Edexcel GCSE Higher June 2022 Paper 2 (calculator)

22 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 (5 marks)
(a)
Simplify (x³)⁵
(1 mark)
(b)
Expand and simplify 4(x + 3) + 7(4 – 2x)
(2 marks)
(c)
Factorise fully 15x³ + 3x²y
(2 marks)
Question 2 (2 marks)
Diagram: Two shaded L-shapes on a coordinate grid: shape S below the x-axis on the right, and shape T above the x-axis on the left, the same way up.
Describe fully the single transformation that maps shape S onto shape T.
(2 marks)
Question 3 (2 marks)
The length of a football pitch is 90 metres, correct to the nearest metre.
Complete the error interval for the length of the football pitch.
……… m ≤ length < ……… m
(2 marks)
Question 4 (5 marks)
Festival A will be in a rectangular field with an area of 80 000 m²
The greatest number of people allowed to attend Festival A is 425
Festival B will be in a rectangular field 700 m by 2000 m.
The greatest number of people allowed to attend Festival B is 6750
The area per person allowed for Festival B is greater than the area per person allowed
for Festival A.
(a)
How much greater?
Give your answer correct to the nearest whole number.
(4 marks)
(b)
Callum says,
“300 cm² is the same as 3 m² because there are 100 cm in 1 m so you divide by 100”
Callum’s method is wrong.
Explain why.
(1 mark)
Question 5 (4 marks)
The points L, M and N are such that LMN is a straight line.
The coordinates of L are (–3, 1)
The coordinates of M are (4, 9)
Given that LM : MN = 2 : 3,
find the coordinates of N.
(4 marks)
Question 6 (3 marks)
A new phone cost £679
The value of the phone decreases at a rate of 4% per year.
Work out the value of the phone at the end of 3 years.
(3 marks)
Question 7 (4 marks)
In Spain, Sam pays 27 euros for 18 litres of petrol.
In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol.
1 euro = £0.85
4.5 litres = 1 gallon
Sam thinks that petrol is cheaper in Spain than in Wales.
Is Sam correct?
You must show how you get your answer.
(4 marks)
Question 8 (2 marks)
Use your calculator to work out
dfrac3√(1.57⁴ + tan 60°)7.2^(1/2)
Give your answer correct to 3 significant figures.
(2 marks)
Question 9 (3 marks)
A box in the shape of a cuboid is placed on a horizontal floor.
pressure = dfracforcearea
The box exerts a force of 180 newtons on the floor.
The box exerts a pressure of 187.5 newtons/m² on the floor.
The face in contact with the floor is a rectangle of length 1.2 metres and width x metres.
Work out the value of x.
(3 marks)
Question 10 (5 marks)
The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month.
Diagram: Online store: lowest 60, lower quartile 160, median 200, upper quartile 350, highest 420.
(a)
Andrew says, “Three quarters of the given data lies between 160000 and 350000 because these are the values of the lower quartile and the upper quartile.”
Andrew is wrong. Explain why.
(1 mark)
(b)
The table shows information about the sales, in £000s, in a shop each month.
Sales (£000s)
least value 30
lower quartile 80
median 170
upper quartile 260
greatest value 350
On the grid below, draw a box plot for this information.
Diagram: Shop: blank grid.
(2 marks)
(c)
Compare the distribution of the sales of the online store with the distribution of the sales in the shop.
(2 marks)
Question 11 (3 marks)
Kieron has 13 workers he can use for a job.
He knows that 6 workers would take 141/2 days to complete this job.
Show that Kieron has enough workers to finish this job in less than 7 days.
(3 marks)
Question 12 (2 marks)
The equation of the line L₁ is y = 2x + 3
The equation of the line L₂ is 5y – 10x + 4 = 0
Show that these two lines are parallel.
(2 marks)
Question 13 (2 marks)
Diagram: A coordinate grid with x from –8 to 14 and y from –10 to 10. A shaded shape has vertices (–6, –4), (–2, –4), (–3, –2), (–5, –2).
Enlarge the shaded shape by scale factor –2 with centre of enlargement (0, 0)
(2 marks)
Question 14 (3 marks)
Saffron wants to work out an estimate for the total number of fish in a lake.
On Friday, Saffron catches 180 fish from the lake.
She puts a tag on each of these fish and puts them back into the lake.
On Saturday, Saffron catches 305 fish from the same lake.
She finds that 45 of the 305 fish are tagged.
Work out an estimate for the total number of fish in the lake.
(3 marks)
Question 15 (4 marks)
