C2 Past Paper Booklet - The Grange School Blogs

Jan 20101 (i) Show that the equationcan be expressed in the form22 sin 2 x = 5 cos x − 12 cos 2 x + 5 cos x − 3 = 0. [2](ii) Hence solve the equation2 sin 2 x = 5 cos x − 1,giving all values of x between 0 ◦ and 360 ◦ . [4]2 The gradient of a curve is given by dydxand (p, 5).= 6x − 4. The curve passes through the distinct points (2, 5)(i) Find the equation of the curve. [4](ii) Find the value of p. [3]3 (i) Find and simplify the first four terms in the expansion of (2 − x) 7 in ascending powers of x. [4](ii) Hence find the coefficient of w 6 in the expansion of (2 − 1 4 w2 ) 7 . [2]4 (i) Use the trapezium rule, with 4 strips each of width 0.5, to find an approximate value for5 log 10(2 + x) dx,3giving your answer correct to 3 significant figures. [4]5(ii) Use your answer to part (i) to deduce an approximate value for 3log 10√2 + x dx, showing yourmethod clearly. [2]© OCR 2010 4722 Jan10