Edexcel GCSE Higher November 2024 Paper 3 (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)
The table shows information about the times, in minutes, 100 people took to complete a
bike race.Time (t minutes) Frequency 120 ≤ t < 140 12 140 ≤ t < 160 28 160 ≤ t < 180 30 180 ≤ t < 200 22 200 ≤ t < 220 8 On the grid below, draw a frequency polygon for this information.
Diagram: A blank grid. Time (t minutes) from 120 to 220 across, frequency from 0 to 35 up.
(2 marks)
Question 2 (2 marks)
(a)
Write 3.402 × 10⁵ as an ordinary number.
(1 mark)
(b)
Write 0.8026 in standard form.
(1 mark)
Question 3 (2 marks)
Use ruler and compasses to construct the bisector of angle ABC.
You must show your construction lines.Diagram: Two straight lines BA and BC meeting at B, making the angle ABC.
(2 marks)
Question 4 (4 marks)
Dan is playing cards.
The probability that he will win a game of cards is 0.3
Dan plays two games of cards.
(a)
Complete the probability tree diagram.
Diagram: A probability tree diagram for Game 1 and Game 2. Game 1: wins (0.3) or does not win (a blank). After each, Game 2: wins or does not win, with a blank, a blank, a blank, a blank on the four branches.
(2 marks)
(b)
Work out the probability that Dan does not win either game.
(2 marks)
Question 5 (5 marks)
Robyn buys a total of 240 pens and pencils, where
number of pens : number of pencils = 3 : 5
Robyn pays 9p for each pen.
She sells each pen for 11p.Robyn pays 6p for each pencil.
She sells each pencil for 10p.Robyn sells all of the pens and pencils.
Work out Robyn’s percentage profit.
Give your answer correct to 1 decimal place.
You must show all your working.(5 marks)
Question 6 (4 marks)
The stem and leaf diagram shows the test scores of 23 students from School A.
Diagram: Stem and leaf diagram. Stem 3, leaves 0; Stem 4, leaves 1 2 4 4 5 7; Stem 5, leaves 3 4 4 6 7 8 8 9; Stem 6, leaves 0 8 8 9 9; Stem 7, leaves 1 3 9. Key: 3 | 0 represents 30.
23 students from School B did the same test.
Their median score was 56
The range of their scores was 47Compare the distribution of the test scores of the students from School A with the
distribution of the test scores of the students from School B.(4 marks)
Question 7 (2 marks)
Jana used her calculator to find the value of a number t.
The answer on her calculator began 10.2Complete the error interval for t.
……… ≤ t < ………
(2 marks)
Question 8 (2 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC. AB goes across the top, the right angle is at B, and BC is 7.6 cm, going straight down from B to C. The angle at C is 62°.
Calculate the length of AB.
Give your answer correct to 1 decimal place.(2 marks)
Question 9 (3 marks)
(a)
Simplify fully 2x³y⁵ × 7x²y
(2 marks)
(b)
Simplify (m²)⁻³
(1 mark)
Question 10 (2 marks)
In a sale, the normal prices are reduced by 15%
Amina buys a dress in the sale for £46.75Work out the normal price of the dress.
(2 marks)
Question 11 (3 marks)
OAB is a sector of a circle with centre O and radius 4.7 m.
Diagram: A sector OAB of a circle with centre O. The radius OA is 4.7 m. The sector is the large part of the circle: its angle at O is a reflex angle.
The sector has a perimeter of 34.3 m.
Find the size of the reflex angle AOB.
Give your answer correct to the nearest degree.(3 marks)
Question 12 (6 marks)
Rudi invests £4500 in a savings account.
He gets compound interest at a rate of2.4% for the first year
1.8% for each extra year.(a)
Work out the value of Rudi’s investment at the end of 3 years.
(3 marks)
(b)
Bruna buys a car for £7500
The value of the car depreciates by x% each year.
At the end of 2 years the value of the car is £4107Work out the value of x.
