Edexcel - Foundation
Ratio, proportion and rates of change
2022 GCSE Advance Information
Sparx Topics & Key Questions
We are always looking for ways to support maths teachers and students. In
order to help you and your year 11s this year we’ve pulled together a list of key
questions which may be useful to practise with your students based on the exam
board topic lists.
These 66 key questions are all taken from our library of over 45,000 high-quality
questions in Sparx Maths. If you are a Sparx Maths School then your students
can use the Topic Codes provided to search the full content library directly within
the independent learning section of Sparx Maths to help target their revision.
Please note this is not an exhaustive topic guide it is simply designed to help
you pull together some key questions to use to check for understanding in
lessons, starters, or as worksheets with your learners.
sparxmaths.com
Edexcel - Foundation
Ratio, proportion, and rates of Sparx Topic
Topics
change Codes
U388, U902,
Conversion Length, mass, time, area
U248
Compound units U151, U256
Scale drawing U257
Percentages Percentage to fraction U888
Decimal to percentage U888
Percentage of an amount U554
Percentage increase/decrease U773, U278, U671
Percentage profit U671, U278
One quantity as a percentage of
U349
another
Depreciation U988
Reverse percentage U286
Ratio Write as a ratio U687
Share in a ratio U577
Use of ratio U753, U176, U577
1:n form U687
Proportion Direct proportion U721, U640, U238
Compound Measures Speed U151
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Edexcel - Foundation
Ratio, proportion, and rates of change Topics Sparx Topic Codes
Compound Measures Average speed U151, U462
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Edexcel - Foundation (back to topics)
Conversion - Length, mass, time, area
Converting units of length, mass and capacity U388
Decide which of the given units would be the most appropriate to use for
a) the height of a building: kilometres, metres or centimetres?
b) the mass of a pencil: grams, tonnes or kilograms?
c) the capacity of a bathtub: millilitres or litres?
Convert 3060 millimetres (mm) into
a) centimetres (cm)
b) metres (m)
Reading, converting and calculating with time U902
What time is 5 hours and 42 minutes before 4.06 pm?
Give your answer using the 12 hour clock.
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Edexcel - Foundation (back to topics)
Calum`s calendar is shown below.
How many days after his first exam is his last exam?
Jessica is meeting a friend at 17:00 at Summer Park.
To get there, she will catch a bus from Upper Bridge, which is a 10 minute walk from her
home.
What is the latest time she can leave home to get there on time?
Fully convert 26 days into weeks and days.
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Edexcel - Foundation (back to topics)
A magic show starts at 17:11 and lasts for 156 minutes.
When does the show end?
Give your answer using the 24 hour clock.
Converting units of area U248
What is 6.3 mm2 in cm2 ?
An environmental charity set a target to plant trees on 9000 m2 of land in July.
2
In July, it planted trees on 0.014 km of land.
a) What area of land did the charity plant trees on? Give your answer in m2 .
b) Did it reach its target?
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Edexcel - Foundation (back to topics)
Conversion - Compound units
Calculating with speed U151
It takes a bus 1 hour and 30 minutes to travel 36 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
Calculating with rates U256
A goat has a heart rate of 80 beats per minute (bpm).
How long would it take for the goat`s heart to beat 10,000 times?
Give your answer in hours and minutes.
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Edexcel - Foundation (back to topics)
Conversion - Scale drawing
Drawing and interpreting scale diagrams U257
In the scale drawing below, 1 cm represents 2 m.
a) What is the width, in metres, of the building in real life?
b) The real building is 4.6 m tall. What is the height of the drawing of the building, in
centimetres?
The scale on a map is 1 : 200,000.
The length of a road on the map is 4 cm.
What is the length of the road in real life?
Give your answer in kilometres.
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Edexcel - Foundation (back to topics)
Percentages - Percentage to fraction
Converting between fractions, decimals and percentages U888
64
What is 200written as a decimal?
What is 132% written as a decimal?
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Edexcel - Foundation (back to topics)
Two new films, "Infinite Tracks" and "Paper Trains", were reviewed by four different
magazines. The scores that each magazine gave each film are shown in the table below.
What score did "Earth Publications" give "Paper Trains"?
Give your answer as a percentage.
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Edexcel - Foundation (back to topics)
Percentages - Decimal to percentage
Converting between fractions, decimals and percentages U888
64
What is 200written as a decimal?
