AQA GCSE Mathematics Paper 2 (Higher), June 2025
Every question from AQA GCSE Mathematics Paper 2 (Higher), June 2025 (8300): 25 questions, 80 marks, each with its mark scheme and topic.
- Question 1 3 marks
Find the highest common factor of 16 and 24, the lowest common multiple of 10 and 15, and express 42 as a product of prime factors.
Number · 3.1.1 Structure and calculation
- Question 2 2 marks
State the equation of a vertical straight line and the gradient of a horizontal straight line drawn on a coordinate grid.
Algebra · 3.2.2 Graphs
- Question 3 5 marks
Draw a time series graph representing advert views over 6 days and estimate the earnings on day 7 given a rate per view in pence.
Statistics · Number · 3.6 Statistics · 3.1.3 Measures and accuracy
- Question 4 3 marks
Calculate the total percentage of discs removed from a box given the percentages of red and blue discs and the percentage removed of each color.
Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change
- Question 5 4 marks
Find the error interval for a length given to the nearest 10 cm, and show whether the maximum combined length of three fence panels is less than 6.2 m.
Number · Ratio, proportion and rates of change · 3.1.3 Measures and accuracy · 3.3 Ratio, proportion and rates of change
- Question 6 1 mark
Identify which given algebraic expression is a factor of 3x + 15.
Algebra · 3.2.1 Notation, vocabulary and manipulation
- Question 7 3 marks
Given the probabilities of outcomes A and B for a set of mutually exclusive and exhaustive outcomes, with conditions P(C) = P(B) + 0.1 and P(D) = P(E), work out P(D).
Probability · 3.5 Probability
- Question 8 4 marks
Given a circle with circumference 20 cm, calculate the area of a shaded 90° sector, and determine the effect on the area if the angle is smaller than 90°.
Geometry and measures · 3.4.2 Mensuration and calculation
- Question 9 1 mark
Evaluate whether doubling follower count from 35 000 to 70 000 represents an increase of 200%, giving a reason.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 10 3 marks
Use trigonometry to calculate the unknown side length x of a right-angled triangle given an adjacent side of 4 cm and an angle of 36°.
Geometry and measures · 3.4.2 Mensuration and calculation
- Question 11 3 marks
Work out the size of angle x formed by a diagonal connecting opposite vertices of a regular octagon.
Geometry and measures · 3.4.1 Properties and constructions
- Question 12 4 marks
Evaluate the representativeness of a lunchtime survey sample, then calculate the number of students who gave a particular response using given percentages and frequencies.
Statistics · Number · 3.6 Statistics · 3.1.2 Fractions, decimals and percentages
- Question 13 4 marks
Determine whether Emma or Chan takes less time to complete a 154-mile journey, given their respective speeds across different sections of the journey.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 14 3 marks
Find one possible set of positive integer values for a, b, and c given the identity a(9x + 2) ≡ 45x + 3b + c.
Algebra · 3.2.1 Notation, vocabulary and manipulation
- Question 15 2 marks
Solve the quadratic equation 3x^2 + 5x - 9 = 0, giving the solutions as decimals.
Algebra · 3.2.3 Solving equations and inequalities
- Question 16 3 marks
Calculate the number of full years required for the value of a car to decrease by more than half when it depreciates by 12.1% each year.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 17 3 marks
Calculate how many times more likely a player is to spin four heads than alternating heads and tails given the ratio of heads to tails is 5 : 2.
Probability · Ratio, proportion and rates of change · Number · 3.5 Probability · 3.3 Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages
- Question 18 4 marks
Calculate the length of line segment AD formed by two intersecting line segments using angle properties of isosceles triangles and the cosine rule.
Geometry and measures · 3.4.1 Properties and constructions · 3.4.2 Mensuration and calculation
- Question 19 4 marks
Use the histogram showing the ages of 500 gym members to estimate the total annual fees paid, given that members under 65 pay £275 and members 65 or over pay £129.
Statistics · 3.6 Statistics
- Question 20 1 mark
Identify and explain an error in a number line representation of the solution to the quadratic inequality x² < 16.
Algebra · 3.2.3 Solving equations and inequalities
- Question 21 5 marks
Find the equation of a circle centered at the origin with radius √45, and find the equation of the tangent to the circle at the point (6, -3).
Algebra · Geometry and measures · 3.2.2 Graphs · 3.4.1 Properties and constructions
- Question 22 3 marks
Describe the single transformation that maps shape A to shape B on the coordinate grid.
Geometry and measures · 3.4.1 Properties and constructions
- Question 23 5 marks
Given quadrilateral ABCD with intersecting diagonals at P, vector AB = 9b - 2a, vector BC = 5a, vector DC = 10b, and ratio BP : PD = 3 : 2, find the value of k if AP : PC = 1 : k.
Geometry and measures · Ratio, proportion and rates of change · 3.4.3 Vectors · 3.3 Ratio, proportion and rates of change
- Question 24 3 marks
Work out the percentage increase in a student's exam mark if their exam mark is directly proportional to the cube root of total revision time and they double their revision time.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 25 4 marks
Prove algebraically that fg(x) - a f^(-1)(x) is always a multiple of 3 given f(x) = ax + b and g(x) = (x + b)/a.
Algebra · 3.2.1 Notation, vocabulary and manipulation