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AQA GCSE Higher November 2024 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)
Work out the reciprocal of 10/3
Give your answer as a decimal.
(2 marks)
Question 2 (3 marks)
The table shows information about the number of houses with solar panels in a town.
Year 2017 2018 2019 2020 2021 2022 Number of houses 50 65 115 210 275 350 (a)
Diagram: A graph of the number of houses against the year, with a grid line every 10 houses. Crosses at 2017: 50, 2018: 65, 2019: 115, joined with straight lines.
Complete the graph.
(2 marks)
(b)
Use the graph to estimate the number of houses with solar panels in 2023
(1 mark)
Question 3 (4 marks)
A building in the shape of a cylinder has diameter 40 m and height 55 m
Diagram: A cylinder standing on one end: an arrow across the top marks the diameter, 40 m, and an arrow up the side marks the height, 55 m.
(a)
On the centimetre grid, draw a plan of the building. Use a scale of 1 cm to 10 m
Diagram: A centimetre grid, 8 squares by 8 squares.
(2 marks)
(b)
On this centimetre grid, draw the front elevation of the building. Use a scale of 1 cm to 10 m
Diagram: A centimetre grid, 8 squares by 8 squares.
(2 marks)
Question 4 (3 marks)
To the nearest pound, Rosie has £12
She wants to buy 6 drinks.
Each drink costs £1.89Show that Rosie definitely has enough money to buy the 6 drinks.
(3 marks)
Question 5 (2 marks)
The total cost of a taxi ride is calculated by adding
a fixed charge of £4
and
a charge of £2 per mile.Write a formula to work out the total cost, £C, of a journey of m miles.
(2 marks)
Question 6 (5 marks)
Three shops sell shirts.
Shop A Shop B Shop C Pack of 2
£19.00One shirt
Was £12.40
Now 25% offPack of 3
£37.40
Buy one pack,
get another pack
half priceAt which shop is it cheapest to buy 6 shirts?
Show working to support your answer.(5 marks)
Question 7 (4 marks)
(a)
At a school
there are 912 students
the ratio of students to teachers is 15.2 : 1The number of students stays the same.
The number of teachers increases by 2Work out the new ratio of students to teachers.
Give your answer in the form n : 1(3 marks)
(b)
On a school trip, one teacher is needed for every group of 10 or fewer students.
72 students want to go on the trip.Lexi tries to work out how many teachers are needed.
72 ÷ 10 = 7.2 7 teachers are needed. What is wrong with her answer?
(1 mark)
Question 8 (4 marks)
A triangle is drawn using the lines
y = x
x = -2
y = 4Diagram: A coordinate grid with x and y from –6 to 6.
Work out the coordinates of the three vertices of the triangle.
(4 marks)
Question 9 (2 marks)
When x is divided by 2 the remainder is 1
When x is divided by 3 the remainder is 1
When x is divided by 4 the remainder is 1Work out two possible values of x.
(2 marks)
Question 10 (3 marks)
A car will travel 60 miles.
Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours.
You may use the table to help you.
Time taken (hours) 1 2 3 4 5 6 Average speed (mph) 60 30 10 Diagram: A blank grid: time taken (hours) from 0 to 7 across, average speed (mph) from 0 to 65 up.
(3 marks)
Question 11 (2 marks)
Factorise fully 12t + 4t³
(2 marks)
Question 12 (4 marks)
The population of a country is now 67 200 000
The population is predicted toincrease by 1% per year for 6 years
and then
decrease by 1.2% per year for 2 years.Work out the predicted population of the country 8 years from now.
Give your answer to 3 significant figures.(4 marks)
Question 13 (2 marks)
A bag contains one £5 note, one £10 note, one £20 note and one £50 note.
Amaan picks two of the notes at random without replacement.Work out the probability that he has picked at least £30
(2 marks)
Question 14 (6 marks)
A test consists of two sections, A and B.
• 85% of people pass section A.
• 78% of people who pass section A also pass section B.
• 36% of people who fail section A also fail section B.(a)
Complete the tree diagram.
Diagram: Probability tree diagram: Section A then Section B.
(2 marks)
(b)
40% of people who fail at least one section take the test again. 5000 people take the test.
How many of these 5000 people are expected to take the test again?(4 marks)
Question 15 (3 marks)
Match each equation to a statement to show what happens when the value of x is doubled.
One has been done for you.
Diagram: Two columns of boxes. On the left, headed Equation, top to bottom: y = 1 over x², y = 8x, y = 10 over x, y = 3x². On the right, headed What happens when the value of x is doubled, top to bottom: The value of y is doubled; The value of y is divided by 4; It is not possible to say what happens to the value of y; The value of y is multiplied by 4; The value of y is halved. A line joins y = 1 over x² to "The value of y is divided by 4".
(3 marks)
Question 16 (3 marks)
Rearrange y = √((x/2 + 1)) to make x the subject.
(3 marks)
Question 17 (4 marks)
A stone falls vertically from 300 metres above ground.
• The stone falls d metres in t seconds.
• d is directly proportional to the square of t.
• The stone falls 20 metres in the first 2 seconds.Work out the total time taken for the stone to reach the ground.
(4 marks)
Question 18 (4 marks)
The table shows information about the height of 40 plants.
Height, h cm Frequency Class width 0 ≤ h < 5 6 5 ≤ h < 15 15 15 ≤ h < 25 9 25 ≤ h < 50 10 Draw a histogram to represent the heights.
Diagram: A blank grid: height, h cm, from 0 to 60 across, frequency density up with no scale.
(4 marks)
Question 19 (3 marks)
Diagram: A triangle with a 54 cm side along the bottom. The angle at the bottom left is 35° and the angle at the top is 117°. The side x runs from the top down to the bottom right, opposite the 35° angle.
Use the sine rule to work out length x.
You must show your working.(3 marks)
Question 20 (2 marks)
Factorise fully 3x² + 23x + 30
(2 marks)
Question 21 (3 marks)
A bag contains 25 discs.
11 are red, 9 are blue and 5 are yellow.Ashley picks three of the discs at random without replacement.
Ashley’s first disc is red.Work out the probability that all three discs are different colours.
(3 marks)
Question 22 (4 marks)
The metal used to make a sphere costs £4320
The metal costs £3.60 per gram.
Each cubic centimetre of metal has a mass of 17.3 grams.Work out the radius, r, of the sphere.
Volume of a sphere = 4/3π r³ (4 marks)
Question 23 (3 marks)
The distance of a particle from a point is d metres after t seconds.
d = a × b^t where a and b are constantsDiagram: A graph of d against t. t goes from 0 to 4 across and d from 0 to 55 up. The curve starts at (0, 3) and rises more and more steeply through (1, 6), (2, 12) and (3, 24) to (4, 48).
Work out the values of a and b.
(3 marks)
Question 24 (5 marks)
A curve has the equation y = x² + 4x – 4
A straight line has the equation y = 3x – 2Work out the two points of intersection of the curve and the straight line.
(5 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.