AQA GCSE Mathematics Paper 3 (Higher), June 2025
Every question from AQA GCSE Mathematics Paper 3 (Higher), June 2025 (8300): 24 questions, 80 marks, each with its mark scheme and topic.
- Question 1 2 marks
Convert 8.25 pounds into kilograms using the conversion 2.2 pounds = 1 kilogram.
Ratio, proportion and rates of change · Number · 3.3 Ratio, proportion and rates of change · 3.1.3 Measures and accuracy
- Question 2 1 mark
Identify the outlier from a given set of temperatures in six cities.
Statistics · 3.6 Statistics
- Question 3 3 marks
Match the labelled parts of a circle, including a sector, a tangent, and a segment, to their correct terms.
Geometry and measures · 3.4.1 Properties and constructions
- Question 4 4 marks
Work out the perimeter of an equilateral triangle whose sides are given algebraically as 6x - 8 and 2x + 12.
Algebra · Geometry and measures · 3.2.3 Solving equations and inequalities · 3.2.1 Notation, vocabulary and manipulation · 3.4.1 Properties and constructions
- Question 5 3 marks
Calculate the number of matches lost using a pie chart showing that 30 matches were won (180°), with 132° representing matches lost.
Statistics · Ratio, proportion and rates of change · 3.6 Statistics · 3.3 Ratio, proportion and rates of change
- Question 6 5 marks
Use a scale grid to calculate the actual distance between two points in kilometres and determine a three-figure bearing.
Ratio, proportion and rates of change · Geometry and measures · 3.3 Ratio, proportion and rates of change · 3.4.2 Mensuration and calculation
- Question 7 4 marks
Convert units to write one quantity as a fraction of another, express a ratio with mixed units in the form 1 : n, and express a ratio of fractions as a single fraction.
Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change
- Question 8 3 marks
Work out the nth term of a linear sequence given that the 2nd term is 6 and the 5th term is 18.
Algebra · 3.2.4 Sequences
- Question 9 3 marks
Calculate how much money Ary has given that Cat has £280, Cat's amount is 2/3 of Bea's amount, and the ratio of Ary's amount to Bea's amount is 5 : 12.
Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change
- Question 10 2 marks
Work out the value of x given a Venn diagram with sets A and B, where n(A only) = 30, n(A ∩ B) = 20, n(outside) = 6, and P(A) = 1/2.
Probability · Algebra · 3.5 Probability · 3.2.3 Solving equations and inequalities
- Question 11 2 marks
Find the equation of a line parallel to a given linear equation, and identify the equation of a straight line given its gradient and a point it passes through.
Algebra · 3.2.2 Graphs
- Question 12 4 marks
Estimate the percentage increase in Rob's mean driving time compared to last year using grouped frequency data.
Statistics · Ratio, proportion and rates of change · 3.6 Statistics · 3.3 Ratio, proportion and rates of change
- Question 13 5 marks
Complete a cumulative frequency table, draw the cumulative frequency diagram, and estimate the number of employees with a salary less than £32 000.
Statistics · 3.6 Statistics
- Question 14 7 marks
Use upper bounds of rounded masses to determine if a plane can take off safely, and draw a speed-time graph for a journey of 1250 miles in 2 hours 30 minutes at constant speed.
Number · Algebra · Ratio, proportion and rates of change · 3.1.3 Measures and accuracy · 3.2.2 Graphs · 3.3 Ratio, proportion and rates of change
- Question 15 3 marks
Calculate how many more three-digit integers Becky can make compared to Amy using the product rule for counting with given restrictions on the digits.
Number · 3.1.1 Structure and calculation
- Question 16 3 marks
Explain, without expanding brackets, why there is only one positive even value of x for which y = (x - 3)(x - 5)(x + 6) is negative.
Algebra · Number · 3.2.1 Notation, vocabulary and manipulation · 3.1.1 Structure and calculation
- Question 17 2 marks
Use the sine rule to calculate the length of an unknown side in a triangle.
Geometry and measures · 3.4.2 Mensuration and calculation
- Question 18 3 marks
Find an algebraic expression for the nth term of the quadratic sequence with first four terms 6, 15, 28, and 45.
Algebra · 3.2.4 Sequences
- Question 19 4 marks
Identify and label region R on the grid defined by the inequalities x + y < 5, y < 2x + 4, and y ≥ 1.
Algebra · 3.2.2 Graphs · 3.2.3 Solving equations and inequalities
- Question 20 3 marks
Factorise the quadratic expression 3n² + 5n + 2 fully, and deduce whether any term in the sequence generated by this nth term is a prime number.
Algebra · Number · 3.1.1 Structure and calculation · 3.2.1 Notation, vocabulary and manipulation · 3.2.4 Sequences
- Question 21 4 marks
Find the fraction of the space inside a cylinder that is filled by five identical spheres of radius r that just fit inside it.
Geometry and measures · Ratio, proportion and rates of change · 3.4.2 Mensuration and calculation · 3.3 Ratio, proportion and rates of change
- Question 22 4 marks
Solve the quadratic inequality 2x^2 > 12 - 5x.
Algebra · 3.2.3 Solving equations and inequalities
- Question 23 2 marks
Given the quadratic formula for the height of a roller coaster, identify two criticisms of a student's plotted graph of the function.
Algebra · 3.2.2 Graphs
- Question 24 4 marks
Given two similar triangles ABC and DEF, with side AC = 6 cm, angle C = 127°, side EF = 4.4 cm, angle F = 127°, and the area of ABC being 26.355 cm², calculate the area of triangle DEF.
Geometry and measures · Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change · 3.4.2 Mensuration and calculation