OCR 2023 GCE FURTHER MATHEMATICS B MEI Y420/01: CORE PURE A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

(a) The complex number a+ib is denoted by z. (i) Write down z*. [1] (ii) Find Re(iz). [2] (b) The complex number w is given by w = 5+i 3 . 2 -i 3 (i) In this question you must show detailed reasoning. Express w in the form x +iy . [2] (ii) Convert w to modulus-argument form. [2] 2 In this question you must show detailed reasoning. Find the angle between the vector 3i+2j+k and the plane -x+3y+2z = 8. [5] 3 (a) Using partial fractions and the method of differences, show that 1 1 + 1 + 1 +… + 1 = 3 - an+b , # 3 2#4 3#5 n(n + 2) 4 2 (n + 1)(n + 2) where a and b are integers to be determined. [5] (b) Deduce the sum to infinity of the series. 1 1 + 1 + 1 +…. [1] 4 (a) (i) Given that f(x) = 1+2x, find fl(x) and f m (x). [2] (ii) Hence, find the first three terms of the Maclaurin series for 1+2x. [2] (b) Hence, using a suitable value for x, show that 5 . 143 . [2] 3 © OCR 2023 Y420/01 Jun23 Turn over 5 (a) In this question you must show detailed reasoning. Determine the sixth roots of -64, expressed in re ii form. [4] (b) Represent the roots on an Argand diagram. [3] J 0 1 N J 2 0 N 6 The matrices M and N are K O and K O respectivel