A-level MATHEMATICS Paper 3

A-level MATHEMATICS Paper 3 Time allowed: 2 hours Materials  You must have the AQA Formulae for A‑level Mathematics booklet.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the space provided for that question. 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 not write outside the box around each page or on blank pages.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 100. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. (JUN) PB/Jun22/E7 7357/3 Section A Answer all questions in the spaces provided. 1 State the range of values of x for which the binomial expansion of rffi1ffiffiffi—ffiffiffiffiffixffiffi box is valid. Circle your answer. 1 jxj < 4 jxj < 1 jxj < 2 jxj < 4 [1 mark] 2 The shaded region, shown in the diagram below, is defined by x2 — 7x þ 7 ≤ y ≤ 7 — 2x box y O 5 x Identify which of the following gives the area of the shaded region. Tick (3) one box. ð (7 — 2x) d x — ð (x2 — 7x þ 7) d x [1 mark] 5 (x2 0 ð5 — 5x) d x 2 (5x x 0 ð5 2 ) d x Turn over for the next question Turn over 3 The function f is defined by Solve the equation Circle your answer. f (x) ¼ 2x þ 1 f (x) ¼ f —1ðx) [1 mark] box x ¼ —1 x ¼ 0 x ¼ 1 x ¼ 2 4 Find ð x2 1 þ x2 d x [2 marks] 5 (a) Sketch the graph of