Edexcel GCSE Higher June 2025 Paper 3 (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 (2 marks)
The table shows information about the distances that 60 people travel to work.
Distance (d miles) Frequency 0 < d ≤ 10 12 10 < d ≤ 20 25 20 < d ≤ 30 10 30 < d ≤ 40 8 40 < d ≤ 50 5 Draw a frequency polygon for the information in the table.
Diagram: A blank grid. Distance (d miles) from 0 to 50 across, frequency from 0 to 30 up.
(2 marks)
Question 2 (3 marks)
(a)
Ben is trying to make m the subject of p = m/3 + 5
Here is his working.
p – 5 = m/3
3 × p – 5 = m
m = 3p – 5Ben’s answer is wrong.
What mistake has Ben made?
(1 mark)
(b)
Factorise fully 2x³y + 4xy²
(2 marks)
Question 3 (3 marks)
Mia pays £25 for 200 oranges.
Mia puts the oranges into bags.
She puts 5 oranges into each bag.Mia sells all the bags of oranges for £1 each bag.
Work out Mia’s percentage profit.
(3 marks)
Question 4 (4 marks)
In London, 2 kg of carrots cost £3.75
In New York, 5 lbs of carrots cost 4.90 US dollars.£1 = 1.20 US dollars
1 kg = 2.2 lbsIn which city are carrots better value for money, London or New York?
You must show how you get your answer.(4 marks)
Question 5 (2 marks)
Karim rounds a number, n, to 1 decimal place.
The result is 23.8Complete the error interval for n.
……… ≤ n < ………
(2 marks)
Question 6 (3 marks)
A plane takes 2 hours 24 minutes to fly from Luton to Alicante.
The plane flies a distance of 1512 kilometres.Work out the average speed of the plane.
Give your answer in kilometres per hour.(3 marks)
Question 7 (3 marks)
ABC is a straight line.
Diagram: A sketch of a straight line on a pair of axes. Points A (2, 7), B (8, 12) and C are marked with crosses along the line, in that order, going up to the right. C is not labelled with its coordinates.
Point A has coordinates (2, 7)
Point B has coordinates (8, 12)BC = 1/2AB
Find the coordinates of point C.
(3 marks)
Question 8 (5 marks)
The diagram shows trapezium ABCD.
Diagram: Trapezium ABCD. AB is the bottom side, 12 cm, and DC is the longer top side, parallel to AB. AD is a vertical side of 8 cm with right angles at A and D. BC slopes up to the right from B to C.
AB = 12 cm
AD = 8 cmThe trapezium has an area of 112 cm²
Work out the perimeter of the trapezium.
Give your answer correct to 3 significant figures.(5 marks)
Question 9 (2 marks)
(a)
Write 5.73 × 10⁶ as an ordinary number.
(1 mark)
(b)
Write 0.035 in standard form.
(1 mark)
Question 10 (2 marks)
Use your calculator to work out
dfrac(1.8^text3 × cos 35°)²3√(17.4 – tan 85°)
Give your answer correct to 3 significant figures.
(2 marks)
Question 11 (4 marks)
dfrac3ⁿ × 3²⁰ 3^text8 = 3¹⁴
(a)
Find the value of n.
(2 marks)
(b)
Write (64m¹²)^(2/3) in the form am^b where a and b are integers.
(2 marks)
Question 12 (4 marks)
The price of a holiday is increased by 10%
After the increase, the price of the holiday is £440Jim says,
“10% of £440 is £44 so the price of the holiday before the increase was £396”(a)
Is Jim correct?
Explain your answer.(1 mark)
(b)
Tina sells bikes.
In November, Tina sold 25% fewer bikes than she sold in October.
In December, Tina sold 50% more bikes than she sold in November.
In December, Tina sold 180 bikes.How many bikes did Tina sell in October?
(3 marks)
Question 13 (3 marks)
Here are some graphs.
Graph A
Diagram: Graph A: a curve falling from top left, crossing the y-axis above O, and getting closer and closer to the x-axis on the right.
Graph B
Diagram: Graph B: an upside-down U-shaped curve with its highest point on the y-axis, above O.
Graph C
Diagram: Graph C: two curves, top right and bottom left, never touching the axes.
