AQA GCSE Mathematics Paper 1 (Higher Tier) Exam 2026/2027: Questions with Fully Worked and Verified Solutions.

GCSE MATHEMATICS Foundation Tier Paper 1 Non-Calculator Morning Time allowed: 1 hour 30 minutes Materials For this paper you must have: • mathematical instruments • the Formulae Sheet (enclosed). You must not use a calculator. 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 8300/1F 2 Answer all questions in the spaces provided. Do not write outside the box 1 (a) Work out 280 ÷ 7 [1 mark] Answer 1 (b) Work out 1062 – 438 [2 marks] Answer IB/M/Jun24/8300/1F 3 2 (a) Complete the statement. [1 mark] Do not write outside the box 2 metres = centimetres 2 (b) Complete the statement. [1 mark] 8 kilograms = grams 2 (c) Convert 24 kilometres to miles. Use 8 kilometres = 5 miles [2 marks] Answer miles Turn over ► IB/M/Jun24/8300/1F 4 3 (a) Here is a centimetre grid. What percentage of the grid is shaded? [1 mark] Do not write outside the box Answer % 3 (b) Kai has shaded two small squares on this centimetre grid. He wants 3 of the grid to be shaded. 4 How many more small squares must he shade? [2 marks] Answer IB/M/Jun24/8300/1F 5 4 (a) Here is a list of four numbers. 6.92 7.27 7.18 7.14 Use one number from the list to complete each statement. [2 marks] Do not write outside the box The number closest in value to 7 is The number that rounds to 7.2 to 1 decimal place is 4 (b) Here is a list of six numbers. –10 –5 –2 4 6 10 Use two numbers from the list to complete each statement. [2 marks] Two numbers that add to make –1 are and Two numbers that multiply to make 20 are and Turn over for the next question Turn over ► IB/M/Jun24/8300/1F 6 5 (a) Here are four lines on a square grid. Which two lines are parallel? [1 mark] Do not write outside the box line and line 5 (b) Here is a different grid. There are four points on this grid that each have both coordinates that are whole numbers and x-coordinate + y-coordinate = 3 Plot the four points on the grid. [2 marks] IB/M/Jun24/8300/1F 7 6 (a) Write down the value of 32 [1 mark] Do not write outside the box Answer 6 (b) Write down the value of 144 [1 mark] Answer 6 (c) Work out the value of 24 [1 mark] Answer Turn over for the next question Turn over ► IB/M/Jun24/8300/1F 8 7 (a) At a restaurant, vegan pizzas have two different toppings. The toppings are sweetcorn (S) mushrooms (M) peppers (P) Complete the table to list all the possible pairs of toppings. [1 mark] Do not write outside the box SM 7 (b) At the restaurant, dough balls can be ordered in small portions and large portions. A group of people want to order exactly 44 dough balls. Show how they can do this. [2 marks] Number of Small portions Number of Large portions IB/M/Jun24/8300/1F 9 8 Salma has £10 to buy apples and oranges. She buys 9 apples and as many oranges as possible. How many oranges does she buy? [4 marks] Do not write outside the box Answer Turn over ► IB/M/Jun24/8300/1F 10 9 Alina and Sue play netball. The number of goals they scored in 8 games is shown. Do not write outside the box Alina 12 15 17 17 21 22 24 26 Sue 13 13 17 20 22 23 24 31 9 (a) Complete this table. [2 marks] Range Median Alina 19 Sue 18 9 (b) Which player scored the more consistent number of goals? Tick a box. Alina Sue Give a reason for your answer. [1 mark] IB/M/Jun24/8300/1F 11 10 Work out 35% of 1200 [3 marks] Do not write outside the box Answer Turn over for the next question Turn over ► IB/M/Jun24/8300/1F 12 11 A window cleaner uses this formula. C = cost, in £, for the customer W = number of windows to be cleaned 11 (a) How much does it cost for 6 windows to be cleaned? [2 marks] Do not write outside the box Answer £ 11 (b) The cost for another customer was £24 Show why this cost must be incorrect. [1 mark] IB/M/Jun24/8300/1F 13 12 Two bags, X and Y, each contain coloured discs. Do not write outside the box In bag X, 7 20 of the discs are red. In bag Y, 2 5 of the discs are red. Which bag has the greater proportion of red discs, X or Y? You must show your working. [2 marks] Answer Turn over for the next question Turn over ► IB/M/Jun24/8300/1F 14 13 (a) Two friends share £240 in the ratio 1 : 3 Work out the larger share. [2 marks] Do not write outside the box Answer £ 13 (b) A tennis player wins or loses matches in the ratio win : lose = 5 : 9 What fraction of the matches do they win? [1 mark] Answer IB/M/Jun24/8300/1F 15 14 Here is a multiplication table. × 61 63 65 67 61 3721 3843 3965 4087 63 3843 3969 4095 4221 65 3965 4095 4225 4355 67 4087 4221 4355 4489 Use the table to answer the following questions. 14 (a) Work out 3843 ÷ 63 [1 mark] Do not write outside the box Answer 14 (b) Work out 6.1 × 6.7 [1 mark] Answer 14 (c) Work out 63 × 66 [2 marks] Answer Turn over ► IB/M/Jun24/8300/1F 16 15 These two triangles are congruent. Write down the value of x. Not drawn accurately [1 mark] Do not write outside the box x = cm 16 c and d are positive numbers. c is even. d is odd. Tick a box for each expression. [3 marks] Even Odd Cannot tell c + d 4c c 2 IB/M/Jun24/8300/1F 17 17 A linear sequence has • 1st term = 10 • 1st term + 2nd term = 39 Work out the 5th term. [4 marks] Do not write outside the box Answer 18 Not drawn accurately Work out the area of this triangle. [2 marks] Answer cm2 Turn over ► IB/M/Jun24/8300/1F 18  3  19 The vector     translates A to B. Do not write outside the box Write down the vector that translates B to A. [1 mark]   Answer     20 The attendance for a rugby match is 8400 people to the nearest 100 20 (a) Write down the minimum possible attendance. [1 mark] Answer 20 (b) Write down the maximum possible attendance. [1 mark] Answer IB/M/Jun24/8300/1F 19 21 The table shows the number of workers at a company in different years. Do not write outside the box Year 2015 2016 2017 2018 2019 2020 2021 2022 Number of workers 29 34 42 52 62 70 76 80 A time-series graph is drawn to represent the data. The first four points have been plotted. 