A-level FURTHER MATHEMATICS Paper 2 June 2023

Answer all questions in the spaces provided. outside the box 1 Given that y ¼ sin x þ sinh x , find d2y d x2 þ y Circle your answer. 2 sin x —2 sin x 2 sinh x —2 sinh x 2 Which one of the expressions below is not equal to zero? Circle your answer. [1 mark] [1 mark] lim (x2 e—x ) lim (x5 ln x) lim ex lim (x3ex) x !1 x ! 0 x !1 x5 x ! 0 1 1 1 3 The determinant A ¼ 2 0 2 3 2 1 Which one of the determinants below has a value which is not equal to the value of A? outside the box Tick (3) one box. 3 1 3 2 0 2 . 3 2 1 . . 1 0 2 . . 1 2 1 . . 1 0 1 . . 3 2 1 . . 3 2 1 . . 2 0 2 . 4 It is given that f (x) ¼ cosh—1 (x — 3) [1 mark] Which of the sets listed below is the greatest possible domain of the function f ? Circle your answer. fx : x ≥ 4g fx : x ≥ 3g fx : x ≥ 1g fx : x ≥ 0g [1 mark] Turn over 5 Josh and Zoe are solving the following mathematics problem: outside the box Josh says that to solve this problem you must first carry out the transformation on C1 to find C2, and then find the asymptotes of C2 Zoe says that you will get the same answer if you first find the asymptotes of C1, and then carry out the transformation on these asymptotes to obtain the asymptotes of C2 Show that Zoe is correct. [5 marks]