Edexcel GCSE Higher June 2024 Paper 1 (non-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)
Here are the first four terms of an arithmetic sequence.
1 5 9 13
Find an expression, in terms of n, for the nth term of this sequence.
(2 marks)
Question 2 (3 marks)
(a)
Work out 34/5 – 12/3
(2 marks)
(b)
Kevin was asked to work out 21/3 × 5/8
Here is his working and his answer.
beginaligned 21/3 × 5/8 &= 7/3 × 5/8 \\[4pt] &= 35/24 \\[4pt] &= 19/24 endaligned
Kevin’s answer is wrong.
What mistake has Kevin made?
(1 mark)
Question 3 (5 marks)
The diagram shows a plan of a floor.
Diagram: A plan of a floor made of rectangles.
Petra is going to cover the floor with paint.
Petra has 3 tins of paint.
There are 2.5 litres of paint in each tin.Petra thinks 1 litre of paint will cover 10 m² of floor.
(a)
Assuming Petra is correct, does she have enough paint to cover the floor?
You must show all your working.(4 marks)
(b)
Actually, 1 litre of paint will cover 11 m² of floor.
Does this affect your answer to part (a)?
You must give a reason for your answer.(1 mark)
Question 4 (3 marks)
Here is a Venn diagram.
Diagram: Venn diagram with sets P and Q. Only P: 12, 15. Both: 18. Only Q: 10, 14. Neither: 11, 13, 16, 17.
(a)
Write down the numbers that are in set P’
(1 mark)
(b)
A number is chosen at random from the universal set, ℰ.
Find the probability that this number is in the set P ∪ Q
(2 marks)
Question 5 (4 marks)
Sophie drives a distance of 513 kilometres on a motorway in France.
She pays 0.81 euros for every 10 kilometres she drives.(a)
Work out an estimate for the total amount that Sophie pays.
(3 marks)
(b)
Is your answer to part (a) an underestimate or an overestimate?
Give a reason for your answer.(1 mark)
Question 6 (4 marks)
Here is a straight line L drawn on a grid.
Diagram: A grid with x from –4 to 4 and y from –3 to 7. Line L passes through (–4, –3), (–2, 0), (0, 3) and (2, 6).
(a)
Find an equation for L.
(3 marks)
(b)
M is a different straight line with equation y = 5x
Write down the equation of a straight line parallel to M.
(1 mark)
Question 7 (5 marks)
Kasim has some small jars, some medium jars and some large jars.
He has a total of 400 jars.3/8 of the 400 jars are empty.
For the empty jars,
number of small jars : number of medium jars = 3 : 4
number of medium jars : number of large jars = 1 : 2Work out the percentage of Kasim’s jars that are empty small jars.
(5 marks)
Question 8 (3 marks)
Len has 8 parcels.
The mean weight of the 8 parcels is 2.5 kg.
The mean weight of 3 of the parcels is 2 kg.Work out the mean weight of the other 5 parcels.
(3 marks)
Question 9 (1 mark)
In a sale, the normal price of a coat is reduced by R\%
Given that
sale price = 0.7 × normal pricefind the value of R.
(1 mark)
Question 10 (4 marks)
Solve the simultaneous equations
5x – 2y = 23
2x – 3y = 18(4 marks)
Question 11 (3 marks)
Diagram: A grid with x and y from –6 to 6. Triangle A has corners (–3, 2), (–2, 2) and (–2, 4).
Triangle A is translated by the vector (6, -4) to give triangle B.
Triangle B is rotated 90° clockwise about the point (1, 2) to give triangle C.
Describe fully the single transformation that maps triangle A onto triangle C.
(3 marks)
Question 12 (3 marks)
Here are some graphs.
Diagram: Graph A: a parabola opening downwards, crossing the y-axis above O. Graph B: two curves, top right and bottom left, never touching the axes. Graph C: a cubic curve rising from bottom left, with a maximum then a minimum, crossing the x-axis three times. Graph D: a straight line with positive gradient, crossing the y-axis above O. Graph E: a cubic curve rising from bottom left to top right, flattening at O. Graph F: a cubic curve falling from top left to bottom right, flattening at O. Graph G: a straight line with negative gradient, through O. Graph H: a parabola opening upwards, crossing the y-axis below O. Graph J: two curves, top left and bottom right, never touching the axes.
Write down the letter of the graph that could have the equation
(i)
y = x² – 4
(1 mark)
(ii)
y = -x³
(1 mark)
(iii)
y = -5/x
(1 mark)
Question 13 (5 marks)
The table gives information about the amount of time that each of 150 people were in a shop.
Time (t minutes) Frequency 0 < t ≤ 10 20 10 < t ≤ 30 70 30 < t ≤ 35 22 35 < t ≤ 50 30 50 < t ≤ 60 8 (a)
On the grid, draw a histogram for this information.
Diagram: A blank grid for drawing a histogram.
(3 marks)
(b)
Work out an estimate for the fraction of these 150 people who were in the shop for between 20 minutes and 40 minutes.
(2 marks)
Question 14 (3 marks)
Expand and simplify (3x – 1)(2x + 3)(x – 5)
(3 marks)
Question 15 (4 marks)
OAB is a sector of a circle with centre O and radius 6 cm.
Diagram: A sector OAB of a circle with centre O and radius 6 cm.
The length of the arc AB is 5π cm.
Work out, in terms of π, the area of the sector.
Give your answer in its simplest form.(4 marks)
Question 16 (2 marks)
There are only n orange sweets and 1 white sweet in a bag.
Saira takes at random a sweet from the bag and eats the sweet.
She then takes at random another sweet from the bag and eats this sweet.Show that the probability that Saira eats two orange sweets is (n – 1)/(n + 1)
(2 marks)
Question 17 (3 marks)
(a)
Rationalise the denominator of dfrac1√7
(1 mark)
(b)
Simplify fully √80 – √5
(2 marks)
Question 18 (3 marks)
Show that 0.1̇5̇ + 0.22̇7̇ can be written in the form m/66 where m is an integer.
(3 marks)
Question 19 (3 marks)
Diagram: Triangle ABD with point C on BD, closer to B. AC is drawn.
ABC and DAB are similar isosceles triangles.
AB = AC
AD = BDBC : CD = 4 : 21
Find the ratio AB : AD
(3 marks)
Question 20 (3 marks)
2^x = dfrac2ⁿ3√(2) 2^y = (√2)⁵
Given that x + y = 8
work out the value of n.
(3 marks)
Question 21 (5 marks)
A solid cuboid has a volume of 300 cm³
The cuboid has a total surface area of 370 cm²The length of the cuboid is 20 cm.
The width of the cuboid is greater than the height of the cuboid.Work out the height of the cuboid.
You must show all your working.(5 marks)
Question 22 (4 marks)
(a)
Sketch the graph of y = sin x° for 0 ≤ x ≤ 360
Diagram: Blank axes: x from 0 to 360, marked at 90, 180, 270 and 360.
(2 marks)
(b)
Solve the equation 2sin x° = -1 for 0 ≤ x ≤ 360
(2 marks)
Question 23 (5 marks)
C is a circle with centre (0, 0)
L is a straight line.The circle C and the line L intersect at the points P and Q.
The coordinates of P are (5, 10)
The x coordinate of Q is -2L has a positive gradient and crosses the y-axis at the point (0, k)
Find the value of k.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.