AQA GCSE Mathematics Paper 3 (Higher Tier) Exam 2026/2027: Questions with Fully Worked and Verified Solutions.

GCSE MATHEMATICS Foundation Tier Paper 3 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/E9 8300/3F 2 Answer all questions in the spaces provided. Do not write outside the box 1 A village has four bus stops. The bar chart shows information about the people at the bus stops at 3 pm one day. 1 (a) Two people were at the Football ground bus stop. Show this information on the bar chart. [1 mark] 1 (b) How many more people were at the School bus stop than at the Post office bus stop? [1 mark] Answer IB/M/Jun24/8300/3F 3 2 Here are four temperatures in degrees C Do not write outside the box –5 3 –7 –1 Write the temperatures in order, starting with the coldest. [2 marks] Answer 3 Here are the first three terms of a linear sequence. 5 11 17 3 (a) Write down the next term. [1 mark] Next term 3 (b) Describe the term-to-term rule. [1 mark] Term-to-term rule Turn over ► IB/M/Jun24/8300/3F 4 4 Luca spends 71p He pays the exact amount with 4 coins. List the coins he uses. [2 marks] Do not write outside the box Answer 5 Complete each statement using one of these symbols. = [3 marks] 2.54 2.508 0.25 1 4 2 5 2 IB/M/Jun24/8300/3F 5 6 Here are three solids. Cube Square-based Cone pyramid 6 (a) How many faces does the cube have? [1 mark] Do not write outside the box Answer 6 (b) How many edges does the square-based pyramid have? [1 mark] Answer 6 (c) How many vertices does the cone have? [1 mark] Answer Turn over ► IB/M/Jun24/8300/3F 6 7 (a) Here is a number machine. Complete the number machine. [1 mark] Do not write outside the box 7 (b) Here is a different number machine. Complete the number machine. [1 mark] IB/M/Jun24/8300/3F 7 7 (c) Here is a different number machine. When x = 5 y = 13 and when x = 10 y = 28 Complete the number machine. [2 marks] Do not write outside the box Turn over for the next question Turn over ► IB/M/Jun24/8300/3F 8 8 • A pack of pegs costs 40p • A bar of soap costs £2.20 • A basket costs £7 Dan buys two packs of pegs, one bar of soap and one basket. What fraction of the total cost is the cost of the basket? [3 marks] Do not write outside the box Answer 9 Calculate 625 + 73 [2 marks] Answer IB/M/Jun24/8300/3F 9 10 8400 fans go to a rugby match. 6850 of the fans support the Home team. The remaining fans support the Away team. 20% of the Home fans wear a scarf. 2319 of all the fans wear a scarf. Complete the frequency tree. [5 marks] Do not write outside the box Turn over for the next question Turn over ► IB/M/Jun24/8300/3F 10 11 11 (a) Work out the coordinates of B. [1 mark] Do not write outside the box Answer ( , ) 11 (b) Point C is reflected in the line x = 6 to point D. Work out the coordinates of D. [1 mark] Answer ( , ) IB/M/Jun24/8300/3F 11 12 Liz records the distance of some runs and the time each run takes. Distance (km) 3 4 5.5 6 6.5 7 8 8.5 Time (min) 14 17 22 23 26 31 38 42 The scatter graph shows some of the information from the table. Running distances and time taken 12 (a) Complete the graph by adding the missing label and plotting the two missing points. [2 marks] Do not write outside the box 12 (b) Describe the correlation shown in the scatter graph. [2 marks] Type of correlation Strength of correlation Turn over ► IB/M/Jun24/8300/3F 12 13 AB is a straight line. Is y half of x ? Tick a box. Yes No Not drawn accurately Do not write outside the box Show working to support your answer. [3 marks] IB/M/Jun24/8300/3F 13 14 Multiply out 3(2x + 8) [2 marks] Do not write outside the box Answer 15 Complete these statements. [3 marks] 9x y2 t Turn over for the next question Turn over ► IB/M/Jun24/8300/3F 14 16 Tins of beans are sold in shop A and shop B. At which shop is it cheaper to buy 20 tins? State how much cheaper. [5 marks] Do not write outside the box Shop Cheaper by IB/M/Jun24/8300/3F 15 17 (a) There are 30 students in a class. 12 of the students have school lunch. Work out the ratio students having school lunch : students not having school lunch Give your answer in its simplest form. [2 marks] Do not write outside the box Answer : 17 (b) In a different class students wearing glasses : students not wearing glasses = 3 : 8 What fraction of students in this class wear glasses? [1 mark] Answer 17 (c) The ratio 4 : 9 is written in the form 1 : n Work out the value of n. [1 mark] n = Turn over ► IB/M/Jun24/8300/3F 16 18 Here are the first three Patterns in a sequence made up of small squares. 