Edexcel GCSE Higher November 2023 Paper 3 (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 (2 marks)
(a)
Write 468 000 in standard form.
(1 mark)
(b)
Write 5.037 × 10⁻⁴ as an ordinary number.
(1 mark)
Question 2 (2 marks)
Here is a biased spinner.
Diagram: A spinner shaped like a parallelogram, split by its diagonals into four triangles labelled D, C, B, A, with a pointer at the centre.
The table shows the probabilities that when the spinner is spun it will land on A, on B,
on C and on D.Letter Probability A 0.4 B 0.21 C 0.32 D 0.07 Luka will spin the spinner 200 times.
Work out an estimate for the number of times the spinner will land on A.
(2 marks)
Question 3 (4 marks)
Seija works at a weather station.
The table gives information about the temperature, T °C, at midday for each of 50 cities
in the UK on Tuesday.Temperature (T °C) Frequency 10 < T ≤ 15 2 15 < T ≤ 20 8 20 < T ≤ 25 13 25 < T ≤ 30 21 30 < T ≤ 35 6 (a)
Calculate an estimate for the mean temperature.
(3 marks)
(b)
Seija says,
“The median temperature is 22.5 °C because 22.5 is the middle number in the
middle group.”Is Seija correct?
Give a reason for your answer.(1 mark)
Question 4 (4 marks)
(a)
Jenna is asked to show the inequality -3 < x ≤ 4 on a number line.
Here is her answer.
Diagram: A number line for x from -5 to 5, with an open circle at -2, an open circle at 4 and a line between them, drawn just above the number line.
Write down two mistakes Jenna has made.
(2 marks)
(b)
Work out the greatest integer that satisfies the inequality
5y – 7 < 16
(2 marks)
Question 5 (3 marks)
Ali buys packs of balloons and boxes of pencils.
There are 30 balloons in each pack.
There are 24 pencils in each box.Ali buys exactly the same number of balloons and pencils.
Work out how many packs of balloons and how many boxes of pencils she could
have bought.
You must show all your working.(3 marks)
Question 6 (2 marks)
A company orders a large number of plates from a factory.
It would take 30 hours to make all the plates using 4 machines.
How many machines are needed to make all the plates in 6 hours?
(2 marks)
Question 7 (3 marks)
Riley travelled by car and by aeroplane.
He travelled 143 miles by car at an average speed of 55 miles per hour.
Riley then travelled for 5 hours and 20 minutes by aeroplane.Work out, in hours and minutes, Riley’s total travelling time.
(3 marks)
Question 8 (3 marks)
The diagram shows a solid cube placed on a horizontal table.
Diagram: A solid cube, with its hidden edges dashed.
pressure = dfracforcearea The pressure on the table due to the cube is 3.5 newtons/cm²
The force exerted by the cube on the table is 504 newtons.Show that the total surface area of the cube is less than 900 cm²
(3 marks)
Question 9 (3 marks)
The line L is shown on the grid.
Diagram: A straight line L on a grid, x from –2 to 4 and y from –3 to 5. It goes from (–1, 5) down to (3, –3), crossing the y-axis at 3.
Find an equation for L.
(3 marks)
Question 10 (3 marks)
Make m the subject of k = p + 2m/5
(3 marks)
Question 11 (3 marks)
The floor plan of a house is drawn using a scale of 1 : 50
On the plan, a room in the house has a floor area of 48 cm²Work out the real area of the floor of this room.
Give your answer in m²(3 marks)
Question 12 (2 marks)
The diagram shows a shaded sector POQ of a circle with centre O and radius 6.2 cm.
Diagram: A shaded sector POQ of a circle with centre O and radius 6.2 cm. The sector is the major sector, above the radii OP and OQ, and its reflex angle at O is marked x.
The area of the shaded sector is 82.6 cm²
Calculate the size of angle x.
Give your answer correct to 3 significant figures.(2 marks)
Question 13 (6 marks)
Alan grew 80 plants of the same type outside.
The cumulative frequency graph shows information about the heights, in cm, of these plants.Diagram: A cumulative frequency graph for the heights of 80 plants. The S-shaped curve starts at (0, 0), passes through about (25, 10), (40, 20), (50, 29), (60, 40), (75, 60), (90, 74) and (100, 77), and ends at (125, 80).
One of the plants is chosen at random.
(a)
Find an estimate for the probability that this plant will have a height greater than 90 cm.
(2 marks)
(b)
Use the graph to find an estimate for the median height.
(1 mark)
(c)
Use the graph to find an estimate for the interquartile range of the heights.
(2 marks)
(d)
Alan also grew plants of the same type inside.
The interquartile range of the heights of these plants is 30 cm.Give one comparison between the distribution of the heights of the plants grown inside with the distribution of the heights of the plants grown outside.
(1 mark)
Question 14 (2 marks)
Here are the first six terms of a quadratic sequence.
5 11 21 35 53 75
Find an expression, in terms of n, for the nth term of this sequence.
(2 marks)
Question 15 (2 marks)
The diagram shows triangle ABC and triangle AED.
Diagram: Triangle ABC with D on AB and E on AC, and the line DE drawn. AD = 32 cm, DB = 22 cm, AE = 21.6 cm and EC = 58.4 cm.
