there are exactly two possible values for A. (Total for Question 9 is 5 marks) ___________________________________________________________________________ 10. In a geometric series the common ratio is and sum to terms is r n Sn Given = S S6 show that , where is an integer to be found. r k (Total for Question 10 is 4 marks) ___________________________________________________________________________ 11. Figure 2 Figure 2 shows a sketch of part of the graph = f(x) where y f(x) = 23 + 5, 0 x x – (a) State the range of f. (1) (b) Solve the equation f(x) + 30 x
8. Figure 1 Figure 1 shows a rectangle ABCD. The point A lies on the y-axis and the points B and D lie on the x-axis as shown in Figure 1. Given that the straight line through the points A and B has equation 5y + 2x = 10, (a) show that the straight line through the points A and D has equation 2y − 5x = 4, (4) (b) find the area of the rectangle ABCD. (3) (Total for Question 8 is 7 marks) ___________________________________________________________________________ 9. Given that A is constant and = 2A2, show that there are exactly two possible values for A. (Total for Question 9 is 5 marks) ___________________________________________________________________________ 10. In a geometric series the common ratio is r and sum to n terms is Sn Given S = S6 show that r , where k is an integer to be found. (Total for Question 10 is 4 marks) ___________________________________________________________________________ 11. Figure 2 Figure 2 shows a sketch of part of the graph y = f(x) where f(x) = 23 – x + 5, x 0 (a) State the range of f. (1) (b) Solve the equation f(x) x + 30
02a_a_level_mathematics_sams_-_paper_2_pure_mathematics.docx