What is 132% written as a decimal?
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Edexcel - Foundation (back to topics)
Two new films, "Infinite Tracks" and "Paper Trains", were reviewed by four different
magazines. The scores that each magazine gave each film are shown in the table below.
What score did "Earth Publications" give "Paper Trains"?
Give your answer as a percentage.
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Edexcel - Foundation (back to topics)
Percentages - Percentage of an amount
Finding percentages of amounts without a calculator U554
Toby is driving 586 miles from Exeter to Aberdeen. How many miles has he travelled if he
has completed 10% of his journey?
Calculate 6% of 5100
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Edexcel - Foundation (back to topics)
The table below shows the number of visitors to a theme park on each day last week.
70% of the visitors on Friday were children. How many children visited the theme park on
Friday?
What is 121% of 300?
What is 41% of 70 km?
Give your answer in kilometres (km).
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Edexcel - Foundation (back to topics)
Percentages - Percentage increase/decrease
Percentage change without a calculator U773
The table below shows the amount that Louise paid in rent in different years.
Between 2014 and 2015, the amount of rent she paid increased by 30%.
How much rent did she pay in 2015?
Give your answer in pounds (£).
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Edexcel - Foundation (back to topics)
The table below shows how many drinks of different types a cafe sold yesterday.
The cafe sold 60% fewer lemonades today than it did yesterday.
How many lemonades did the cafe sell today?
Finding the percentage an amount has been changed by U278
If 130 increases to 182, what percentage increase is this?
Copy and complete the sentence below.
510 kg is % less than 750 kg.
Edexcel - Foundation (back to topics)
Percentage change with a calculator U671
The number of drinks sold by a cafe on Saturday was 37% more than the number sold on
Friday.
The cafe sold 500 drinks on Friday.
How many drinks did the cafe sell on Saturday?
What value is 67.4% larger than 260?
The price of a necklace is reduced by 8.5% in a sale. The original price of the necklace was
£54.
Work out the sale price of the necklace.
Give your answer in pounds (£).
Increase £59 by 7%
Give your answer in pounds (£).
C i ht S 2022 th
Edexcel - Foundation (back to topics)
Decrease £67 by 26%
Give your answer in pounds (£).
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Edexcel - Foundation (back to topics)
Percentages - Percentage profit
Percentage change with a calculator U671
The number of drinks sold by a cafe on Saturday was 37% more than the number sold on
Friday.
The cafe sold 500 drinks on Friday.
How many drinks did the cafe sell on Saturday?
What value is 67.4% larger than 260?
The price of a necklace is reduced by 8.5% in a sale. The original price of the necklace was
£54.
Work out the sale price of the necklace.
Give your answer in pounds (£).
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Edexcel - Foundation (back to topics)
Increase £59 by 7%
Give your answer in pounds (£).
Decrease £67 by 26%
Give your answer in pounds (£).
Finding the percentage an amount has been changed by U278
If 130 increases to 182, what percentage increase is this?
Copy and complete the sentence below.
510 kg is % less than 750 kg.
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Edexcel - Foundation (back to topics)
Percentages - One quantity as a percentage of another
Finding percentages of amounts with a calculator U349
A computer costs £968. A tax of 16.5% is then added to the cost of the computer.
Work out the amount of tax that is added to the cost of the computer.
Give your answer in pounds (£).
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Edexcel - Foundation (back to topics)
Percentages - Depreciation
Growth and decay U988
At the end of 2010, a music website had 100,000 users.
The number of users grew at a rate of 40% per year until the end of 2015.
How many more users joined the website between the end of 2012 and the end of 2015?
The town of Arbridge currently has a population of 300,000.
Each year, the population of Arbridge will reduce by 7%.
How many fewer people will live in Arbridge in 5 years compared with now?
Give your answer to 3 s.f.
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Edexcel - Foundation (back to topics)
Percentages - Reverse percentage
Finding original values in percentage calculations U286
135% of a value is 5265 kg.
What is the original value?
Give your answer in kilograms (kg).
During a javelin throwing competition, Shannon achieves a new personal best distance by
throwing the javelin 89.64 m. This is an increase of 8% from her previous personal best
distance.
Work out Shannon`s previous personal best distance.
Give your answer in metres (m).
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Edexcel - Foundation (back to topics)
The price of a book set has been reduced by 35%.
