OCR Monday 4 October 2021 – Afternoon AS Level Further Mathematics A Y531/01 Pure Core. GRADED A+

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Answer all the questions. 1 The lines l 1 and l2 have the following equations. l l r r 8 11 2 253 6 11 8 311 1 2 | | m n = - - + - = - + - - JKKKLJKKKL JKKKL JKKKL NOOOP N... OOOP NOOOP NOOOP (a) Show that l1 and l2 intersect. [4] (b) Write down the point of intersection of l1 and l2. [1] 2 The equation 2 3 2 x x x 3 2 + - + = 5 0 has roots a, b and c. Use a substitution to find a cubic equation with integer coefficients whose roots are a+1, b+1 and c+1. [4] 3 In this question you must show detailed reasoning. The equation x x x 4 3 2 - - + 7 2 218x- = 1428 0 has a root 3 5 - i. Find the other three roots of this equation. [6] 4 (a) A locus C1 is defined by C z 1 = + " | z z i G -2,. (i) Indicate by shading on the Argand diagram in the Printed Answer Booklet the region representing C1. [2] (ii) Find the cartesian equation of the boundary line of the region representing C1, giving your answer in the form ax+ + by c = 0. [2] (b) A locus C2 is defined by C z 2 = + " " | + z z 1 3 G H , , | z-2 2 i . Indicate by shading on the Argand diagram in the Printed Answer Booklet the region representing C2. [3]3 © OCR 2021 Y531/01 Oct21 Turn over 5 Matrices A and B are given by A 1 0 01 = - JKKL NOOP and B 13 5 13 12 13 12 13 = 5 - JKKKKL NOOOOP . (a) Use A and B to disprove the proposition: “Matrix multiplication is commutative”. [2] Matrix B represents the transformation TB. (b) Describe the transformation TB. [2] (c) By considering the inverse transformation of TB, determine B-1. [2] Matrix C is given by C 1 0 03 = - JKKL NOOP and represents the transformation TC. The transformation T BC is transformation TC followed by transformation TB. An object shape of area 5 is transformed by TBC to an image shape N. (d) Determine the area of N. [2] 6 In this question you must show detailed reasoning. (a) Solve the equation 2 1 z z 2 - + 0 25 0 = giving your answers in the form a b + i. [2] (b) Solve the equation 3 2 ~ ~ - = i( ) 5 2 + giving your answer in the form a b + i. [Show More]

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