Official June 2024 AQA AS MATHEMATICS 7356/1 Paper 1 Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4004/E9 7356/1 (JUN247356101) AS MATHEMATICS Paper 1 Thursday 16 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials l You must have the AQA Formulae for A‑level Mathematics booklet. l You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions l Use black ink or black ball-point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer each question in the space provided for that question. l 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). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 80. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not necessarily need to use all the space provided. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 TOTAL Please write clearly in block capitals. Centre number Candidate number Surname _________________________________________________________________________ Forename(s) _________________________________________________________________________ Candidate signature _________________________________________________________________________ I declare this is my own work. 2 Do not write outside the box (02) G/Jun24/7356/1 Section A Answer all questions in the spaces provided. 1 It is given that tan θ° = k, where k is a constant. Find tan (θ + 180)° Circle your answer. [1 mark] –k – 1 k 1 k k 2 Curve C has equation y = 1 (x – 1)2 State the equations of the asymptotes to curve C Tick () one box. [1 mark] x = 0 and y = 0 x = 0 and y = 1 x = 1 and y = 0 x = 1 and y = 1 3 Do not write outside the box (03) G/Jun24/7356/1 Turn over U 3 Express √3 + 3√5 √5 – √3 in the form a + √b, where a and b are integers. Fully justify your answer. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7356/1 4 (a) (i) By using a suitable trigonometric identity, show that the equation sin θ tan θ = 4 cos θ can be written as tan2 θ = 4 [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (a) (ii) Hence solve the equation sin θ tan θ = 4 cos θ where 0° < θ < 360 xss=removed xss=removed> x + 6 Give your answer in exact form using set notation. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 8 Do not write outside the box (08) G/Jun24/7356/1 7 A triangular field of grass, ABC, has boundaries with lengths as follows: AB = 234 m BC = 225 m AC = 310 m The field is shown in the diagram below. B C A 234 m 310 m 225 m 7 (a) Find angle A [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 9 Do not write outside the box (09) G/Jun24/7356/1 Turn over U 7 (b) Farmers calculate the number of sheep they can keep in a field, by allowing one sheep for every 1200 m2 of grass. Find the maximum number of sheep which can be kept in the field ABC [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 10 Do not write outside the box G/Jun24/7356/1 (10) 8 It is given that ln x – ln y = 3 8 (a) Express x in terms of y in a form not involving logarithms. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 8 (b) Given also that x + y = 10 find the exact value of y and the exact value of x [3 marks]