AQA GCSE Maths Paper 2 Higher Tier Exam 2026/2027 Questions With Completed & Verified Solutions.

AQA GCSE Maths Paper 2 Higher Tier Exam 2026/2027 Questions With Completed & Verified Solutions. GCSE MATHEMATICS Foundation Tier Paper 2 Calculator 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. Advice In all calculations, show clearly how you work out your answer. IB/M/Jun24/G4007/E10 8300/2F 2 Answer all questions in the spaces provided. Do not write outside the box 1 (a) Write 0.27 as a fraction. [1 mark] Answer 1 (b) Write 2 5 as a decimal. [1 mark] Answer 1 (c) Write 0.35 as a percentage. [1 mark] Answer % IB/M/Jun24/8300/2F 3 2 (a) Simplify fully x + 4x [1 mark] Do not write outside the box Answer 2 (b) Simplify fully 5 × 2w [1 mark] Answer 2 (c) Simplify fully 2m ÷ m [1 mark] Answer 2 (d) Simplify fully y × y × y [1 mark] Answer Turn over ► IB/M/Jun24/8300/2F 4 3 Here is a quadrilateral. 3 (a) Write down the letter of the obtuse angle. [1 mark] Do not write outside the box Answer 3 (b) Write down the letter of an acute angle. [1 mark] Answer 3 (c) How many lines of symmetry does the shape have? [1 mark] Answer IB/M/Jun24/8300/2F 5 4 (a) One lettuce costs £1.29 How much do seven of these lettuces cost? [1 mark] Do not write outside the box Answer £ 4 (b) Five cucumbers cost £6.40 in total. How much do two of these cucumbers cost? [1 mark] Answer £ Turn over for the next question Turn over ► IB/M/Jun24/8300/2F 6 5 A company sells three types of bottle. The pictogram shows how many bottles they sold one week. 5 (a) The company sold more plastic bottles than glass bottles that week. How many more? [2 marks] Do not write outside the box Answer 5 (b) The company sells each steel bottle for £17.50 Work out the total amount of money made from selling steel bottles that week. [3 marks] Answer £ IB/M/Jun24/8300/2F 7 6 Shape ABCDE is drawn on a centimetre grid. 6 (a) Complete this statement. [1 mark] Do not write outside the box AB : = 5 : 1 6 (b) On this centimetre grid, draw a rectangle with the same area as shape ABCDE. [2 marks] Turn over ► IB/M/Jun24/8300/2F 8 7 Use a ruler for this question. Here is an accurate drawing of an equilateral triangle. By measuring, work out the perimeter of the triangle. State the units of your answer. [3 marks] Do not write outside the box Answer IB/M/Jun24/8300/2F 9 8 There are 56 cubes in a box. The cubes are green, red, blue or white. 17 cubes are green. There are an equal number of red, blue and white cubes. 8 (a) How many red cubes are in the box? [2 marks] Do not write outside the box Answer 8 (b) 24 more cubes are added to the box. A cube is picked at random. The probability that the cube is green is 0.4 How many of the 24 cubes added to the box are green? [3 marks] Answer Turn over ► IB/M/Jun24/8300/2F 10 9 An electric car uses 1 unit of electricity to travel 3 miles. 1 unit of electricity costs 50 pence. Work out the cost of electricity, in pounds, to travel 270 miles. [3 marks] Do not write outside the box Answer £ IB/M/Jun24/8300/2F 11 10 (a) Leema buys 2 metres of linen at £8.50 per metre. She also buys 5 metres of cotton. The total cost is £38 What is the cost of one metre of cotton? [4 marks] Do not write outside the box Answer £ 10 (b) Buttons cost 65p each. The greatest number of buttons Leema can buy with £5 is 7 She says, “The greatest number of buttons I can buy with £10 is 14 because £10 is double £5” Is she correct? Tick a box. Yes No Show working to support your answer. [2 marks] Turn over ► IB/M/Jun24/8300/2F 12 11 Here is a table of values for the equation y = 3x + 1 Do not write outside the box x 1 2 3 4 y 4 7 10 13 11 (a) Draw the graph of y = 3x + 1 for values of x from 1 to 4 [2 marks] 11 (b) Work out the value of y when x = 2.5 [2 marks] y = IB/M/Jun24/8300/2F 13 12 A code has five different digits written in order, starting with the smallest. The last digit is the only square number. The middle digit is the only even number. Work out the code. [3 marks] Do not write outside the box Answer 13 Four numbers have a mean of 10 Three of the numbers are 5 8 9 Work out the other number. [3 marks] Answer Turn over ► IB/M/Jun24/8300/2F 14 14 (a) Rearrange d = h – 4 to make h the subject. [1 mark] Do not write outside the box h = 14 (b) Rearrange p  w 3 to make w the subject. [1 mark] w = 15 A linear sequence begins 2 5 8 11 Work out an expression for the nth term. [2 marks] Answer IB/M/Jun24/8300/2F 15 16 The diagram shows a circle, centre O, and three straight lines. Use one word to describe each shaded region. Choose from Do not write outside the box [2 marks] Region A Region B 17 Work out  1 +  4          [1 mark]   Answer     Turn over ► IB/M/Jun24/8300/2F 16 18 Bag A and bag B contain counters. 