Further Mathematics 8360/1. Level 2 (JUN ) Level 2 Certificate in Further Mathematics June Time allowed * 1 hour 30 minutes

Transcription

1 Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Level 2 Certificate in Further Mathematics June 2014 Further Mathematics 8360/1 Level 2 Paper 1 Non-Calculator Monday 16 June 2014 For this paper you must have: mathematical instruments. You may not use a calculator am to am Pages TOTAL Mark Time allowed 1 hour 30 minutes Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the es at the top of this page. Answer all questions. You must answer the questions in the spaces provided. around each page or on blank pages. Do all rough work in this book. Cross through any work that you do not want to be marked. In all calculations, show clearly how you work out your answer. Information The marks for questions are shown in brackets. The maximum mark for this paper is 70. You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book. (JUN ) P70179/Jun14/E5w 8360/1

2 2 Formulae Sheet Volume of sphere ¼ 4 3 pr 3 Surface area of sphere ¼ 4pr 2 Volume of cone ¼ 1 3 pr 2 h Curved surface area of cone ¼ prl In any triangle ABC Area of triangle ¼ 1 ab sin C 2 Sine rule Cosine rule a sin A ¼ b sin B ¼ c sin C a 2 ¼ b 2 þ c 2 2bc cos A cos A ¼ b2 þ c 2 a 2 2bc The Quadratic Equation The solutions of ax 2 þ bx þ c ¼ 0, where a 6¼ 0, are given by x ¼ b qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðb 2 4acÞ 2a Trigonometric Identities tan y sin y cos y sin 2 y þ cos 2 y 1 (02)

3 3 Answer all questions in the spaces provided. 1 A straight line has gradient 2 and passes through the point ð 3, 10Þ. Work out the equation of the line. Give your answer in the form y ¼ mx þ c [2 marks] y ¼ 4x 3 7x Work out dy dx [2 marks] Turn over for the next question Turn over s 4 (03)

4 4 8 3 A transformation is given by the matrix M, where M ¼ 1 a 9 >: >; 0 2 The image of the point ðb, 5Þ under M is ð5, bþ. Work out the values of a and b. [3 marks] a ¼..., b ¼... 4 Solve 20 þ w < 3ðw þ 2Þ [3 marks] (04)

5 5 5 fðxþ ¼10 x 2 for all values of x. gðxþ ¼ðx þ 2aÞðx þ 3Þ for all values of x. 5 (a) Circle the correct value of fð 4Þ [1 mark] (b) Write down the range of fðxþ. [1 mark] 5 (c) gð0þ ¼24 Show that a ¼ 4 [1 mark]... 5 (d) Hence solve fðxþ ¼gðxÞ [4 marks] Turn over s 13 (05)

6 6 6 The nth term of a sequence is 2n 2 þ 7 3n (a) Work out the 7th term. Give your answer as a fraction in its simplest form. [2 marks] 6 (b) Show that the limiting value of 2n 2 þ 7 3n 2 2 as n!1is 2 3 [2 marks] (06)

7 7 7 ABCD is a cyclic quadrilateral. A y þ 40 Not drawn accurately B 2x x þ 2y y þ 20 D C Work out the values of x and y. [5 marks] x ¼..., y ¼... Turn over s 9 (07)

8 8 8 (a) Factorise fully 3x 2 12 [2 marks] 8 (b) Factorise 5x 2 þ 4xy 12y 2 [3 marks] (08)

9 9 9 ABC is a straight line. BC is 20% of AC. Að 9, 18Þ Not drawn accurately B Cð16, 3Þ Work out the coordinates of B. [4 marks] Answer...,... Turn over for the next question Turn over s 9 (09)

10 10 10 Rationalise the denominator of Give your answer in the form 8 p 3 ffiffiffi 5 p a þ b ffiffiffi 5 where a and b are integers. [3 marks] (10)

11 11 11 (a) Here is triangle ABC. pffiffiffiffiffi pffiffiffi 14 cm 2 cm C Not drawn accurately A p 3 ffiffiffi 2 cm B Show that angle B ¼ 60 [3 marks] (b) Hence work out the area of triangle ABC. [3 marks] Answer... cm 2 Turn over s 9 (11)

12 12 12 The line x ¼ 9 is a tangent to the circle, centre Cð8, 20Þ y B Not drawn accurately C ð8, 20Þ A 9 O x 12 (a) Show that the radius of the circle is 17. [1 mark] 12 (b) The circle intersects the y-axis at A and B. Show that the length AB is 30. [3 marks] (12)

13 13 13 A curve has equation y ¼ x 3 3x 2 þ 5 13 (a) Show that the curve has a minimum point when x ¼ 2 [4 marks] 13 (b) Show that the tangent at the minimum point meets the curve again when x ¼ 1 [3 marks] Turn over s 11 (13)

14 14 14 ðx aþ is a factor of x 3 þ 2ax 2 a 2 x (a) Show that a ¼ 2 [2 marks] 14 (b) Solve x 3 þ 4x 2 4x 16 ¼ 0 [4 marks] (14)

15 15 15 Prove that sin y sin 3 y cos 3 y tan y [3 marks] Turn over for the next question Turn over s 9 (15)

16 x 2 2bx þ 7a 2ðx aþ 2 þ 3 Work out the two possible pairs of values of a and b. [6 marks] a ¼..., b ¼... and a ¼..., b ¼... END OF QUESTIONS Copyright ª 2014 AQA and its licensors. All rights reserved. 6 (16)