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AQA GCSE Higher June 2025 Paper 3 (calculator)
24 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (2 marks)
Convert 8.25 pounds into kilograms.
Use 2.2 pounds = 1 kilogram
(2 marks)
Question 2 (1 mark)
Here are the temperatures in six cities in degrees Celsius.
0°C –3°C 0°C 1.5°C 23°C 4°C
Write down the outlier.
(1 mark)
Question 3 (3 marks)
Here is a circle, centre O
Diagram: A circle with centre O. C points to a straight line touching the circle at the top. D points to a shaded region on the right, cut off by a straight line across the circle. A points to a line from O straight down to the circle. B points to a shaded region between two lines from O to the circle, on the lower left.
Match each letter to the correct word.
One has been done for you: A matches Radius.Diagram: On the left, boxes A, B, C, D. On the right, boxes Arc, Chord, Diameter, Radius, Sector, Segment, Tangent. A line joins A to Radius.
(3 marks)
Question 4 (4 marks)
Here is an equilateral triangle.
All measurements are in centimetres.Diagram: An equilateral triangle. The left side is labelled 6x – 8 and the right side 2x + 12.
Work out the value of the perimeter of the triangle.
(4 marks)
Question 5 (3 marks)
The pie chart represents the results of matches played by a team.
Diagram: A pie chart. Won is the left half of the circle. On the right, Lost has an angle of 132° at the top and Drew has an angle of 48° at the bottom.
30 matches were won.
How many matches were lost?
(3 marks)
Question 6 (5 marks)
Here is a scale diagram showing towns A, B and C on a centimetre grid.
Scale 1 : 200 000
Diagram: A centimetre grid, 10 cm by 10 cm, with North straight up. Town A is at (6, 6), town B at (9, 3) and town C at (3.5, 3), measuring in centimetres from the bottom left corner.
(a)
Work out the actual distance from B to C.
Give your answer in kilometres.(4 marks)
(b)
B is South East of A.
Write down the bearing of B from A.
(1 mark)
Question 7 (4 marks)
(a)
Write 2 weeks as a fraction of 8 days.
Give your answer in its simplest form.(1 mark)
(b)
Write 56 centimetres : 2.73 metres as a ratio in the form 1 : n
(1 mark)
(c)
A : B = 1/5 : 7/10
Write A as a fraction of B.
(2 marks)
Question 8 (3 marks)
A linear sequence has
• 2nd term = 6
• 5th term = 18Work out the nth term of the sequence.
(3 marks)
Question 9 (3 marks)
Ary, Bea and Cat each have an amount of money.
Cat has £280
• Cat’s amount is 2/3 of Bea’s amount.
• Ary’s amount : Bea’s amount = 5 : 12Work out how much money Ary has.
(3 marks)
Question 10 (2 marks)
The Venn diagram shows some of the numbers of items in each set.
Diagram: Venn diagram with sets A and B. Only A: 30. Both: 20. Only B: x. Neither: 6.
P(A) = 1/2
Work out the value of x.
(2 marks)
Question 11 (2 marks)
(a)
Write down the equation of a straight line parallel to y – 2x = 9
(1 mark)
(b)
A straight line
• has gradient 5
• passes through the point (3, 7)Circle the equation of the line.
y = 3x – 2 y = 3x + 7 y = 5x y = 5x – 8 (1 mark)
Question 12 (4 marks)
Rob records the time he takes to drive to work every day for 80 days.
The table shows information about the results.
Time, t (minutes) Frequency 20 ≤ t < 25 16 25 ≤ t < 30 32 30 ≤ t < 40 24 40 ≤ t < 60 8 Total = 80 Last year, the mean time Rob took to drive to work was 25 minutes.
Estimate the percentage increase in the mean driving time for these 80 days.
(4 marks)
Question 13 (5 marks)
The table shows information about the salary of 90 employees.
