Edexcel GCSE Higher November 2022 Paper 2 (calculator)

24 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)
The scatter graph shows information about the amount of rainfall, in mm, and the number of hours of sunshine for each of ten English towns on the same day.
Diagram: A scatter graph of the number of hours of sunshine against the amount of rainfall (mm) for ten towns. Most crosses go down from top left to bottom right; one cross, at (2, 1), is well below the others.
One of the points is an outlier.
(a)
Write down the coordinates of this point.
(1 mark)
(b)
Ignoring the outlier, describe the relationship between the amount of rainfall and the number of hours of sunshine.
(1 mark)
(c)
On the same day in another English town there were 7 hours of sunshine.
Using the scatter graph, estimate the amount of rainfall in this town on this day.
(2 marks)
Question 2 (2 marks)
The front elevation and the plan of a solid are shown on the grid.
On the grid, draw the side elevation of the solid from the direction of the arrow.
Diagram: A centimetre grid. The front elevation is 7 squares wide: its left edge is 5 squares high, the top slopes down to 2 squares high 4 squares along, steps up to 3, then slopes down to 1 square high at the right edge. Under it, the plan is a 7 by 3 rectangle with a line across it 4 squares from the left. An arrow on the right points left at the front elevation.
(2 marks)
Question 3 (4 marks)
Here are the first five terms of an arithmetic sequence.
7 13 19 25 31
(a)
Find an expression, in terms of n, for the nth term of this sequence.
(2 marks)
(b)
The nth term of a different sequence is 8 – 6n
Is -58 a term of this sequence?
You must show how you get your answer.
(2 marks)
Question 4 (5 marks)
The diagram shows a plan of Jason’s garden.
ABCO and DEFO are rectangles.
CDO is a right-angled triangle.
AFO is a sector of a circle with centre O and angle AOF = 90°
Diagram: Jason’s garden: rectangle ABCO at the top right, 11 m by 7 m; rectangle DEFO at the bottom left, 7 m by 9 m; right-angled triangle CDO between them; and a quarter circle AFO at the top left, centre O.
Jason is going to cover his garden with grass seed.
Each bag of grass seed covers 14 m² of garden.
Each bag of grass seed costs £10.95
Work out how much it will cost Jason to buy all the bags of grass seed he needs.
(5 marks)
Question 5 (2 marks)
Diagram: A right-angled triangle with the right angle at the top right. The hypotenuse is 14.5 cm. The angle at the bottom vertex is 53°. The vertical side, between the right angle and the 53° angle, is x cm.
Work out the value of x.
Give your answer correct to 3 significant figures.
(2 marks)
Question 6 (3 marks)
Ella invests £7000 for 2 years in an account paying compound interest.
In the first year, the rate of interest is 3%
In the second year, the rate of interest is 1.5%
Work out the value of Ella’s investment at the end of 2 years.
(3 marks)
Question 7 (4 marks)
Here is the graph of y = x² – 6x + 4
Diagram: The graph of y = x squared minus 6x plus 4, for x from –1 to 7: a U-shaped curve crossing the y-axis at 4, with its lowest point at (3, –5).
(a)
Write down the y intercept of the graph of y = x² – 6x + 4
(1 mark)
(b)
Write down the coordinates of the turning point of the graph of y = x² – 6x + 4
(1 mark)
(c)
Use the graph to find estimates for the roots of x² – 6x + 4 = 0
(2 marks)
Question 8 (3 marks)
Chanda buys a necklace for £120
She sells the necklace for £135
Work out her percentage profit.
(3 marks)
Question 9 (2 marks)
Here are the equations of two straight lines.
y = 1/2x – 6 6y = 3x + 7
Oscar says that these lines are parallel.
Is Oscar correct?
You must give a reason for your answer.
(2 marks)
Question 10 (3 marks)
Aaliyah bought a car.
In the first year after she bought the car, its value depreciated at a rate of 23% per annum.
In the second year after she bought the car, its value depreciated at a rate of 19% per annum.
At the end of the second year the car was worth £10 914.75
What was the value of the car when Aaliyah bought it?
(3 marks)
Question 11 (3 marks)
In an experiment, 60 students each completed a puzzle.
The cumulative frequency graph shows information about the times taken for the 60 students to complete the puzzle.
Diagram: A cumulative frequency graph for the times of 60 students. The S-shaped curve starts at (20, 0), passes through about (30, 4), (40, 13), (50, 25), (60, 39), (70, 51) and (80, 57), and ends at (100, 60).
For these 60 students,
the least time taken was 24 seconds
the greatest time taken was 96 seconds.
On the grid below, draw a box plot for the distribution of the times taken by the students.
Diagram: An empty grid for a box plot, with a time scale from 0 to 100 seconds.
(3 marks)
Question 12 (3 marks)
The number of insects in a population at the start of year n is P_n
The number of insects in the population at the start of year (n + 1) is P_n + 1 where
P_n + 1 = kP_n