18 (a) Complete the tree diagram. [2 marks] Do not write outside the box 18 (b) One counter is taken at random from each bag. Work out the probability that one is red and one is white. [2 marks] Answer IB/M/Jun24/8300/2F 17 19 Not drawn accurately Do not write outside the box Use trigonometry to work out the value of x. [3 marks] x = cm 20 The mass of an iceberg is 2 200 000 kg This value is a 12% reduction from the original mass of the iceberg. Work out the original mass of the iceberg. Give your answer in standard form. [3 marks] Answer kg Turn over ► IB/M/Jun24/8300/2F 18 21 A chef has a tub of blueberries. She wants to use all the blueberries put the same number of blueberries on each dessert. D is the number of desserts. b is the number of blueberries on each dessert. 21 (a) What does the constant k represent? Tick the correct box. [1 mark] Do not write outside the box The number of blueberries in the tub The number of desserts The number of blueberries on each dessert None of the above 21 (b) Complete the table. b 2 6 D 120 30 [2 marks] IB/M/Jun24/8300/2F 19 22 (a) A fair spinner has six equal sections, each with the number 5, 6, 7 or 8 Each number appears at least once. P(even number) = P(7) Work out P(5) You may use the blank spinner to help you. [3 marks] Do not write outside the box Answer 22 (b) A different spinner has ten sections, each labelled A, B, C or D. A B C D Probability 0.1 0.5 0.2 0.3 Give one reason why there must be a mistake in the table. [1 mark] Turn over ► IB/M/Jun24/8300/2F 20 23 (a) Here is a sketch of the graph y = –2x + 6 Complete the coordinates of C and D. [2 marks] Do not write outside the box C ( 0 , ) D ( , 0 ) 23 (b) Here is a sketch of a quadratic graph. Complete the following statements. [2 marks] The value of the y-intercept is The x-coordinate of the turning point, T, is IB/M/Jun24/8300/2F 21 24 Archie flips a biased coin 200 times. Here is some information about the outcomes after each 50 flips. Do not write outside the box Total number of flips 50 100 150 200 Number of heads 10 27 37 52 Work out the best estimate for the probability of flipping a head. Give a reason for your answer. [2 marks] Answer Reason Turn over for the next question Turn over ► IB/M/Jun24/8300/2F 22 25 A lion is sprinting in a straight line away from its den. The graph shows the lion’s distance from the den. Work out the speed of the lion in metres per second. [3 marks] Do not write outside the box Answer m/s END OF QUESTIONS IB/M/Jun24/8300/2F 23 minutes in an hour - ANSWER 60 square number - ANSWER a number that is times by itself digit - ANSWER a single whole number (0 to 9) double - ANSWER twice as much formula - ANSWER A mathematical relationship or rule expressed in symbols. simplify - ANSWER To write a fraction or expression in simplest form information - ANSWER facts provided or learned about something or someone. sum - ANSWER to add equilateral triangle - ANSWER a triangle with 3 same sides acute angle - ANSWER an angle that measures less than 90 degrees right angle - ANSWER an angle that measures 90 degrees factors - ANSWER a number that divides into another number exactly with no remainders. exact value - ANSWER number that has not been rounded circular - ANSWER having the shape of a circle rim - ANSWER edge degrees Celsius - ANSWER metric unit of temperature degrees Fahrenheit - ANSWER a unit of measurement for temperature mean - ANSWER An average. Add up the scores and then divide by the number of scores ratio - ANSWER a comparison of two numbers by division increase - ANSWER make bigger or more outcome - ANSWER result Frequency - ANSWER how often something happens relative frequency - ANSWER A ratio that compares the frequency of each category to the total. population - ANSWER group of individuals that live in the same area area - ANSWER the space inside a shape discrete data - ANSWER data that can only take certain values. For example: the number of students in a class (you can't have half a student). Transformation - ANSWER Changing a shape using: Turn Flip Slide, or Resize prisms - ANSWER A solid object with two identical ends and flat sides. volume - ANSWER The amount of space an object takes up cross section - ANSWER A view into the inside of something made by cutting through it. sequence - ANSWER an ordered list of numbers Do not write outside the box PhysicsAndMathsT 25 Question number Additional page, if required. Write the question numbers in the left-hand margin. IB/M/Jun24/8300/2F Do not write outside the box PhysicsAndMathsT 26 Question number Additional page, if required. Write the question numbers in the left-hand margin. IB/M/Jun24/8300/2F Do not write outside the box PhysicsAndMathsT 27 Question number Additional page, if required. Write the question numbers in the left-hand margin. IB/M/Jun24/8300/2F Do not write outside the box PhysicsAndMathsT 28 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Do not write outside the box Copyright information For confidentiality purposes, all acknowledgements of third-party copyright material are published in a separate booklet. This booklet is published after each live examination series and is available for free download from . Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team. Copyright © 2024 AQA and its licensors. All rights reserved. IB/M/Jun24/8300/2F