2024_AQA-GCSE MATHEMATICS – HIGHER TIER PAPER 3: CALCULATOR (MERGED QUESTION PAPER AND MARKING SCHEME) MONDAY 10 JUNE 2024

2024_AQA-GCSE MATHEMATICS – HIGHER TIER PAPER 3: CALCULATOR (MERGED QUESTION PAPER AND MARKING SCHEME) MONDAY 10 JUNE 2024 Candidate number I declare this is my own work. GCSE MATHEMATICS Higher Tier Paper 3 Calculator H Monday 10 June 2024 Morning Time allowed: 1 hour 30 minutes Materials For this paper you must have: • a calculator • mathematical instruments • the Formulae Sheet (enclosed). 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. Information • The marks for questions are shown in brackets. • The maximum mark for this paper is 80. • You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book. For Examiner’s Use Pages Mark 2–3 4–5 6–7 8–9 10–11 12–13 14–15 16–17 18–19 20–21 22–23 24–25 26 TOTAL Advice In all calculations, show clearly how you work out your answer. *JUN2483003H01* IB/M/Jun24/G4007/E10 8300/3H GCSE Mathematics Higher Tier Paper 3: Calculator Summary The GCSE Mathematics Higher Tier Paper 3: Calculator, scheduled for June 2025, will assess students' abilities to apply advanced mathematical concepts with the use of a calculator. The focus will be on higher-level topics, including algebra, geometry, and statistics, and the exam will involve problem-solving, calculations, and reasoning. Key areas covered include: 1. Algebra:  Expanding and Factorizing: Expanding algebraic expressions and factorizing quadratics, cubic expressions, and other polynomial expressions.  Solving Equations: Solving linear, quadratic, and cubic equations, both algebraically and using a calculator for complex solutions. Includes simultaneous equations (both linear and non-linear) and inequalities.  Functions and Graphs: Interpreting and drawing graphs of functions, including quadratic, cubic, exponential, and trigonometric functions, using the calculator to find intersections and solve equations graphically.  Sequences: Investigating arithmetic, geometric, and quadratic sequences, including finding nth terms and the sum of terms. 2. Geometry and Trigonometry:  Coordinate Geometry: Using the distance formula, mid-point formula, and gradient to solve problems involving lines and coordinates.  Transformations: Understanding translations, reflections, rotations, and enlargements, and applying these to solve geometric problems.  Trigonometry: Using trigonometric ratios (sine, cosine, tangent) to solve problems involving right-angled triangles, and applying the sine and cosine rules to solve problems in non-right-angled triangles.  Circle Theorems: Applying circle theorems to solve problems involving angles, chords, tangents, and cyclic quadrilaterals. 3. Vectors and Matrices:  Vector Arithmetic: Solving problems involving vector addition, subtraction, and scalar multiplication, and using vectors in geometric contexts such as finding parallel or perpendicular vectors.  Matrices: Performing matrix operations, including addition, subtraction, and multiplication, and solving problems involving transformations and systems of equations using matrices. 4. Probability and Statistics:  Data Analysis: Interpreting data using mean, median, mode, range, variance, and standard deviation. Creating and interpreting different types of graphs, such as histograms, box plots, and cumulative frequency curves, with a focus on using the calculator to analyze and represent data.  Probability: Solving probability problems, including compound events, conditional probability, and the use of tree diagrams and Venn diagrams.  Statistical Distributions: Understanding and applying normal and binomial distributions and calculating probabilities associated with them using the calculator.  Regression and Correlation: Using calculators for linear regression, including finding the line of best fit and interpreting correlation coefficients to determine relationships between variables. 5. Rates of Change and Proportions:  Rates of Change: Solving problems involving direct and inverse proportionality, speed, density, and other rate related problems, and understanding how to calculate the gradient of a curve.  Proportional Reasoning: Solving problems involving proportional relationships, scaling, and percentage increases/decreases, using both algebraic and calculator-based methods. 6. Financial Mathematics:  Interest: Solving problems involving simple and compound interest, including applying formulas and using calculators to compute financial scenarios.  Currency Conversion: Solving problems related to exchange rates and currency conversion using proportion and percentages.  Financial Planning: Understanding financial planning, including budgeting, profit and loss, and understanding the cost of credit. 7. Functions and Graphs:  Types of Functions: Exploring various types of functions, such as exponential functions, logarithmic functions, and trigonometric functions.  Solving Graphically: Using the calculator to find solutions to equations and inequalities by interpreting graphs, and analyzing intersections and critical points. 8. Calculus (Basic Concepts):  Differentiation: Understanding the concept of differentiation, including calculating gradients of curves and understanding its applications in real-world problems.  Integration: Basic integration techniques, including finding areas under curves, particularly in practical applications of physics and economics. 2 Answer all questions in the spaces provided. 1 Here are the first three Patterns in a sequence made up of small squares. 1 (a)On the grid, draw Pattern 4 [1 mark] Do not write outside the box *02* IB/M/Jun24/8300/3H 3 1 (b) The expression for the number of small squares in Pattern n is n2 + 4 Work out the least value of n for which the number of small squares is greater than 500 [1 mark] n = 2 Not drawn accurately Use Pythagoras’ theorem to work out the value of x. Give your answer as a decimal. [3 marks] Answer cm Turn over ► Do not write outside the box 5 *03* IB/M/Jun24/8300/3H 4 3 Rick claims most of the flats in his 8-floor building are energy efficient. He samples 45 flats from floors 1 to 5 Give a reason why this sample may not be useful in testing Rick’s claim. [1 mark] 4 3(x – 1) ≡ 3x – 3 is an identity. Tick one box. [1 mark] It is true for all values of x It is true for some values of x It is true for