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AQA GCSE Higher June 2025 Paper 2 (calculator)
25 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 (3 marks)
(a)
Work out the highest common factor (HCF) of 16 and 24
(1 mark)
(b)
Work out the lowest common multiple (LCM) of 10 and 15
(1 mark)
(c)
Write 42 as a product of its prime factors.
(1 mark)
Question 2 (2 marks)
Here are lines A and B.
Diagram: A squared grid with x from –1 to 4 and y from 0 to 4. Line A is a vertical line through 3 on the x-axis. Line B is a horizontal line through 2 on the y-axis.
Complete these statements.
The equation of line A is
The gradient of line B is(2 marks)
Question 3 (5 marks)
Youssuf posted an advert on his social media channel.
The table shows the number of views of the advert during its first 6 days.Day Number of views 1 49 000 2 95 000 3 87 000 4 77 000 5 64 000 6 48 000 (a)
On the grid, draw a time series graph to represent the data.
Diagram: A grid for a time series graph: Day across, from 0 to 8 (labelled 1 to 7); Number of views up the side, from 0 to 110 000 (labelled every 10 000). Two small squares make one day across and 10 000 views up. Nothing is plotted.
(2 marks)
(b)
Youssuf receives 0.018p for each view of the advert.
Estimate how much he receives from views of the advert on day 7(3 marks)
Question 4 (3 marks)
70% of the discs in a box are red and the rest are blue.
• 40% of the red discs are removed.
• 50% of the blue discs are removed.In total, what percentage of the discs are removed from the box?
(3 marks)
Question 5 (4 marks)
(a)
The length of a fence panel is 160 cm to the nearest 10 cm
Complete the error interval.
(2 marks)
(b)
A different fence panel measures 2 metres to the nearest 10 cm
Kim says that the total length of three of these fence panels must be less than 6.2 mShow that Kim is correct.
(2 marks)
Question 6 (1 mark)
Circle the expression which is a factor of 3x + 15
3x x + 12 x + 5 x + 15 (1 mark)
Question 7 (3 marks)
The five possible outcomes of an event are A, B, C, D and E.
The table shows some of the probabilities.
Outcome A B C D E Probability 0.18 0.2 P(C) = P(B) + 0.1
P(D) = P(E)Work out P(D)
(3 marks)
Question 8 (4 marks)
Here is a circle, centre O.
Diagram: A circle with centre O. Two radii, one going right and one going straight up, make an angle x at O. The sector between them is shaded.
(a)
The circle has a circumference of 20 cm
Assume that angle x is 90°Work out the shaded area.
Give your answer as a decimal.(3 marks)
(b)
In fact, angle x is smaller than 90°
What does this mean about the shaded area?
Tick one box.It is smaller than the answer to part (a) square It is the same as the answer to part (a) square It is larger than the answer to part (a) square It could be any of the above square (1 mark)
Question 9 (1 mark)
The number of people that follow an influencer increases from 35 000 to 70 000
The influencer says,
“My number of followers has increased by 200%, because 70 000 is 35 000 times 2”
Are they correct?
Tick a box.Yes square No square Give a reason for your answer.
(1 mark)
Question 10 (3 marks)
Diagram: A right-angled triangle with the right angle at the bottom left. The base is 4 cm, the vertical side is x and the angle at the bottom right is 36°.
Use trigonometry to work out the value of x.
You must show your working.(3 marks)
Question 11 (3 marks)
A straight line is drawn across a regular octagon.
Diagram: A regular octagon with a vertical side on the left and on the right. A straight line goes from the bottom of the left side to the top of the right side. Angle x is between the left side and the line.
Work out the size of angle x.
(3 marks)
Question 12 (4 marks)
Greg and Hanna want to know if students at their school think lunchtime clubs are important.
(a)
Greg asks 15 people at the lunchtime chess club.
Give one reason why his results may not represent the whole school.
(1 mark)
(b)
Here are Hanna’s results.
• 62% answered Important.
• 24% answered Not Important.
• The rest answered Don’t Know.93 students answered Important.
How many students answered Don’t Know?
(3 marks)
Question 13 (4 marks)
Emma and Chan each drive 154 miles from A to B.
