Direct and inverse proportion

T is inversely proportional to w. w is directly proportional to the cube root of d. When w = 6, T = 20 When w = 1, d = 8 Find the value of d when T = 48

Here is a table of values of x and y.

Nadia says that y is directly proportional to x because the value of y increases by 4 as the value of x increases by 2

Is Nadia correct? You must give a reason for your answer.

w is directly proportional to the square root of t. w = 140 when t = 64

Calculate the value of w when t = 7.84

On the axes below, sketch a graph to show the relationship between w and t.

f is inversely proportional to d² f = 3.5 when d = 8

Find an equation for f in terms of d.

Find the positive value of d when f = 10 Give your answer correct to 3 significant figures.

y is proportional to x² y = 3 when x = 0.5 x is inversely proportional to w x = 2 when w = 0.2 Find the value of y when w = 2

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?

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?

Here is the list of ingredients for making 20 biscuits.

Harry wants to make 60 biscuits. How much flour does Harry need?

y is directly proportional to x. y = 24 when x = 1.5 Work out the value of y when x = 5

It takes 14 hours for 5 identical pumps to fill a water tank. How many hours would it take 4 of these pumps to fill another water tank of the same size?

It takes 14 hours for 5 identical pumps to fill a water tank. How many hours would it take 4 of these pumps to fill another water tank of the same size?

p is inversely proportional to t Complete the table of values.

Water flows through each of the pipes that fill a lake at the same rate. It takes 4 of the pipes 12 hours to fill the lake. Work out how many hours it would take 6 pipes to fill of the lake.

You can use this graph to change between ounces and grams.

Change 850 grams to ounces.

Change 80 ounces to grams.

Here is a list of ingredients for making 10 scones.

Martin has 100 g butter 1 kg self‑raising flour 50 g sugar 4 eggs Martin wants to make 25 scones. He has not got enough of some of the ingredients. Work out how much more of each of these ingredients he needs.

18Here is a list of ingredients for making 10 scones.

Mia wants to make 25 scones. Work out how much sugar she needs.

y is directly proportional to the square root of t. y = 15 when t = 9 t is inversely proportional to the cube of x. t = 8 when x = 2 Find a formula for y in terms of x. Give your answer in its simplest form.

Kieron has 13 workers he can use for a job. He knows that 6 workers would take 14 days to complete this job. Show that Kieron has enough workers to finish this job in less than 7 days.

17Heidi wants to make some biscuits using this recipe.

Heidi thinks that she has, 500 g butter 700 g flour 250 g sugar Assuming that these weights are correct,

work out the greatest number of biscuits Heidi can make. You must show all your working.

Heidi is wrong. She has more than 250 g of sugar.

Does this affect the greatest number of biscuits Heidi can make? Give a reason for your answer.

On Monday, 12 people took 5 hours to clean a number of cars. On Tuesday, 15 people cleaned the same number of cars. Assuming that all the people worked at the same rate,

work out how many hours the 15 people took to clean the cars.

The assumption is wrong.

How might this affect the time taken for the 15 people to clean the cars?

x is directly proportional to the square of y. y is directly proportional to the cube of z. z = 2 when x = 32 Find a formula for x in terms of z.

y is increased by 44% Work out the percentage increase in x.

Scott wants to make orange juice. He is going to buy boxes of oranges.

Scott needs to buy enough oranges to make 8 litres of orange juice.

Work out the number of boxes of oranges that Scott needs to buy. You must show all your working.

Scott also buys 1260 apples 280 bananas

Write down the ratio of the number of apples that Scott buys to the number of bananas that he buys. Give your ratio in its simplest form.

18This graph can be used to change between US dollars ($) and British pounds (£).

Rosie bought a ring in the USA. She paid 345 US dollars. Work out in pounds the amount Rosie paid for the ring.

Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9 m. Grass seed is sold in 2 kg boxes. Maisie wants to make a rectangular lawn 10 m by 14 m. She has 5 boxes of grass seed.

Has Maisie got enough grass seed to make a lawn 10 m by 14 m? You must show all your working.

Maisie opens the 5 boxes of grass seed. She finds that 4 of the boxes contain 2 kg of grass seed. The other box contains 1 kg of grass seed.

Does this affect whether Maisie has enough grass seed to make her lawn? Give a reason for your answer.

Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9 m. Grass seed is sold in 2 kg boxes. Maisie wants to make a rectangular lawn 10 m by 14 m. She has 5 boxes of grass seed.

Has Maisie got enough grass seed to make a lawn 10 m by 14 m? You must show all your working.

Maisie opens the 5 boxes of grass seed. She finds that 4 of the boxes contain 2 kg of grass seed. The other box contains 1 kg of grass seed.

Does this affect whether Maisie has enough grass seed to make her lawn? Give a reason for your answer.

Each person in a fitness club is going to get a free gift. Stan is going to order the gifts.

Stan takes a sample of 50 people in the fitness club. He asks each person to tell him the gift they would like.

The table shows information about his results.

There are 700 people in the fitness club.

Work out how many sports bags Stan should order.

Write down any assumption you made and explain how this could affect your answer.

y is inversely proportional to the square of x.

y = 8 when x = 2.5

Deon needs 50 g of sugar to make 15 biscuits. She also needs three times as much flour as sugar two times as much butter as sugar Deon is going to make 60 biscuits.

Work out the amount of flour she needs.

Deon has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250 g packs.

How many packs of butter does Deon need to buy?

h is inversely proportional to p

Given that h = 10 and t = 144 when p = 6 find a formula for h in terms of t

There are 84 calories in 100 g of banana. There are 87 calories in 100 g of yogurt. Priti has 60 g of banana and 150 g of yogurt for breakfast. Work out the total number of calories in this breakfast.

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.

Work out the total number of days taken to make all the boxes.

It would take 120 minutes to fill a swimming pool using water from 5 taps.

How many minutes will it take to fill the pool if only 3 of the taps are used?

State one assumption you made in working out your answer to part (a).

It would take 120 minutes to fill a swimming pool using water from 5 taps.

How many minutes will it take to fill the pool if only 3 of the taps are used?

State one assumption you made in working out your answer to part (a).

y is inversely proportional to x³

y = 44 when x = a

Show that y = 5.5 when x = 2 a

y is inversely proportional to d² When d = 10, y = 4

d is directly proportional to x² When x = 2, d = 24

Find a formula for y in terms of x. Give your answer in its simplest form.

Find the value of y when x = 64

There are only 3 cleaners to clean all the rooms in the hotel today.

Each cleaner is paid 8.20 for each hour or part of an hour they work.

How much will each cleaner be paid today?

2.5 kg of apples cost £3.60

Work out the cost of 3.5 kg of apples.