21 (a) Complete the graph. [2 marks] 21 (b) Estimate the number of workers at the company in 2023. [1 mark] Answer Turn over ► IB/M/Jun24/8300/1F 20 22 Here is a cone. 22 (a) Do not write outside the box Beth tries to work out the curved surface area in terms of π What mistake has she made? [1 mark] IB/M/Jun24/8300/1F 21 22 (b) Adam uses π = 3 to estimate the area of the base of the cone. Work out his estimate. [2 marks] Do not write outside the box Answer cm2 22 (c) Beth uses π = 3.14 to estimate the area of the base of the cone. Is Beth’s estimate more than or less than Adam’s estimate? Tick a box. More than Less than Give a reason for your answer. [1 mark] Turn over for the next question Turn over ► IB/M/Jun24/8300/1F 22 23 Each day, Erik drinks Do not write outside the box 1 of a pint of milk in the morning 4 and 1 of a pint of milk in the afternoon. 2 How many pints of milk does he drink in 30 days? [3 marks] Answer IB/M/Jun24/8300/1F 23 24 Solve 7x – 22 = 4x + 29 [3 marks] Do not write outside the box x = 25 In a house the floor area of the living room is 26 m2 the floor area of the kitchen is 16.4 m2 Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form. [3 marks] Answer Turn over ► IB/M/Jun24/8300/1F 24 26 (a) Represent –2 x 4 on the number line. [1 mark] Do not write outside the box 26 (b) Solve 5y + 14 ⩾ 11 [2 marks] Answer IB/M/Jun24/8300/1F 25 Do not write outside the 27 box Describe fully the single transformation that maps shape A to shape B. [3 marks] END OF QUESTIONS IB/M/Jun24/8300/1F 26 BIDMAS - ANSWER Brackets, Indices, Division, Multiplication, Addition Subtraction Integer - ANSWER A whole number Factors of a number - ANSWER Numbers that divide into it Prime number - ANSWER Only divides by itself and one What does LCM stand for? - ANSWER Lowest Common Multiple What is LCM? - ANSWER The smallest number that can divide by all the numbers in the question What does HCF stand for? - ANSWER Highest Common Factor What is HCF? - ANSWER The biggest number that can divide into all the numbers in the question To simplify a fraction you? - ANSWER Divide the top and bottom of the fraction by the same number A mixed number fraction is also called an? - ANSWER Improper fraction To multiply a fraction you? - ANSWER Multiply across all the fractions To divide a fraction you? - ANSWER Turn the second fraction upside down and then multiple across When adding and subtracting fractions you need to make sure they have.... - ANSWER Same denominator How to find a fraction of something? - ANSWER Divide the number by the bottom and then multiply by the top The first significant number is? - ANSWER The first digit of a number that isn't a zero Upper and lower bounds - ANSWER When a measurement is rounded to a given unit, the actual measurement can be anything up to half a unit bigger or smaller To find the minimum bound you... - ANSWER Multiple both the smallest bounds To find the maximum bound you... - ANSWER Multiple both the biggest bounds A number in standard form should be written in the form of? - ANSWER A x (10)n The first number in standard form should always be between? - ANSWER 1 and 10 If mixed numbers are negative then... - ANSWER Pairs are positive When multiplying powers you... - ANSWER Add the powers When dividing powers you... - ANSWER Subtract the powers The power of 0 always equals... - ANSWER 1 1 to the power of anything still equals... - ANSWER 1 Anything to the power of 1 is... - ANSWER Itself For negative powers you need to... - ANSWER Flip it upside down (reciprocal) The power of 1/2 means... - ANSWER Square root The power of 1/3 means... - ANSWER Cube root The power of 1/4 means... - ANSWER Fourth root The difference of two squares is... - ANSWER One thing squared take away another thing squared Surds are - ANSWER Expressions with irrational square roots that can't be written as fractions How to solve an equation - ANSWER Rearrange the equation so that all the x's are on one side When fractions are in an equation make sure you... - ANSWER Get rid of the fractions before doing anything else The standard format for being able to solve a quadratic is? - ANSWER (x)2 + b(x) + c = 0 To find two brackets (factorise) for solving a quadratic you need to... - ANSWER Find two numbers that add/subtract to get b and multiple to get c Quadratic formula is? - ANSWER x = -b +or- the square root of b squared - 4ac divided by 2a How many solutions do you end up with for a quadratic? - ANSWER 2 One other method of solving quadratics is? - ANSWER Completing the square means - ANSWER Less than means - ANSWER Greater than When you multiple or divide by a negative number in inequalities you... - ANSWER Flip the inequality sign An open circle on a number line means.... - ANSWER or A coloured in circle on a number line means... - ANSWER Less than or equal to or greater than or equal to Iteration is.. - ANSWER Repeating a calculation in order to get closer approximations to the solution you want