A-level MATHEMATICS Paper 3

A-level MATHEMATICS Paper 3 Thursday 20 June 2024 Afternoon 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. G/LM/Jun24/G4005/E6 7357/3 Section A Answer all questions in the spaces provided. 1 Each of the series below shows the first four terms of a geometric series. Identify the only one of these geometric series that is convergent. [1 mark] box Tick () one box. 0.1 + 0.2 + 0.4 + 0.8 + … 1 – 1 + 1 – 1 + … 128 – 64 + 32 – 16 + … 1 + 2 + 4 + 8 + … 2 The quadratic equation box 4x2 + bx + 9 = 0 has one repeated real root. Find b Circle your answer. [1 mark] b = 0 b = ±12 b = ±13 b = ±36 Turn over for the next question Turn over U 3 One of the graphs shown below cannot have an equation of the form y = ax where a 0 box Identify this graph. Tick () one box. y [1 mark] O x y O x 4 A curve has equation y = x4 + 2x Find an expression for dy dx [2 marks] box Turn over for the next question Turn over U 5 The diagram below shows a sector of a circle OAB. The chord AB divides the sector into a triangle and a shaded segment. Angle AOB is π radians. 6 The radius of the sector is 18 cm. box Show that the area of the shaded segment is k (π – 3) cm2 where k is an integer to be found. [3 marks] Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Turn over U 6 (a) Find ∫ 6x2 – 5 d x √x [3 marks] box 6 (b) The gradient of a curve is given by dy = 6x2 – 5 box dx √x The curve passes through the point (4, 90). Find the equation of the curve. [2 marks] Turn over for the next question Turn over U 7 The graphs with equations