Edexcel GCSE Higher June 2025 Paper 2 (calculator)
23 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 (4 marks)
(a)
Express 250 as a product of its prime factors.
(2 marks)
(b)
Find the lowest common multiple (LCM) of 30 and 25
(2 marks)
Question 2 (3 marks)
Sid, Tam and Musa share £6900 in the ratio 2 : 3 : 5
Work out how much money each person receives.
(3 marks)
Question 3 (5 marks)
Here is a plan of part of Macsen’s garden.
There is a circle inside a triangle.
The circle has a diameter of 7 m.Diagram: A triangle with a base of 16 m and a height of 14 m; its two sloping sides are the same length. A circle of diameter 7 m is inside the triangle. The triangle is shaded, except for the circle.
Macsen will cover the shaded area with gravel.
Gravel is sold in bags.
Each bag of gravel covers an area of 12.5 m²(a)
Work out the number of bags of gravel Macsen will need.
(4 marks)
(b)
Macsen finds that each bag of gravel only covers an area of 11 m²
How does this affect your answer to part (a)?
(1 mark)
Question 4 (1 mark)
The point C is shown on a centimetre grid.
Diagram: A centimetre grid, 7 squares across and 7 squares up. The point C is marked with a cross. A circle of radius 2 cm with centre C is drawn, and the inside of the circle is shaded.
A point P is at least 2 cm from the point C.
Nadia is asked to shade the region where point P could be.Her answer is shown on the grid.
Explain the mistake Nadia has made.
(1 mark)
Question 5 (3 marks)
This year the total weight of potatoes grown on a farm is 1/5 less than last year.
This year the total weight of potatoes grown is 8000 tonnes.
Work out the total weight of potatoes grown last year.
(3 marks)
Question 6 (5 marks)
Here are two lists of numbers.
List A 276 400 157 139
List B 530 500 270 x 440 320mean of list A : mean of list B = 3 : 5
Work out the value of x.
(5 marks)
Question 7 (2 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC. AB is 7 cm across the top. The right angle is at B. BC is 4 cm, going straight down from B to C. The angle at C is marked x°.
Calculate the value of x.
Give your answer correct to 1 decimal place.(2 marks)
Question 8 (3 marks)
Metal rods are made from steel with density 8 g/cm³
Each metal rod has a volume of 1500 cm³The maximum mass of metal rods that can be put on a trolley is 300 kg.
Work out the greatest number of metal rods that can be put on the trolley.
(3 marks)
Question 9 (2 marks)
3x⁻¹(4x – x³) = a + bxⁿ for all the values of x that are not zero.
Find the value of a, the value of b and the value of n.
(2 marks)
Question 10 (2 marks)
Solve (14 – x)/3 = 3x
(2 marks)
Question 11 (5 marks)
Freya and Ria each do an exam.
The probability that Freya will pass the exam is 0.8
The probability that Ria will pass the exam is 0.85(a)
Complete the probability tree diagram.
Diagram: A probability tree diagram. The first branches are for Freya: pass (0.8) and fail (blank). After each, branches for Ria: pass (0.85) and fail (blank) after pass; pass (blank) and fail (blank) after fail.
(2 marks)
(b)
Work out the probability that only one of Freya or Ria will pass the exam.
(3 marks)
Question 12 (5 marks)
The table gives some information about the ages, in years, of 32 actors.
Lowest age 21 Highest age 80 Lower quartile 31 Upper quartile 42 Median 35 (a)
Draw a box plot to represent this information.
Diagram: A squared grid with a horizontal scale of age in years from 10 to 90.
(3 marks)
(b)
Work out an estimate for the number of these actors with an age
between 31 years and 42 years.(1 mark)
(c)
Mary says,
“At least one of the actors is 35 years old because the median is 35”
Is Mary correct?
