OCR 2023 GCE FURTHER MATHEMATICS A Y541/01: PURE CORE 2 A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

(a) The matrix P is given by P = K L 0 - 2 2 N 2 - 2 O. (i) Write down the dimensions of P. [1] (ii) Write down the transpose of P. [1] J 3 (b) The matrices Q, R and S are given by Q = ^1 2h, R = K L -4 N O and S = ^3 P -2h. Write down the sum of the two of these matrices which are conformable for addition. [1] (c) The dimensions of matrix A are 4 by 5. The matrices A and B are conformable for multiplication so that the matrix C = BA can be formed. The matrix C has 6 rows. (i) Write down the number of columns that C has. [1] (ii) Write down the dimensions of B. [1] (iii) Explain whether the matrix AB can be formed. [1] J -2 3 NJ c 5 N J c 5 NJ -2 3 N (d) Find the value of c for which K OK O = K OK O. [2] L 6 10PL10 13P L 10 13PL 6 10P 2 In this question you must show detailed reasoning. (a) Write the complex number -24 + 7i in modulus-argument form. [3] (b) Solve the simultaneous equations given below, giving your answers in cartesian form. iz -6z + 3w = -7i + 5iw = 3+13i [4] 3 (a) Show that d ^sinh-1 uh = 1 . [2] (b) Find the equation of the normal to the graph of y = sinh-1 2x at the point where x = 6. Give your answer in the form y = mx + c where m and c are given in exact, non-hyperbolic form. [4] 4 2 3 3 © OCR 2023 Y541/01 Jun23 Turn over 2 4 In this question you must show detailed reasoning. The region R is bounded by the curve with equation y = 1 , the x-axis and the lines with equations x = 1 and x = 1 (see diagram). The units of the axes are cm. y 2 1 R y