FURTHER MATHEMATICS Level 2 Certificate Paper 1 Non-Calculator

FURTHER MATHEMATICS Level 2 Certificate Paper 1 Non-Calculator Friday 14 June 2019 Afternoon Time allowed: 1 hour 30 minutes Materials For this paper you must have: • mathematical instruments. You must not use a calculator. Instructions • Use black ink or black ball-point pen. Draw diagrams in pencil. • Fill in the boxes at the top of this page. • Answer all questions. • You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. • If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). • Do all rough work in this book. Cross through any work 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. *jun19 * IB/M/Jun19/E8 8360/1 Volume of sphere = 4 r 3 3 Formulae Sheet outside the box Surface area of sphere = 4r 2 Volume of cone = 1 r 2 h 3 Curved surface area of cone = r l In any triangle ABC Area of triangle = 1 ab sin C 2 Sine rule a sin A = b sin B = c sin C Cosine rule a 2 = b 2 + c 2 – 2bc cos A cos A = b2  c2  a2 2bc The Quadratic Equation 2 The solutions of ax + bx + c = 0, where a  0, are given by x = 2a Trigonometric Identities tan θ  sin θ cos θ sin2 θ + cos2 θ  1 Answer all questions in the spaces provided. 1 A straight line passes through the points (−2, 11) and (1, 2) Work out the equation of the line. Give your answer in the form y = mx + c [3 marks] Answer Turn over for the next question box Turn over ► 2 Write 5 + a as a single fraction. 6a 4 Give your answer in its simplest form. [2 marks] Answer 3 Work out the smallest integer value of x that satisfies the inequality 8 – 5x ˂ 26 [2 marks] Answer 4 p(x – 1) + 2(3x + k) ≡ 4(x + 2) where p and k are integers. Work out the values of p and k. [4 marks] Answer p = , k = Turn over ► outside the 7 A function is given by f(x) = −2x −1 ⩽ x ˂ 0 = x(4 – x) 0 ⩽ x ˂ 3 = 2x – 3 3 ⩽ x ⩽ 4 Draw the graph of y = f(x) on the grid. [4 marks] *07* Turn over ► 8 ABC is a straight line. A is the point (−4, 5) C is the point (20, −7) AB : BC = 5 : 3 Work out the coordinates of B. [4 marks] Answer ( , ) *0* 9 y = 2x(x2 – 5x) Circle the expression for dy dx [1 mark] 2(2x – 5) 6x2 – 20 3x2 – 10x 6x2 – 20x 10 Factorise fully 6x2 + 26xy – 20y2 [3 marks] Answer Turn over for the next question Turn over ► 11 A cone has base radius r cm, perpendicular height h cm and slant height l cm The curved surface area is 60π cm2 l = 3r Work out the value of h. Give your answer in the form a 10 where a is an integer greater than 1 You must show your working. [5 marks] Answer 12 A curve has the equation y = x3 + ax2 − 7 where a is a constant. The gradient of the curve when x = 4 is twice the gradient of the curve when x = −1 Work out the value of a. You must show your working. [5 marks] Answer Turn over for the next question Turn over ► 13 Prove that (3x + 5)2 – 5x(x + 10) ⩾ 0 for all values of x. [4 marks] 14 Here are two transformations. A Rotation 90° clockwise about the origin. B Reflection in the line y = x Use matrix multiplication to work out the single matrix which represents the combined transformation A followed by B. [4 marks] Answer Turn over for the next question Turn over ► 15 Here is a sketch graph of y = cos x for 0° ⩽ x ⩽ 360° You are given that cos 36° = 0.8090 Solve cos x = −0.8090 for 0° ⩽ x ⩽ 360° [2 marks] Answer 16 Rationalise the denominator and simplify fully 21 11 5 3  5 [4 marks] Answer Turn over for the next question Turn over ► 17 A, B and C are points on the circumference of a circle, centre O. ECD is a tangent to the circle at C. Angle AOB = 2x + 46° Angle OBC = 37° Angle ACD = 3x Work out the value of x. [4 marks] box Answer degrees Turn over for the next question *17* Turn over ► 18 ADEF is a trapezium. ABCD is a straight line. BCEF is a square of side 6 cm 18 (a) Show that AB = 2 cm [1 mark] 18 (b) Show that DE = 2 6 cm [1 mark] *1* 18 (c) Work out the perimeter of the trapezium ADEF. Give your answer in the form t 2 + w 6 where t and w are integers. You must show your working. [3 marks] Answer cm Turn over for the next question Turn over ► 19 f(x) = x  3 2x Solve f(x + 1) – f(2x) = 0.5 You must show your working. [6 marks] Answer END OF QUESTIONS There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Question number Additional page, if required. Write the question numbers in the left-hand margin. *27* There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Copyright information For confidentiality purposes, from the November 2015 examination series, acknowledgements of third-party copyright material are published in a separate booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available for free download from after the live examination series. Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House, Guildford, GU2 7XJ. Copyright © 2019 AQA and its licensors. All rights reserved. *2* *196g6360/1*