Here is a list of ingredients for making 18 scones.

Farah wants to make 45 scones.
How much of each ingredient will Farah need?
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Exam code: 1MA1
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Here is a list of ingredients for making 18 scones.

Farah wants to make 45 scones.
How much of each ingredient will Farah need?
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The two numbers, P and Q, are shown on a scale.

The difference between P and Q is 35.
Work out the value of P and the value of Q.
P = ...........................
Q = ...........................
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These graphs show four different proportionality relationships between and

Match each graph with a statement in the table below.
Proportionality relationship | Graph letter |
|---|---|
| |
| |
| |
|
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A cake contains 30 grams of sugar in every 100 grams.
A whole cake has a weight of 800 g.
It is cut into 12 equal slices.
Work out the amount of sugar in each slice.
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Yesterday it took cleaners
hours to clean all the rooms in a hotel.
There are only cleaners to clean all the rooms in the hotel today.
Each cleaner is paid £ for each hour or part of an hour they work.
How much will each cleaner be paid today?
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is inversely proportional to
.
When
Find the value of when
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is inversely proportional to
When
Find the value of when
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is inversely proportional to
When
Find the value of when
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At a depth of metres, the temperature of the water in an ocean is
. At depths below
metres,
is inversely proportional to
.
is given by
Work out the difference in the temperature of the water at a depth of metres and the temperature of the water at a depth of
metres.
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Here are four graphs.

One of the graphs could show that is inversely proportional to
.
Choose the letter corresponding to this graph.
Choose your answer
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is directly proportional to the cube of
when
Find a formula for in terms of
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Work out the value of when
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is inversely proportional to
.
Complete the table.
12 | 6 |
| |
| 4 | 8 |
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The diagrams show the position of a tap when off and fully on.
The tap is fully on when the angle of turn is °

When fully on, water flows out of the tap at litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned
°

The water flows into a tank with a capacity of litres. Will it take less than
minutes to fill the tank?
You must show your working.
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To complete a task in 15 days a company needs
4 people each working for 8 hours per day.
The company decides to have
5 people each working for 6 hours per day.
Assume that each person works at the same rate.
How many days will the task take to complete? You must show your working.
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Comment on how the assumption affects your answer to part (a).
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is directly proportional to
.
Which graph shows this?

Choose your answer
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Carol makes birthday cards. Each card takes the same amount of time to make.
She makes 3 cards in 48 minutes.
She has an order for 80 cards.
Can she complete this order in 3 days if she works 8 hours each day?
Show how you decide.
..................... because .................................................................................................
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y is inversely proportional to x.
y = 0.04 when x = 80.
Find the value of y when x = 32.
y = ...................
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The table shows values of x and y.
x | 4 | 16 | 36 |
y | 6 | 3 | 2 |
Show that these values fit the relationship that y is inversely proportional to .
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Sam and two friends put letters in envelopes on Monday.
The three of them take two hours to put 600 letters in envelopes.
On Tuesday Sam has three friends helping.
Working at the same rate, how many letters should the four of them be able to put in envelopes in two hours?
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Working at the same rate, how much longer would it take four people to put 1000 letters in envelopes than it would take five people?
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Sam says
It took two hours for three people to put 600 letters in envelopes. |
If I assume they work all day, then in one day three people will put 7200 letters in envelopes because 600 × 12 = 7200. |
Why is Sam’s assumption not reasonable? What effect has Sam’s assumption had on her answer?
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Donald swims 3 lengths of a swimming pool in 93 seconds.
i) Use this information to show that he could swim 100 lengths in under 55 minutes.
[4]
ii) What assumption did you make in part (i)?
[1]
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Donald tries to swim the 100 lengths in under 55 minutes.
Suggest one reason why he might not achieve this.
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To make orange juice
the number of cups of concentrate : the number of cups of water
= 3 : 7
Use this information to draw a graph to show the relationship between the number of cups of concentrate and the number of cups of water needed to make orange juice.

