Direct and inverse proportion

y is inversely proportional to x³

y = 4 when x = 3

Work out the value of x when y = 864

F is inversely proportional to the cube of r

F = 6 when r = 2

Find a formula for F in terms of r

Find the value of r when F = 3072

Here is a list of ingredients needed to make 6 biscuits.

Asha makes some of these biscuits. She uses 450 g of flour.

How many biscuits does Asha make?

Julie makes 84 of these biscuits.

What weight of butter does Julie use?

Asha and Julie pay a total of 624 rupees for the ingredients. The ratio of the amount Asha pays to the amount Julie pays is 3: 5

How much does Julie pay?

17Here is a list of ingredients to make spaghetti carbonara for 4 people.

Joe is going to make spaghetti carbonara for 12 people.

Work out how much cheese he needs.

Ruhi makes spaghetti carbonara. She uses 180 g of butter.

Work out how many people Ruhi makes the spaghetti carbonara for.

Vivienne makes bread.

The weight of yeast she uses is 1% of the weight of flour she uses.

Vivienne uses 750 g of flour.

Work out the weight of yeast she uses.

Bernard makes currant buns.

For every 400 g of flour he uses, he uses 125 g of currants.

Bernard uses 2000 g of flour.

Work out the weight of currants he uses.

F is inversely proportional to the square of r

F = 36 when r = 4

Find a formula for F in terms of r

Work out the value of F when r = 48

P is inversely proportional to y² When y = 4, P = a

Find a formula for P in terms of y and a

find a formula for P in terms of x and a

A is inversely proportional to C²

A = 40 when C = 1.5

Calculate the value of C when A = 1000

Given that y = 8 when T = 25

find the exact value of T when y = 27

Sabbir has some boxes of bananas and some sacks of tomatoes. The weight of each box of bananas is the same and the weight of each sack of tomatoes is the same.

The weight of 3 boxes of bananas is 42 kg. The weight of 8 sacks of tomatoes is 68 kg.

Work out the total weight of 9 boxes of bananas and 15 sacks of tomatoes.

The diagram shows a container for water in the shape of a prism.

The rectangular base of the prism, shown shaded in the diagram, is horizontal. The container is completely full of water.

Tuah is going to use a pump to empty the water from the container so that the volume of water in the container decreases at a constant rate.

The pump starts to empty water from the container at 10 30 and at 12 00 the water level in the container has dropped by 20 cm.

Find the time at which all the water has been pumped out of the container.

F is inversely proportional to the square of v.

Given that F = 6.5 when v = 4

find a formula for F in terms of v.

The following table gives values of x and y where y is inversely proportional to the square of x.

Find a formula for y in terms of x.

Given that x 0

find the value of x when y = 144

y is directly proportional to the cube of x y = 20 h when x = h (h 0)

Find a formula for y in terms of x and h

Find x in terms of h when y = 67.5 h Give your answer in its simplest form.

R is proportional to t² The graph shows the relationship between R and t for 0 ≤ t 4

Find a formula for R in terms of t.