OCR A Level Further Mathematics A Paper 1 Y540-01 Pure Core 1 June 2022 QUESTION PAPER

Document Content and Description Below

In this question you must show detailed reasoning. (a) Show that cosh( ) 2 3 ln 9 41 = . [2] The region R is bounded by the curve with equation y x = sinh , the x-axis and the line with equation x... = 2 3 ln (see diagram). The units of the axes are centimetres. x y R O y x = sinh x = 2 3 ln A manufacturer produces bell-shaped chocolate pieces. Each piece is modelled as being the shape of the solid formed by rotating R completely about the x-axis. (b) Determine, according to the model, the exact volume of one chocolate piece. [4] 3 © OCR 2022 Y540/01 Jun22 Turn over 2 The matrix A is given by A 2 1 2 3 = - J L K K N P O O. (a) Calculate det A. [1] (b) Write down A-1 . [1] (c) Hence solve the equation A x y 1 2 = - J L K K J L K K N P O O N P O O. [2] (d) Write down the matrix B such that AB = 4I. [1] Matrices C and D are given by C 2 0 1 = J L K K K N P O O O and D = ( ) 0 2 p where p is a constant. (e) Find, in terms of p, • the matrix CD • the matrix DC. [3] It is observed that CD ! DC. (f) The result that CD ! DC is a counter exam [Show More]

Last updated: 1 year ago

Preview 1 out of 8 pages