Emma drives the whole way at an average speed of 56 miles per hour.
Chan drives
85 miles at an average speed of 50 miles per hour
and then
the rest of the way at an average speed of 60 miles per hour.Who takes less time, Emma or Chan?
Show working to support your answer.(4 marks)
Question 14 (3 marks)
a, b and c are positive integers.
a(9x + 2) equiv 45x + 3b + c
Work out one possible set of values for a, b and c.
(3 marks)
Question 15 (2 marks)
Solve 3x² + 5x – 9 = 0
Give your solutions as decimals.
(2 marks)
Question 16 (3 marks)
The value of a second-hand car decreases by 12.1% per year.
Work out the number of full years until the car loses more than half its value.
You must show your working.(3 marks)
Question 17 (3 marks)
When a biased coin is spun, P(Heads) : P(Tails) = 5 : 2
In a game, the player spins the coin four times.
The player can win in two ways.1st way to win 2nd way to win Spin 4 heads Spin a Head, then a Tail, then a Head, then a Tail How many times more likely is a player to win the 1st way than the 2nd way?
(3 marks)
Question 18 (4 marks)
Lines AB, BC, CD and AD form two triangles.
Diagram: Lines AB and CD cross. C is at the bottom left and B at the bottom right, joined by CB. A is at the top left and D on the right, joined by AD. From C to the crossing is 4.1 cm and from the crossing to D is 2.8 cm. From A to the crossing is 9.6 cm and from the crossing to B is 4.1 cm. Angle BCD is 32°.
Work out the length of AD.
(4 marks)
Question 19 (4 marks)
The histogram represents the ages of the 500 members of a gym.
The first bar represents the members aged at least 16 and under 20Ages of Members
Diagram: A histogram of the ages of the members, in years. Bars: 16 to 20 years, frequency density 11.5; 20 to 30 years, frequency density 13.2; 30 to 40 years, frequency density 14.6; 40 to 60 years, frequency density 6; 60 to 80 years, frequency density 2.8.
Each member pays an annual fee based on their age.
Age Under 65 65 or over Annual fee £275 £129 Use the histogram to estimate the total annual fees paid by these members.
(4 marks)
Question 20 (1 mark)
David has solved the inequality x² < 16 and represented his solution on the number line below.
Diagram: A number line for x from –5 to 5, with a filled-in circle at –4, a filled-in circle at 4 and a line between them, drawn just above the number line.
Give one reason why David’s solution is wrong.
(1 mark)
Question 21 (5 marks)
A circle with centre O and radius √45 has a tangent drawn at point P(6, –3)
Diagram: A sketch of a circle with centre O at the origin. The point P(6, –3) is on the circle, and a straight line touches the circle at P.
(a)
Write down the equation of the circle.
(1 mark)
(b)
Work out the equation of the tangent.
Give your answer in the form y = mx + c(4 marks)
Question 22 (3 marks)
Shape A and shape B are shown on the grid.
Diagram: A grid with x and y from 0 to 10. Shape A is a triangle with vertices (6, 1), (10, 1), (10, 7). Shape B is a triangle with vertices (1, 4), (1, 7), (3, 7).
Describe the single transformation that maps shape A to shape B.
(3 marks)
Question 23 (5 marks)
ABCD is a quadrilateral.
AC and BD intersect at P.overrightarrowAB = 9mathbfb – 2mathbfa
overrightarrowBC = 5mathbfa
overrightarrowDC = 10mathbfbDiagram: Quadrilateral ABCD with A at the bottom, B on the right, C at the top and D on the left. The diagonals AC and BD cross at P. Arrows show the vectors AB, BC and DC.
BP : PD = 3 : 2
AP : PC = 1 : kWork out the value of k.
You must show your working.(5 marks)
Question 24 (3 marks)
A study suggests a student’s exam mark, m, is directly proportional to the cube root of total revision time, t hours.
A student doubles their total revision time.
Work out the percentage increase in their exam mark.
(3 marks)
Question 25 (4 marks)
f(x) = ax + b and g(x) = (x + b)/a where a and b are positive integers.
Prove that fg(x) – af⁻¹(x) is always a multiple of 3
(4 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.