Show that triangle ABC and triangle AED are similar.
(2 marks)
Question 16 (3 marks)
Zia has to set a 4-digit security passcode on her phone.
Each digit of the passcode is a number from 1 to 9
She can use each number more than once.Zia tells her friend Amber that
the first digit is a cube number
the second digit is a prime number
the third digit is greater than 6
the fourth digit is an odd number.The diagram shows one possible 4-digit passcode.
Diagram: A passcode shown as four digits, each in its own circle: 1, 3, 8, 3.
Amber is going to have one attempt at guessing Zia’s passcode.
Work out the probability that Amber guesses Zia’s passcode on the first attempt.
(3 marks)
Question 17 (7 marks)
(a)(i)
Write x² – 8x + 3 in the form (x – a)² – b where a and b are integers.
(2 marks)
(ii)
Hence, write down the coordinates of the turning point on the graph of y = x² – 8x + 3
(1 mark)
(b)
Solve 7x² + 8x – 5 = 0
Give your solutions correct to 3 significant figures.(3 marks)
(c)
Alex has to find the solutions of the quadratic equation 3k² + 10k – 8 = 0
Here is his working and answer.
(3k – 2)(k + 4) = 0
k = 2 or k = -4What mistake has Alex made?
(1 mark)
Question 18 (3 marks)
Diagram: Triangle P on a grid, with corners at (–8, 1), (–8, 5) and (–6, 1).
(a)
Enlarge triangle P by scale factor -11/2 with centre of enlargement (–2, –1)
Label your image Q.(2 marks)
(b)
Triangle P is transformed by a combined transformation of a rotation of 90° anticlockwise about the origin followed by a translation to give triangle R.
Exactly one vertex of triangle P is invariant under the combined transformation.
Find one possible column vector for the translation.
(1 mark)
Question 19 (4 marks)
Diagram: A frustum F: a cone, point down, with its top part kept. The top circle has diameter 24 cm and the frustum is 5 cm deep. Below it, the removed small cone is drawn dashed down to the point.
Volume of sphere = 4/3π r³ Volume of cone = 1/3π r² h
The diagram above shows a frustum F of a cone.
The frustum is made by removing a cone with height 10 cm from a solid cone with height 15 cm and base diameter 24 cm.The solid S is made by removing F from a solid hemisphere as shown in the diagram below.
Diagram: A hemisphere, flat face up, with diameter 24 cm. The frustum F is cut out of its flat face, shown dashed, 5 cm deep.
The hemisphere has diameter 24 cm.
Calculate the volume of solid S.
Give your answer correct to 3 significant figures.(4 marks)
Question 20 (3 marks)
The turning point on the graph of y = g(x) has coordinates (–3, 6)
(a)
Write down the coordinates of the turning point on the graph of y = g(x – 7)
(1 mark)
(b)
The graph of y = f(x) is shown on the grid.
Diagram: The graph of y = f(x): an upside-down U-shaped curve with its highest point at (–2, 3), crossing the y-axis at 2, with its ends at (–6, –7) and (2, –7).
On the grid, sketch the graph of y = f(-x) + 3
(2 marks)
Question 21 (4 marks)
Diagram: A circle with centre O and points A, B, C and D on it. AC is a diameter. The line from A through D carries on outside the circle to E, and the line from B through C also carries on to E. BD and CD are drawn. Angle DAC is 35° and angle AEB is 28°.
A, B, C and D are points on the circumference of a circle, centre O.
AC is a diameter of the circle.ADE and BCE are straight lines.
Work out the size of angle BDC.
Write down any circle theorems that you use.(4 marks)
Question 22 (4 marks)
Ebony makes some bracelets to sell.
The materials to make all the bracelets cost £190, correct to the nearest £5
Ebony sells all the bracelets for a total of £875, correct to the nearest £5
The total time taken to make and sell all these bracelets was 72 hours, correct to the nearest hour.Ebony uses this method to calculate her hourly rate of pay
Hourly rate of pay = (total selling price – total cost of materials) ÷ total time taken
The minimum hourly rate of pay for someone of Ebony’s age is £8.20
By considering bounds, determine if Ebony’s hourly rate of pay was definitely more than £8.20
You must show all your working.(4 marks)
Question 23 (4 marks)
Given that (2x² + y²)/(4x² – y²) = 43/11 where x > 0 and y > 0
find, in its simplest form, the ratio x : y
(4 marks)
Question 24 (4 marks)
The diagram shows a triangular prism with a horizontal rectangular base ABCD.
Diagram: A triangular prism lying on its rectangular base ABCD. A is at the front, B to the right, C at the back right and D to the left. M is the midpoint of AD and T, the top of the triangular end above AD, is directly above M. The hidden edges DC, CB and TM are dashed.
M is the midpoint of AD.
The vertex T of the prism is vertically above M.AB = 14.7 cm BC = 3.8 cm MT = 2.3 cm
P is the point on AB such that
AP : PB = 5 : 2
Calculate the size of the angle between TP and the base ABCD of the prism.
Give your answer correct to 1 decimal place.(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.