The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5
Both Marta and Khalid get an increase of £1.50 in their hourly pay.
The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13 : 11
Work out the hourly pay before the increase for Marta and for Khalid.
(4 marks)
Question 16 (6 marks)
A shop manager wants to advertise special offers on social media platforms.
The manager asks 100 customers which of type A, type B or type C they use.
Of these customers,
4 use all three types    16 do not use any of type A, type B or type C
8 use both type A and type B, but not type C    14 use both type B and type C
62 in total use type A    all 20 who use type C also use at least one of type A and type B.
(a)
Complete the Venn diagram for this information.
Diagram: A blank Venn diagram: three overlapping circles A, B and C inside a rectangle for the universal set.
(4 marks)
(b)
One of the customers is chosen at random.
Given that this customer uses type A,
find the probability that this customer also uses type B.
(2 marks)
Question 17 (5 marks)
A solid cone is joined to a solid hemisphere to make the solid T shown below.
Diagram: Solid T: a cone, point up, standing on a hemisphere of the same width. The diameter across the join is labelled 7 cm and the total height is labelled y cm.
Volume of sphere = 4/3π r³
Volume of cone = 1/3π r² h
The diameter of the base of the cone is 7 cm.
The diameter of the hemisphere is 7 cm.
The total volume of T is 120π cm³
The total height of T is y cm.
(a)
Calculate the value of y.
Give your answer correct to 3 significant figures.
(4 marks)
(b)
The diameter of the base of the cone and the diameter of the hemisphere are both increased by the same amount.
Assuming the total volume of T does not change,
explain the effect this would have on your answer to part (a).
(1 mark)
Question 18 (4 marks)
PQR and QRS are triangles.
Diagram: Triangles PQR and QRS share the side QR. PQ is 11 cm, PR is 9.4 cm and angle QPR is 27°. In triangle QRS, angle QRS is 88° and angle RSQ is 41°.
Calculate the length of QS.
Give your answer correct to 3 significant figures.
You must show all your working.
(4 marks)
Question 19 (4 marks)
The functions g and h are such that
g(x) = 3√(2x – 5) h(x) = 1/x
(a)
Find g(16)
(1 mark)
(b)
Find hg⁻¹(x)
Give your answer in terms of x in its simplest form.
(3 marks)
Question 20 (4 marks)
A, B, C and D are points on the circumference of a circle, centre O.
ADE and BCE are straight lines.
Diagram: A circle with centre O and points A, B, C and D on it. Lines AD and BC carry on outside the circle and meet at E. AB, OB, OD and CD are drawn. Angle BOD is 132° and angle AEB is 16°.
Work out the size of angle CDE.
Give a reason for each stage of your working.
(4 marks)
Question 21 (3 marks)
The graph of y = f(x) is shown on the grid below.
Diagram: A graph.
(a)
On the grid above, sketch the graph of y = f(-x)
(1 mark)
(b)
Here is a sketch of the graph of y = tan x°
Diagram: A sketch of y = tan x°, with dashed vertical asymptotes and the repeating tan curve between them. The point Q is where the curve crosses the x-axis, two branches to the right of O.
The graph of y = tan x° is translated to give the graph of y = g(x)
Following the translation the point Q, shown on the graph above, moves to point R.
Point R has coordinates (90, –5)
Find an expression for g(x) in terms of x.
(2 marks)
Question 22 (5 marks)
Find algebraically the set of values of x for which
x² – 49 > 0 and 5x² – 31x – 72 > 0
(5 marks)


pressure = dfracforcearea

	Sales (£000s)
least value	30
lower quartile	80
median	170
upper quartile	260
greatest value	350


Volume of sphere = 4/3π r³
Volume of cone = 1/3π r² h

Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.

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Edexcel GCSE Higher June 2022 Paper 2 (calculator)

Question 1 (5 marks)

Question 2 (2 marks)

Question 3 (2 marks)

Question 4 (5 marks)

Question 5 (4 marks)

Question 6 (3 marks)

Question 7 (4 marks)

Question 8 (2 marks)

Question 9 (3 marks)

Question 10 (5 marks)

Question 11 (3 marks)

Question 12 (2 marks)

Question 13 (2 marks)

Question 14 (3 marks)

Question 15 (4 marks)

Question 16 (6 marks)

Question 17 (5 marks)

Question 18 (4 marks)

Question 19 (4 marks)

Question 20 (4 marks)

Question 21 (3 marks)

Question 22 (5 marks)