(3 marks)
Question 13 (3 marks)
ABC and AED are straight lines.
BE and CD are parallel.Diagram: Triangle ACD with B on AC and E on AD. BE is parallel to CD. Angle ABE and angle ACD are right angles.
BE = 4.2 cm
CD = 6.3 cm
AC = 10.8 cmWork out the area of trapezium BCDE.
(3 marks)
Question 14 (3 marks)
Prove algebraically that 0.46̇2̇ can be written as 229/495
(3 marks)
Question 15 (4 marks)
Make p the subject of the formula t = (2(2p – 3))/(5 – 2p)
(4 marks)
Question 16 (5 marks)
OBCD is a rectangle.
DCE is a straight line.Diagram: Axes x and y crossing at O. OBCD is a rectangle with O at the origin, B below the x-axis and to the right of the y-axis, D above the x-axis, and C just below the x-axis. The side DC carries on in a straight line down to E.
B has coordinates (2, –4)
E has coordinates (12, –6.5)Work out the coordinates of D.
You must show all your working.(5 marks)
Question 17 (4 marks)
Here is triangle ABC.
Diagram: Triangle ABC. AB is 14.6 cm, BC is 18.2 cm and CA is 7.9 cm. The angle at A is obtuse.
Work out the area of triangle ABC.
Give your answer correct to 3 significant figures.(4 marks)
Question 18 (4 marks)
Maria wants to find an estimate for the number of frogs in a lake.
On Saturday she catches 40 of the frogs.
She puts a tag on each frog and releases them.On Monday she catches 55 of the frogs.
11 of the frogs have tags.(a)
Work out an estimate for the total number of frogs in the lake.
You must show all your working.(3 marks)
(b)
State one assumption you have made.
(1 mark)
Question 19 (4 marks)
The diagram shows a cone.
Diagram: A cone standing on its circular base.
Curved surface area of cone = π rl
Diagram: A cone with its slant height l, its vertical height h and its base radius r marked.
The radius of the base of the cone is 3/4 of the height of the cone.
The total surface area of the cone is 54π cm²Work out the height of the cone.
(4 marks)
Question 20 (4 marks)
Solve the simultaneous equations
y² = 3x² + 4
y + 2x = 7Give your solutions correct to 3 significant figures.
(4 marks)
Question 21 (4 marks)
(a)
Here is the graph of y = f(x)
Diagram: A grid with x and y axes from –5 to 6, with no numbers. The graph of y = f(x) is made of straight lines: from (–3, 3) down to (–2, –2), up through O to (3, 3), then level at y = 3 to (6, 3).
On the grid, draw the graph of y = -f(x)
(1 mark)
(b)
Diagram: A sketch of y = sin x° with no scale. The curve starts at O, rises to a highest point, falls through the x-axis to a lowest point, marked P with a cross, and rises back to the x-axis.
Here is a sketch of the graph of y = sin x°
The point marked P is a turning point on the graph.
The graph of y = sin x° is translated to give the graph of y = sin (x + 180)° + 4
Following the translation the point P, shown on the graph above, moves to point R.Find the coordinates of R.
(3 marks)
Question 22 (3 marks)
Here is a velocity-time graph for an aeroplane.
Diagram: A velocity-time graph. Time is from 0 to 35 seconds and velocity from 0 to 100 m/s. The curve starts at 0, rises steeply to about 39 m/s at 5 seconds, then less steeply: 54 m/s at 10 seconds, 76 at 20, 92 at 30 and 96 at 35 seconds.
Work out an estimate for the distance the aeroplane travelled in the first 30 seconds.
Use 3 strips of equal width.(3 marks)
Question 23 (5 marks)
Sketch the graph of
y = x² – 6px – 7 where p > 0
showing the coordinates of the turning point, in terms of p, and the coordinates of the intercept with the y-axis.
You must show all your working.Diagram: A pair of axes, x and y, crossing at O. There is no scale.
(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.