Edexcel GCSE Higher June 2025 Paper 1 (non-calculator)
17 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)
Find the highest common factor (HCF) of 54 and 120
(2 marks)
Question 2 (5 marks)
There are only red counters, white counters, blue counters and green counters in a bag.
Chris is going to take at random a counter from the bag.The table shows the probability that he will take a red counter and the probability that
he will take a white counter.Colour red white blue green Probability 0.3 0.1 There are twice as many blue counters as there are green counters in the bag.
(a)
Work out the probability that Chris will take a blue counter.
(3 marks)
(b)
There are 45 red counters in the bag.
Work out the total number of counters in the bag.
(2 marks)
Question 3 (5 marks)
(a)
Complete the table of values for y = x² + x – 4
x –3 –2 –1 0 1 2 y 2 –4 (2 marks)
(b)
On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 2
Diagram: A graph.
(2 marks)
(c)
Write down the coordinates of the turning point of the graph of y = x² + x – 4
(1 mark)
Question 4 (6 marks)
There are 280 chocolates in a box.
There are only dark chocolates, milk chocolates and white chocolates.1/7 of the 280 chocolates are dark chocolates.
The number of milk chocolates : the number of white chocolates = 1 : 3
The number of white chocolates : the number of dark chocolates = n : 1(a)
Work out the value of n.
You must show all your working.(5 marks)
(b)
10 milk chocolates from the box are eaten.
Does this affect your answer to part (a)?
Give a reason for your answer.(1 mark)
Question 5 (3 marks)
Work out 5.7 × 10² + 9.8 × 10³
Give your answer in standard form.(3 marks)
Question 6 (4 marks)
AB, BC, CD and DE are four sides of a regular polygon with n sides.
Diagram: Four sides AB, BC, CD and DE of a regular polygon, with CD vertical and the polygon to its right. Inside it are the triangle BCX on side BC and the square CDYX on side CD, sharing the side CX.
BCX is an equilateral triangle.
CDYX is a square.Work out the value of n.
You must show all your working.(4 marks)
Question 7 (6 marks)
(a)
Simplify (3(2 – m)²)/(2 – m)
(1 mark)
(b)
Solve 7 + x ≤ 5x/2 – 8
(3 marks)
(c)
Solve 9 < 2y + 4 < 12
(2 marks)
Question 8 (5 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC with the right angle at C: AC is vertical, 18 cm (marked with an arrow beside it), and CB is horizontal, 30 cm. E is on AC and D is on AB; ED is horizontal, 20 cm, and arrows show ED is parallel to CB.
AEC and ADB are straight lines.
ED is parallel to CB.(a)
Prove that triangle ABC is similar to triangle ADE.
(2 marks)
(b)
ED = 20 cm CB = 30 cm AC = 18 cm
Work out the length of EC.
(3 marks)
Question 9 (4 marks)
For part (a)
Diagram: A grid with x and y from –7 to 7. Shape A has corners (1, 2), (2, 5), (5, 5) and (2, 1). Shape B has corners (–2, 3), (–3, 2), (–6, 3) and (–6, 6).
For part (b)
Diagram: A grid with x and y from –6 to 8. A shaded triangle has corners (3, 3), (3, 7) and (7, 3).
(a)
Describe fully the single transformation that maps shape A onto shape B.
(2 marks)
(b)
Enlarge the triangle by scale factor 1/2 centre (-1, -3)
(2 marks)
Question 10 (3 marks)
Prove that the difference in the squares of two consecutive even numbers is always a multiple of 4
(3 marks)
Question 11 (5 marks)
T is inversely proportional to w.
w is directly proportional to the cube root of d.When w = 6, T = 20
When w = 1, d = 8Find the value of d when T = 48
(5 marks)
Question 12 (7 marks)
The graph shows the velocity, v m/s, of a particle t seconds after it starts to move.
Diagram: A velocity-time graph. The curve starts at 0 and rises, less steeply as time goes on: about 16 m/s at 1 s, about 30 m/s at 2 s, about 42 m/s at 3 s, about 50 m/s at 4 s, about 56 m/s at 5 s, about 60 m/s at 6 s.
(a)(i)
Work out an estimate of the gradient of the graph at t = 3
You must show how you get your answer.(3 marks)
(ii)
What does this gradient represent?
(1 mark)
(b)
Work out an estimate for the distance the particle travelled in the first 6 seconds.
Use 3 strips of equal width.(3 marks)
Question 13 (5 marks)
x = 0.2̇ y = 0.68̇1̇
Work out the value of xy.
Give your answer as a fraction in its simplest form.(5 marks)
Question 14 (5 marks)
There are nine balls labelled 1 to 9 in a box.
Lee will take at random two balls from the box.Lee says,
“The probability that the sum of the numbers on the two balls will be an even number is greater than the probability that the product of the numbers will be an even number.”
Is Lee correct?
You must show how you get your answer.(5 marks)
Question 15 (4 marks)
The histogram gives information about the weights, in grams, of some biscuits.
Diagram: A histogram of weights in grams. Bars: 0 to 10 g, frequency density 3; 10 to 30 g, frequency density 5; 30 to 45 g, frequency density 8; 45 to 60 g, frequency density 10.
One of these biscuits is taken at random.
Work out an estimate for the probability that the biscuit will have a weight between 20 grams and 40 grams.
(4 marks)
Question 16 (6 marks)
(a)
Rationalise the denominator of dfrac35√7
Give your answer in its simplest form.
(2 marks)
(b)
dfrac√27 – 12 – √3 can be written in the form a + b√3 where a and b are integers.
Work out the value of a and the value of b.
(4 marks)
Question 17 (5 marks)
g(x) = 1 – 3x h(x) = 2x² – 1
Show that 3gh(x) + hg(x) = 0 has just one solution for x.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.