Salary, s (£) Frequency Cumulative frequency 0 < s ≤ 20 000 44 44 20 000 < s ≤ 40 000 22 66 40 000 < s ≤ 60 000 14 60 000 < s ≤ 80 000 5 80 000 < s ≤ 100 000 2 100 000 < s ≤ 120 000 3 (a)
Complete the cumulative frequency table.
(1 mark)
(b)
Draw a cumulative frequency diagram to represent the data.
Diagram: A grid with salary, s (£), from 0 to 120 000 across and cumulative frequency from 0 to 90 up the side.
(2 marks)
(c)
Estimate the number of employees with a salary less than £32 000
(2 marks)
Question 14 (7 marks)
(a)
For a small plane,
• the mass of the empty plane is 800 kg, to the nearest 100 kg
• the mass of fuel is 190 kg, to the nearest 5 kg
• the mass of the passengers is 163 kg, to the nearest kgThe total mass of a plane is calculated by adding these three masses.
The maximum mass for the plane to take off safely is 1200 kgCan this plane definitely take off safely?
Tick a box.Yes square No square
Show working to support your answer.(4 marks)
(b)
A different plane travels 1250 miles in 2 hours 30 minutes at a constant speed.
On the grid, draw a speed/time graph to represent this information.
Diagram: A blank square grid with two axes and no scales.
(3 marks)
Question 15 (3 marks)
Amy and Becky each make integers using three single digits.
In any integer, digits may be repeated.
• Amy makes even integers with a first digit greater than 7
• Becky makes odd integers with a first digit that is non-zero.They each make as many different integers as possible.
How many more integers than Amy does Becky make?
(3 marks)
Question 16 (3 marks)
x is a positive even number.
y = (x – 3)(x – 5)(x + 6)
Without expanding brackets,
explain why there is only one value of x for which y is negative.(3 marks)
Question 17 (2 marks)
Diagram: A triangle. The bottom side is x. The angle at the bottom left is 31°. The angle at the top is 119°. The side from the top to the bottom right is 6.3 cm.
Use the sine rule to work out x.
(2 marks)
Question 18 (3 marks)
Here are the first four terms of a quadratic sequence.
6 15 28 45
Work out an expression for the nth term.
(3 marks)
Question 19 (4 marks)
On the grid, identify the region represented by
x + y < 5 and y < 2x + 4 and y ≥ 1
Label the region R.
Diagram: A grid with x and y axes from –7 to 7.
(4 marks)
Question 20 (3 marks)
(a)
Factorise fully 3n² + 5n + 2
(2 marks)
(b)
A sequence has nth term 3n² + 5n + 2
Are any of the terms in the sequence a prime number?
Tick a box.Yes square No square
Give a reason for your answer.(1 mark)
Question 21 (4 marks)
Five identical spheres just fit inside a cylinder.
Each sphere has radius r.
Diagram: 5 identical spheres in a row, touching, inside a cylinder lying on its side. The spheres touch the curved surface and the two ends of the cylinder.
Volume of a sphere = 4/3π r³ What fraction of the space inside the cylinder is filled by the spheres?
You must show your working.(4 marks)
Question 22 (4 marks)
Solve 2x² > 12 – 5x
(4 marks)
Question 23 (2 marks)
A roller coaster starts at ground level.
The height above ground level, h, in metres, of the roller coaster is given by
h = -(t – 7)² + 49
where t is the time in seconds after the roller coaster starts.
Sam draws a graph of h against t for 0 ≤ t ≤ 14
Diagram: Sam’s graph: axes h up and t across, with O at the corner. The curve starts on the h-axis at 49, rises to a highest point a little to the right of the label 7 and higher than 49, then falls to meet the t-axis at 14. The labels 0, 7 and 14 on the t-axis are not evenly spaced.
Make two criticisms of Sam’s graph.
(2 marks)
Question 24 (4 marks)
Triangles ABC and DEF are similar.
Diagram: Two similar triangles. Triangle ABC: AC is 6 cm and the angle at C is 127°. Triangle DEF is smaller: the angle at F is 127° and FE is 4.4 cm.
The area of ABC is 26.355 cm²
Work out the area of DEF.
(4 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.