The new price is £49.40.
What was the original price of the book set? Give your answer in pounds (£).
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Edexcel - Foundation (back to topics)
Ratio - Write as a ratio
Writing and simplifying ratios U687
A garden contains 51 flowers.
18 of the flowers are sunflowers, 21 are petunias and the rest are lilies.
What is the ratio of sunflowers to petunias to lilies in its simplest form?
On a given day, a greengrocer sold 81 oranges and 43 melons.
Write the ratio of oranges to melons in the form 1 : n.
Give any decimals in your answer to 2 d.p.
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Edexcel - Foundation (back to topics)
Ratio - Share in a ratio
Sharing amounts in a given ratio U577
Dry concrete can be made by mixing sand, gravel and cement in the ratio 1 : 3 : 4. If you
want 1600 kg of dry concrete, how much of each will you need? Give your answers in
kilograms (kg).
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Edexcel - Foundation (back to topics)
Ratio - Use of ratio
Using equivalent ratios to find unknown amounts U753
There are 15 leeches in this pond.
How many toads are there?
Converting between ratios, fractions and percentages U176
3
8 of the animals in a pet shop are rabbits. What is the ratio of rabbits to other animals in the
pet shop in its simplest form?
Beau and Esha shared a whole pizza. They shared the pizza in the ratio 7 : 13. What
percentage of the pizza did Beau eat?
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Edexcel - Foundation (back to topics)
Sharing amounts in a given ratio U577
Dry concrete can be made by mixing sand, gravel and cement in the ratio 1 : 3 : 4. If you
want 1600 kg of dry concrete, how much of each will you need? Give your answers in
kilograms (kg).
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Edexcel - Foundation (back to topics)
Ratio - 1:n form
Writing and simplifying ratios U687
A garden contains 51 flowers.
18 of the flowers are sunflowers, 21 are petunias and the rest are lilies.
What is the ratio of sunflowers to petunias to lilies in its simplest form?
On a given day, a greengrocer sold 81 oranges and 43 melons.
Write the ratio of oranges to melons in the form 1 : n.
Give any decimals in your answer to 2 d.p.
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Edexcel - Foundation (back to topics)
Proportion - Direct proportion
Solving direct proportion word problems U721
A carton of apple juice displays the nutritional information shown below.
How many grams of sugar are there in a 200 ml glass of juice?
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Edexcel - Foundation (back to topics)
Lois and Alexander bought petrol from different petrol stations.
a) Was Lois`s petrol or Alexander`s petrol better value for money?
b) How much would 30 litres of petrol cost from the cheaper petrol station?
Give your answer in pounds (£).
Finn is stacking identical cube-shaped boxes. He stacks 7 boxes to make a tower that is
112 cm tall. He adds 1 more box to the tower. How tall is the tower now? Give your answer
in centimetres (cm).
Interpreting direct proportion equations U640
The number of minutes, n, that it takes to paint a wall is directly proportional to the area, a,
of the wall in m2 .
The equation of proportionality is n = 3a.
Work out the area of a wall that takes 24 minutes to paint.
If your answer is a decimal, give it to 1 d.p.
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Edexcel - Foundation (back to topics)
r and t are in direct proportion.
The equation of proportionality is r = 12t.
If t increases from 3 to 5, how much will r increase by?
If your answer is a decimal, give it to 1 d.p.
Graphs of direct and inverse proportion U238
y∝x
Which of the graphs below shows this relationship?
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Edexcel - Foundation (back to topics)
y is inversely proportional to x.
Which of the graphs below shows this relationship?
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Edexcel - Foundation (back to topics)
Compound Measures - Speed
Calculating with speed U151
It takes a bus 1 hour and 30 minutes to travel 36 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
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Edexcel - Foundation (back to topics)
Compound Measures - Average speed
Calculating with speed U151
It takes a bus 1 hour and 30 minutes to travel 36 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
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Edexcel - Foundation (back to topics)
Calculating speed from distance-time graphs U462
This distance-time graph shows part of the journey of a train.
Calculate the speed of the train.
Give your answer in metres per second (m/s) and give any decimal answers to 1 d.p.
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Edexcel - Foundation (back to topics)
This distance‑time graph shows part of the journey of a bee travelling away from its hive.
Calculate the average speed of the bee for this part of the journey.
If your answer is a decimal, give it to 1 d.p.
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