C2 Past Paper Booklet - The Grange School Blogs

June 200621 Find the binomial expansion of (3x − 2) 4 . [4]2 A sequence of terms u 1, u 2, u 3,...isdefinedbyu 1= 2 and u n+1= 1 − u nfor n ≥ 1.(i) Write down the values of u 2, u 3and u 4. [2](ii) Find100∑ u n. [3]n=13 The gradient of a curve is given by dydx = 2x−1 2, and the curve passes through the point (4, 5). Findtheequation of the curve. [6]4The diagram shows the curve y = 4 − x 2 and the line y = x + 2.(i) Find the x-coordinates of the points of intersection of the curve and the line. [2](ii) Use integration to find the area of the shaded region bounded by the line and the curve. [6]5 Solve each of the following equations, for 0 ◦ ≤ x ≤ 180 ◦ .(i) 2sin 2 x = 1 + cos x. [4](ii) sin 2x =−cos 2x. [4]4722/S06