2024_AQA A-Level Mathematics Paper 2 (Merged Question Paper and Marking Scheme)

2024_AQA A-Level Mathematics Paper 2 (Merged Question Paper and Marking Scheme) Please write clearly in block capitals. Centre number Surname Forename(s) Candidate signature Candidate number I declare this is my own work. A-level MATHEMATICS Paper 2 Tuesday 11 June 2024 Materials Afternoon  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 Time allowed: 2 hours  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. 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 20 21 TOTAL A-Level Mathematics: Paper 2 (Tuesday 11 June 2024). Exam Preparation Areas This paper focuses on Pure Mathematics and Applied Mathematics, including topics from Mechanics and Statistics. Here’s a breakdown of the key areas typically covered: 1. Pure Mathematics:  Algebra: o Quadratic Equations: Solving using factoring, completing the square, and the quadratic formula. o Polynomials: Factorization, finding roots, and using the Remainder and Factor Theorems. o Exponents and Logarithms: Solving exponential and logarithmic equations, including using the laws of indices.  Functions and Graphs: o Graphing functions such as quadratics, cubics, exponentials, and logarithms, and analyzing key features such as intercepts, turning points, and asymptotes. o Transformations of functions: translations, stretches, and reflections.  Trigonometry: o Solving trigonometric equations, using identities (e.g., Pythagorean identities, double angle formula), and applying inverse trigonometric functions.  Calculus: o Differentiation: Basic differentiation rules (power, product, quotient, and chain rule), solving problems involving rates of change, and finding tangents and normals. o Applications of Differentiation: Finding stationary points (minima, maxima, points of inflection) and solving optimization problems. o Integration  Coordinate Geometry: o Straight Line Equations: Finding the equation of a line given a gradient and a point, or two points. o Circles: Equation of a circle in standard form, and solving problems involving tangents and distances from a point to a line. 2. Applied Mathematics:  Mechanics: o Kinematics: Motion under constant acceleration, equations of motion, and solving problems involving velocity and displacement. o Forces and Newton's Laws: Solving problems involving forces, friction, tension, and equilibrium using Newton's second law. o Energy and Momentum: Work, power, kinetic and potential energy, and conservation of momentum in collisions.  Statistics: o Data Representation: Constructing and interpreting histograms, cumulative frequency graphs, and box plots. o Probability: Using probability rules (addition and multiplication rules), tree diagrams, and solving problems involving conditional probability. o Distributions: Understanding and applying binomial and normal distributions, and solving problems involving these. o Statistical Measures: Calculating and interpreting mean, median, mode, variance, and standard deviation. 7357/2 G/LM/Jun24/G4005/E7 2 Do not write outside the Section A Answer all questions in the spaces provided. 1 One of the equations below is the equation of a circle. Identify this equation. Tick () one box. (x + 1)2 – (y + 2)2 = –36 (x + 1)2 – (y + 2)2 = 36 (x + 1)2 + (y + 2)2 = –36 (x + 1)2 + (y + 2)2 = 36 box [1 mark] G/Jun24/7357/2 3 Do not write outside the G/Jun24/7357/2 2 The graph of y = f (x) intersects the x‑axis at (–3, 0), (0, 0) and (2, 0) as shown in the diagram below. box y A – 3 The shaded region A has an area of 189 The shaded region B has an area of 64 2 Find the value of ∫–3 f (x) dx Circle your answer. 2 x B [1 mark] –253 – Turn over for the next question Turn over U 3 Solve the inequality 4 Do not write outside the box (1 – x)(x – 4) < 0 Tick () one box. ∩ {x : x < 1} {x : x > 4} {x : x < 1} ∩ {x : x > 4} ∩ {x : x < 1} {x : x ≥ 4} {x : x < 1} ∩ {x : x ≥ 4} [1 mark] G/Jun24/7357/2 5 Do not write outside the G/Jun24/7357/2 4 Use logarithms to solve the equation 5x–2 = 71570 box Give your answer to two decimal places. [3 marks] Turn over for the next question Turn over U 5 6 Do not write outside the Given that find dy dx box y = x3 sin x [3 marks] G/Jun24/7357/2 7 Do not write outside the G/Jun24/7357/2 6 It is given that and that θ is obtuse. (2 sin θ + 3 cos θ)2 + (6 sin θ – cos θ)2 = 30 box Find the exact value of sin θ. Fully justify your answer. [6 marks] Turn over U 7 8 Do not write outside the On the first day of each month, Kate pays £50 into a savings account. Interest is paid on the total amount in the account on the last day of each month. The interest rate is 0.2% At the end of the nth month, the total amount of money in Kate’s savings account is £Tn Kate correctly calculates T1 and T2 as shown below: T1 = 50 × 1.002 = 50.10 T2 = (T1 + 50) × 1.002 = ((50 × 1.002) + 50) × 1.002 = 50 × 1.0022 + 50 × 1.002 ≈ 100.30 7 (a) 7 (b) Show that T3 is given by T3 = 50 × 1.0023 + 50 × 1.0022 + 50 × 1.002 [1 mark] Kate uses her method to correctly calculate how much money she can expect to have in her savings account at the end of 10 years. 7 (b) (i) Find the amount of money Kate expects to have in her savings account at the end of 10 years. [3 marks] G/Jun24/7357/2 box 9 Do not write outside the G/Jun24/7357/2 box 7 (b) (ii) The amount of money in Kate’s savings account at the end of 10 years may not be the amount she has correctly calculated. Explain why. [1 mark] Turn over for the next question Turn over U 8 10 Do not write outside the A zookeeper models the median mass of infant monkeys born at their zoo, up to the age of 2 years, by the formula y = a + b log10 x where y is the median mass in kilograms, x is age in months and a and b are constants. The zookeeper uses the data shown below to determine the values of a and b. Age in months (x) 3 Median mass (y) 24 6.4 8 (a) 12 The zookeeper uses the data for monkeys aged 3 months to write the correct equation 6.4 = a + b log10 3 8 (a) (i) Use the data for monkeys aged 24 months to write a second equation. [1 mark] 8 (a) (ii) Show that b = 5.6 log10 8 [3 marks] G/Jun24/7357/2 box 11 Do not write outside the G/Jun24/7357/2 box 8 (a) (iii) Find the value of a. Give your answer to two decimal places.