Given that k has a constant value of 1.13
(a)
find out how many years it takes for the number of insects in the population to double.
You must show how you get your answer.
(2 marks)
(b)
The value of k actually increases year on year from its value of 1.13 in year 1
How does this affect your answer to part (a)?
(1 mark)
Question 13 (2 marks)
A and B are points on a centimetre grid.
A is the point with coordinates (–7, 6)
B is the point with coordinates (8, –5)
Work out the length of AB.
Give your answer correct to 1 decimal place.
(2 marks)
Question 14 (3 marks)
Using algebra, prove that 1.062̇ can be written as 114/225
(3 marks)
Question 15 (4 marks)
Faiza is studying the population of rabbits in a park.
She wants to estimate the number of rabbits in the park.
On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park.
On Tuesday she catches a random sample of 42 rabbits in the park.
12 of the rabbits are marked with a tag.
(a)
Find an estimate for the number of rabbits in the park.
(3 marks)
(b)
Albie is studying the population of rabbits in a wood.
One day, he catches 55 rabbits and finds that 40 of these rabbits are marked with a tag.
Albie estimates there are 50 rabbits in the wood.
Explain why Albie’s estimate cannot be correct.
(1 mark)
Question 16 (4 marks)
The shaded region shown on the grid is bounded by four straight lines.
Diagram: A grid from –7 to 7 on both axes with four straight lines: y = 6 (horizontal), x = –3 (vertical), a steep line through (–2, 0) and (0, 6), and a line sloping down through (0, 1) and (2, 0). The shaded region has corners at about (–3, 6), (0, 6), (–1.4, 1.7) and (–3, 2.5).
Find the four inequalities that define the shaded region.
(4 marks)
Question 17 (4 marks)
The diagram shows two similar solid triangular prisms, A and B.
Diagram: Two similar triangular prisms. Each cross section is a right-angled triangle with its right angle at the bottom left. Prism A is small, with the height of its triangle marked h cm. Prism B is three times as long in every direction, with the base of its triangle marked 8.1 cm and the area of the triangle marked 43.74 cm².
The volume of prism A is 58.806 cm³
The volume of prism B is 1587.762 cm³
The cross section of each prism is a right-angled triangle.
For prism B
the length of the base of the triangle is 8.1 cm
the area of the triangle is 43.74 cm²
The height of the triangle for prism A is h cm.
Work out the value of h.
(4 marks)
Question 18 (2 marks)
Here is a triangle.
Diagram: A triangle with sides of 11.2 cm and 4.3 cm meeting at an angle of 118°.
Work out the area of the triangle.
Give your answer correct to 3 significant figures.
(2 marks)
Question 19 (3 marks)
Solve 6x² + 5x – 6 = 0
(3 marks)
Question 20 (4 marks)
ABCDEFGH is a cuboid.
Diagram: A cuboid ABCDEFGH. ADEF is the front face, with A top left, D top right, E bottom right and F bottom left. B, C, H and G are behind A, D, E and F. The edges FG, GH and BG are hidden (dashed).
AD = 9 cm
FD = 13 cm
Angle GHF = 49°
Work out the size of angle FAH.
Give your answer correct to the nearest degree.
(4 marks)
Question 21 (4 marks)
The graph below gives the volume, in litres, of water in a container t seconds after the water starts to fill the container.
Diagram: A curve starting at the origin and getting steeper: about 2.3 litres at 5 seconds, 4.8 at 10, 8.2 at 15, 13.6 at 20 and 22.8 at 25 seconds.
(a)
Calculate an estimate for the gradient of the graph when t = 17.5
You must show how you get your answer.
(3 marks)
(b)
Describe fully what the gradient in part (a) represents.
(1 mark)
Question 22 (3 marks)
f(x) = 3√(x)
g(x) = 2x + 3
h(x) = fg(x)
Find h⁻¹(x)
(3 marks)
Question 23 (5 marks)
A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km.
Sam runs the race in a time of 31 minutes 48 seconds, correct to the nearest second.
Sam’s average speed in this race is V km/hour.
By considering bounds, calculate the value of V to a suitable degree of accuracy.
You must show all your working and give a reason for your answer.
(5 marks)
Question 24 (4 marks)
A circle has equation x² + y² = 12.25
The point P lies on the circle.
The coordinates of P are (2.1, 2.8)
The line L is the tangent to the circle at point P.
Find an equation of L.
Give your answer in the form ax + by = c, where a, b and c are integers.
(4 marks)

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 November 2022 Paper 2 (calculator)

Question 1 (4 marks)

Question 2 (2 marks)

Question 3 (4 marks)

Question 4 (5 marks)

Question 5 (2 marks)

Question 6 (3 marks)

Question 7 (4 marks)

Question 8 (3 marks)

Question 9 (2 marks)

Question 10 (3 marks)

Question 11 (3 marks)

Question 12 (3 marks)

Question 13 (2 marks)

Question 14 (3 marks)

Question 15 (4 marks)

Question 16 (4 marks)

Question 17 (4 marks)

Question 18 (2 marks)

Question 19 (3 marks)

Question 20 (4 marks)

Question 21 (4 marks)

Question 22 (3 marks)

Question 23 (5 marks)

Question 24 (4 marks)