18 (a) On the grid, draw Pattern 4 [1 mark] Do not write outside the box IB/M/Jun24/8300/3F 17 18 (b) The expression for the number of small squares in Pattern n is n2 + 4 Do not write outside the box Work out the least value of n for which the number of small squares is greater than 500 [1 mark] n = 19 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 ► IB/M/Jun24/8300/3F 18 20 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] Do not write outside the box 21 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 no values of x IB/M/Jun24/8300/3F 19 22 Kay hires a digger. The cost per day is • £24.50 for the first 5 days • reduced by 20% for day 6 • the same as day 6 for day 7 onwards. The total cost is £259.70 For how many days did Kay hire the digger? You must show your working. [5 marks] Do not write outside the box Answer Turn over for the next question Turn over ► IB/M/Jun24/8300/3F 20 23 The front elevation of a cuboid is shown on this centimetre grid. The volume of the cuboid is 42 cm3 Draw the side elevation on this centimetre grid. [2 marks] Do not write outside the box IB/M/Jun24/8300/3F 21 24 (a) On Monday, Larrs swims 50 metres in 40 seconds at a constant speed. On Tuesday, Larrs swims 1.5 kilometres. Assume he swims at the same constant speed as on Monday. How many minutes does he swim for on Tuesday? [5 marks] Do not write outside the box Answer minutes 24 (b) In fact, on Tuesday Larrs swims at a slower constant speed than on Monday. What does this mean about the number of minutes he swims for on Tuesday? Tick the correct box. [1 mark] It is less than the answer to part (a) It is the same as the answer to part (a) It is greater than the answer to part (a) It is not possible to say Turn over ► IB/M/Jun24/8300/3F 22 25 Four people are taking part in a television talent show. Here are Amy’s marks from the 6 judges. Do not write outside the box 8 9 9 6 9 10 The pie chart represents the phone vote. Amy’s total score is found by IB/M/Jun24/8300/3F 23 Work out Amy’s total score. [4 marks] Do not write outside the box Answer Turn over for the next question Turn over ► IB/M/Jun24/8300/3F 24 26 House prices on a street increase by 5.1% each year. Show that after 14 years the house prices on the street will be at least double. [2 marks] Do not write outside the box 27 Town A has a population of 84 000 an area of 7 square miles. Town B has a population density of 4695 people per square kilometre. Which town has the greater population density? Use 1 square mile = 2.6 square kilometres Tick a box. Town A Town B Show working to support your answer. [3 marks] END OF QUESTIONS IB/M/Jun24/8300/3F 25 When do you use trigonometry? - ANSWER right angle triangle with a side and an angle (excluding) 90 degrees. When do you use Pythagoras? - ANSWER right angle triangle with 2 sides to find the third side. When do you use Sin rule? - ANSWER When you know a side and it's opposite angle When do you use Cosine rule? - ANSWER when you see an angle sandwiched between 2 known sides What is a geometric sequence? - ANSWER A Geometric Sequence is a sequence of numbers that increases or decreases by multiplying or dividing by the same amount every time. What is the Fibonacci sequence? - ANSWER This is the series of numbers in which the first two terms are 0 and 1 and each number that follows is the sum of the previous two. 0, 1, 2, 3, 5, 8, 13, 21 ... What is the arithmetic sequence? - ANSWER The difference is constant e.g 1,2,3... . Adding or subtracting the same number each time. Frequency density formula - ANSWER Frequency/class width How should you interpret gf(4) - ANSWER What is g when f is 4 What is the rule of the arrow in circle theorems? - ANSWER the bottom angle is double the top angle. What is the cyclic triangle on the diameter rule in circle theorems? - ANSWER the angle not on the circumference is 90 degrees. What is the tangent and radius meet angle rule in circle theorems? - ANSWER the meeting angle is 90 degrees. What is the tangent from a point rule in circle theorems? - ANSWER tangents from a point have equal length. What is the bowtie rule in circle theorems? - ANSWER In a bowtie shape the bottom two angles are equal and the top two angles are equal. What is the cyclic quadrilateral rule in circle theorems? - ANSWER Opposite angles add up to make 180 degrees. How do you find the surface area of a prism? - ANSWER find the area of each face and add them up. What does a Quadratic Graph Look like? - ANSWER U- Parabolah What are the five points on a sin graph? - ANSWER -360,0 then -90,-1 then 90,1 then 270,-1 then 360,0 what are the five points on a cos graph? - ANSWER -360,1 then -180,-1 then 0,1 then 180,-1 then 360,1 what are the roots of a graph? - ANSWER where it passes through x. what does a linear graph look like? - ANSWER straight line What does an exponential graph look like? - ANSWER An exponential graph rises ever increasingly faster, getting steeper and steeper in a certain direction. ( A curved J or l if negative) How is a coordinate shown? - ANSWER (x,y)