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(i) Find the gradient of the line drawn in part (a).
(ii) Explain what this gradient represents.
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A group of volunteers are making and selling jewellery to fundraise for charity.
In one hour, they can make 1200 necklaces or 1440 bracelets.
They start working at 11 am. They take no breaks.
They make 1800 necklaces and then switch to making bracelets. How many bracelets will the volunteers make by 4 pm?
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State one assumption that you have made in part (a).
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Let be directly proportional to the square root of
.
When .
Find the value of when
.
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The time it takes to print a batch of posters is inversely proportional to the number of printers being used.
It takes 6 printers 4 hours to print the batch.
Write an equation linking the time, , in hours and the number of printers,
.
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Calculate how long it would take if only 3 printers were used.
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is directly proportional to the square of
.
When
Find the value of when
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is inversely proportional to the square of
.
When
Find the value of when
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A theatre manager notices that the number of online ticket sales, , is directly proportional to the square of the amount of money spent on advertising,
, in pounds.
When the manager spends £250 on advertising, 500 tickets are sold online.
The manager sets a target to sell at least 1200 tickets online.
They decide to spend £400 on advertising.
Does the theatre manager meet their target?
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Given that , complete this table of values.
1 | 2 | 5 | 10 | |
|
|
| 1 |
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The intensity of the sound, watts/m2, received from a loudspeaker is inversely proportional to the square of the distance,
metres, from the loudspeaker.
When
Work out the value of when
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is inversely proportional to
when
Find the value of when
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The graphs of against
represent four different types of proportionality.
Match each type of proportionality in the table to the correct graph.
Type of proportionality | Graph letter |
| |
| |
| |
|
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A company has to make a large number of boxes.
The company has 6 machines.
All the machines work at the same rate.
When all the machines are working, they can make all the boxes in 9 days.
The table gives the number of machines working each day.
| day 1 | day 2 | day 3 | all other days |
Number of machines working | 3 | 4 | 5 | 6 |
Work out the total number of days taken to make all the boxes.
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is inversely proportional to
= 40 when
= 1.5
Calculate the value of when
= 1000
= ...................................................
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is proportional to
The graph shows the relationship between and
for

Find formula for
in terms of
.
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Given also that
show that is inversely proportional to
for
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is inversely proportional to the square of
Given that when
find a formula for in terms of
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is inversely proportional to
when
Find a formula for in terms of
.
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Work out the value of when
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The following table gives values of and
where
is inversely proportional to the square of
.
1.5 | 2 | 3 | 4 | |
16 | 9 | 4 | 2.25 |
Find a formula for in terms of
.
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Given that 0
find the value of when
144
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is inversely proportional to
= 10 when
0.0064
Find a formula for in terms of
.
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Find the value of when
= 20
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is inversely proportional to
when
Work out an equation connecting and
.
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Work out the value of when
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15 machines work at the same rate.
Together, the 15 machines can complete an order in 8 hours.
3 of the machines break down after working for 6 hours.
The other machines carry on working until the order is complete.
In total, how many hours does each of the other machines work?
............................hours
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where k is a constant. Which two statements are correct?
Tick two boxes.
| |
| |
| |
|
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where
is a constant.
Choose the correct statement.
is directly proportional to
is directly proportional to
is inversely proportional to
is directly proportional to
Choose your answer
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Three people take hours to deliver leaflets to
houses.
Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver leaflets to houses?
Give your answer in hours and minutes.
................. hours ................. minutes
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y is inversely proportional to the square root of x.
y is 40 when x is 9.
Find a formula linking x and y.
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The graph shows the speed, v metres per second (m/s), of a car at time t seconds.

The speed of this car is directly proportional to the square of the time.
Find a formula linking v and t.
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The table shows a set of values for and
.
is inversely proportional to the square of
.
Find an equation for in terms of
.
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Find the positive value of when
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is directly proportional to
when
Find the value of when
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is inversely proportional to
When
is directly proportional to
When
Find a formula for in terms of
.
Give your answer in its simplest form.
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A pendulum of length cm has time period
seconds.
is directly proportional to the square root of
.
The length of the pendulum is increased by 40%.
Work out the percentage increase in the time period.
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is directly proportional to the cube of
.
Mary says that when is doubled, the value of
is multiplied by 6
Mary is wrong.
Explain why.
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These graphs show four different proportionality relationships between and
.

Match each graph with a statement in the table below.
Proportionality relationship | Graph letter |
|
|
|
|
|
|
|
|
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is inversely proportional to
is directly proportional to
Given that and
when
find a formula for in terms of
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is inversely proportional to
is directly proportional to
Given that when
find the exact value of when
.......................................................
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is directly proportional to the cube of
when
Find a formula for in terms of
and
= .....................
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Find in terms of
when
Give your answer in its simplest form.
=.......................
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is inversely proportional to the square of
.
when
.
Find a formula for in terms of
.
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Find the value of when
..............................................
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Beth and Mia translate documents from Spanish into English.
A set of documents that would take Beth 8 days would take Mia 10 days.
Beth starts to translate the documents.
After 2 days Beth and Mia both work on translating the documents.
How many more days will it take to complete the work?
You must show your working.
......................days
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is directly proportional to
when
Work out an equation connecting and
.
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is inversely proportional to
.
The value of is multiplied by 4.
Select what happens to the value of .
Choose your answer
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and
have positive values.
is directly proportional to the square of
.
When
is inversely proportional to
.
When
Work out the value of when
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y is directly proportional to the square of x.
Find the percentage increase in y when x is increased by 15%.
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At a constant temperature, the volume of a gas V is inversely proportional to its pressure p.
By what percentage will the pressure of a gas change if its volume increases by 25%?
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x is directly proportional to y. y is directly proportional to z.
When x = 10, y = 60.
When y = 8, z = 1.6.
Find a formula for z in terms of x.
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