> Monday 4 October 2021 – Afternoon AS Level Further Mathematics B (MEI) Y410/01 Core Pure

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Answer all the questions. 1 Using standard summation formulae, find = r r 3 n 1 2 - r /^ h, giving your answer in fully factorised form. [3] 2 The equation 3 4 x x 2 - +2 0 = has roots a an... d b. Find an equation with integer coefficients whose roots are 3-2a and 3-2b. [3] 3 Three planes have the following equations. , , . x y z x y z x y z 2 3 3 4 2 1 3 2 3 14 - + =- - + = - - + = (a) (i) Write the system of equations in matrix form. [1] (ii) Hence find the point of intersection of the planes. [2] (b) In this question you must show detailed reasoning. Find the acute angle between the planes 2 3 x y - +z =-3 and x y z - + 4 2 = 1. [4] 4 Anika thinks that, for two square matrices A and B, the inverse of AB is A B - - 1 1. Her attempted proof of this is as follows. ( )( ) ( ) ( ) ( )( ) ( ) AB A B A BA B A A B B AA BB I I I Hence AB A B 1 1 1 1 1 1 1 1 1 1 1 # = = = = = = - - - - - - - - - - - (a) Explain the error in Anika’s working. [2] (b) State the correct inverse of the matrix AB and amend Anika’s working to prove this. [3]3 © OCR 2021 Y410/01 Oct21 Turn over 5 Prove by induction that = r n 2 1 ( ) 1 2 n r n 1 1 # - = + - /r for all positive integers n. [5] 6 A transformation T of the plane has associated matrix M 1 1 1 m 1 m = - + - JKKL NOOP , where m is a non-zero [Show More]

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