Give a reason for your answer.(1 mark)
Question 13 (3 marks)
Show that (2x + 3)(x – 1)(x + 2) can be written in the form
ax³ + bx² + cx + d where a, b, c and d are integers.(3 marks)
Question 14 (3 marks)
There are 15 dogs in a dog show.
One dog is awarded first prize.
A different dog is awarded second prize.There are 12 cats in a cat show.
One cat is awarded first prize.
A different cat is awarded second prize.Work out how many different ways these four prizes can be awarded.
(3 marks)
Question 15 (5 marks)
On the grid, show by shading, the region that satisfies all of these inequalities.
x + y < 5 y > 1 x > 2 y < 3x – 2
Label the region R.(a)
Diagram: A graph.
(4 marks)
(b)
Ron says,
“I can remove one of the four inequalities from the grid so that the region R
will not change.”
Ron is correct.Which inequality can be removed so that the region R will not change?
(1 mark)
Question 16 (5 marks)
Two jars are mathematically similar.
Diagram: Two jars of the same shape. The smaller jar has volume 90 cm³ and height h cm. The larger jar has volume 1350 cm³ and height 12 cm.
(a)
Work out the height, h cm, of the smaller jar.
Give your answer correct to 1 decimal place.(4 marks)
(b)
The surface area of the smaller jar is A cm²
The surface area of the larger jar is pA cm²Find the exact value of p.
(1 mark)
Question 17 (2 marks)
Here is a sketch of part of the graph of y = k^x where k is a positive constant.
Diagram: A sketch of a curve that is very high on the left, falls steeply, crosses the y-axis just above the origin and then flattens out just above the x-axis. The point (–1, 1.5) is marked on the curve.
The graph passes through the point with coordinates (–1, 1.5)
Find the value of k.
(2 marks)
Question 18 (3 marks)
At the start of year n, the population of deer in a park is D_n
At the start of the following year, the population of the deer is D_n + 1D_n + 1 = KD_n where K is a constant.
At the start of 2019, the population of the deer was 2000
At the start of 2020, the population of the deer was 2400Show that, at the start of 2022, the population of the deer was greater than 3000
(3 marks)
Question 19 (4 marks)
ABCDEFGH is a cuboid.
Diagram: A cuboid ABCDEFGH. FE is the front bottom edge, with A above F and D above E. G is behind F, H is behind E, B is above G and C is above H. The edges GH, HE and HC are hidden. BH, BE and GE are drawn as dotted lines. Angle GEF is 52°, angle BHG is 27° and EF is 15 cm.
Angle GEF = 52°
Angle BHG = 27°
EF = 15 cmWork out the size of angle GEB.
Give your answer to the nearest degree.(4 marks)
Question 20 (5 marks)
Diagram: A sketch of x and y axes. A straight line goes down from A on the y-axis to B on the x-axis. The point D is on AB, nearer to A. A steeper line L goes up through D, crossing the y-axis just below the origin.
In the diagram
A is the point (0, 8)
B is the point (16, 0)The point D divides the line segment AB in the ratio 1 : 3
The line L passes through D.
The gradient of L is √3L passes through the point with coordinates (–2, f)
Show that f < -4
(5 marks)
Question 21 (2 marks)
Solve (3x – 1)(5x + 2) < 0
(2 marks)
Question 22 (3 marks)
The equation of circle A is x² + y² = 25
Circle A is translated by the vector ( 0 , -2 ) to give circle B.
Sketch circle B.
Show the coordinates of
the centre of circle B
and the points where circle B meets the y-axis.Diagram: A pair of x and y axes crossing at the origin O.
(3 marks)
Question 23 (5 marks)
ABCD is a quadrilateral.
Diagram: Quadrilateral ABCD with A at the top left, B at the top right, C at the bottom and D on the left. DA is 6 cm, DC is 9 cm and CB is 12 cm. Angle DAB is 125° and angle BCD is 60°.
Find the size of angle ABC.
Give your answer correct to the nearest degree.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.