Graph D
Diagram: Graph D: a U-shaped curve crossing the x-axis twice, with its lowest point just to the right of the y-axis, below O.
Graph E
Diagram: Graph E: an S-shaped curve through O, rising from bottom left to top right and flattening at O.
Graph F
Diagram: Graph F: a curve rising from bottom left to a highest point, down through O to a lowest point, then up to top right.
Graph G
Diagram: Graph G: two curves, top left and bottom right, never touching the axes.
Graph H
Diagram: Graph H: a curve close to the x-axis on the left, crossing the y-axis above O and rising more and more steeply to the right.
Each equation in the table is the equation of one of the graphs.
Complete the table.
Equation Letter of graph y = x³ y = 2/x y = 5 – x² y = 3^(x) (3 marks)
Question 14 (2 marks)
Here is triangle ABC.
Diagram: Triangle ABC with BC at the bottom. AB is 8.3 cm, AC is 9.8 cm and angle BAC is 35°.
Calculate the area of triangle ABC.
Give your answer correct to 3 significant figures.(2 marks)
Question 15 (4 marks)
There are only 7 blue pens and 3 red pens in a box.
Raja takes at random one of the pens.
He notes the colour of the pen and puts the pen back into the box.
Raja does this two more times.Show that the probability that Raja takes at least two blue pens is 98/125
(4 marks)
Question 16 (4 marks)
The diagram shows a solid shape made from a cylinder and a cone.
Diagram: A cone standing on top of a cylinder. The cone and the cylinder have the same radius, 8 cm, shown on the top of the cylinder.
Volume of cone = 1/3π r² h
Diagram: A cone with its base radius r and its vertical height h marked.
The cone has a base radius of 8 cm.
The cylinder has a radius of 8 cm.The vertical height of the cone is three times the height of the cylinder.
The volume of the solid shape is 640π cm³
Work out the vertical height of the cone.
You must show all your working.(4 marks)
Question 17 (3 marks)
Solve 5x/(3x – 1) – 2x/(3x + 1) = 1
(3 marks)
Question 18 (6 marks)
Magda carried out a survey to find out the drinks that people like.
She asked 100 people if they like coffee (C) or tea (T) or hot chocolate (H).
32 people like all three drinks. 15 people like coffee and hot chocolate but not tea.
43 people like coffee and tea. 39 people like tea and hot chocolate.
67 people like coffee. 58 people like hot chocolate. 5 people like only tea.(a)
Complete the Venn diagram for this information.
Diagram: A blank Venn diagram: three overlapping circles C, T and H inside a rectangle for the universal set.
(4 marks)
(b)
One of the people is chosen at random.
Given that this person likes coffee,find the probability that this person also likes hot chocolate.
(2 marks)
Question 19 (3 marks)
There are some sheets of paper in a pile.
The height of the pile is 10.4 cm, correct to the nearest mm.
The thickness of each sheet of paper is 0.17 mm, correct to 2 significant figures.Calculate the upper bound for the number of sheets of paper in the pile.
You must show all your working.(3 marks)
Question 20 (4 marks)
A, B, C and D are points on a circle with centre O.
Diagram: A circle with centre O. A, B, C and D are on the circle. Lines AD, AB, DC, CB, DO and OB are drawn. Angle DAB is 80° and angle ODC is 43°.
Find the size of angle OBC.
Write down any circle theorems that you use.(4 marks)
Question 21 (5 marks)
Solve algebraically the simultaneous equations
3x² + 2y² = 44
3x + y = 2(5 marks)
Question 22 (4 marks)
C is a circle with centre (0, 0)
The straight line with equation 3x – 2y = 52 is the tangent to C at the point P.Find the coordinates of P.
(4 marks)
Question 23 (5 marks)
OACB is a quadrilateral.
ACP is a straight line.Diagram: Quadrilateral OACB with AC parallel to OB. The side AC carries on in a straight line to P. M is on OA and N is on BC.
M is the midpoint of OA.
N is the point on BC such that BN : NC = 5 : 3overrightarrowOA = mathbfa overrightarrowOB = 3mathbfb overrightarrowAC = 2mathbfb
overrightarrowCP = k × overrightarrowAC where k is a scalar.
Given that MNP is a straight line, find the value of k.
You must show all your working.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.