Direct and Inverse Proportion

y is directly proportional to x. Complete the table.

A is inversely proportional to the square of B. When A = 2, B = 3. Find the value of A when B = 2.

A is directly proportional to B. When A = 12, B = 3 (a) Find a formula for A in terms of B. (b) Find the value of A when B = 5 (c) Find the value of B when A = 36

T is inversely proportional to N. When T = 30, N = 5.

C is directly proportional to the cube of D When D = 5, C = 175. (a) Work out the value of C when D = 6. (b) Work out the value of D when C = 4725.

y is inversely proportional to the cube root of x When y = 2500, x = 64. (a) Find the value of y when x = 8. (b) Find the value of x when y = 2000.

Z is directly proportion to √x When Z = 12, x = 36. (a) Express Z in terms of x. (b) Work out the value of Z when x = 121. (c) Work out the value of x when Z = 18.

y is inversely proportional to x Complete the table.

y is directly proportional to x. Complete the table.

T is inversely proportional to the cube of L When L = 0.2, T = 5. (a) Write a formula connecting T and L. (b) Work out the value of T when L = 0.5. (c) Work out the value of L when T = 2.

W is inversely proportional to √B When B = 9, W = 9. (a) Express W in terms of B. (b) Work out the value of W when B = 4. (c) Work out the value of B when W = 1.

The volume, V litres, which a fixed mass of gas occupies is inversely proportional to its pressure, P pascals. When the pressure is 200000 pascals, its volume is 6 litres.

W is directly proportional to P³. When P = 2, W = 32. (a) Express W in terms of P. (b) What is the value of W when P = 4? (c) What is the value of P when W = 4000?

An object when dropped, falls d metres in t seconds. d is directly proportional to the square of t. The object falls 80 metres in 4 seconds. Work out how far the object falls in 9 seconds.

w is inversely proportional to f When f = 12, w = 40

E is directly proportional to F. When E = 2, F = 8. (a) Find an equation for E in terms of F. (b) Find the value of E when F = 30. (c) Find the value of F when E = 100.

The cost of a circular table is directly proportional to the square of its radius. A table with a radius of 40cm cost £90. What is the cost of a table with a radius of 60cm?

The table shows a set of values for x and y. y is inversely proportional the the square. (a) Find the equation for y in terms of x. (b) Find the missing value of x.

C is directly proportional to D. When C = 125, D = 5. (a) Find an equation for C in terms of D. (b) Find the value of C when D = 10. (c) Find the value of D when C = 75.

The cost, C pounds, of hiring a car is directly proportional to the number of days, d, it is hired. When d = 5, C = 180

The mass of a paperweight is m grams. The length of the paperweight is L centimetres. m is directly proportional to the cube of L. m = 4968 when L = 12 (a) Work out an equation connecting m and L (b) Work out the mass of a paperweight with

y is directly proportional to the square of x When y = 6.4, x = 4 (a) Find a formula for y in terms of x (b) Find the value of y when x = 8 (c) Find the value of x when y = 78.4

The table shows a set of values for x and y. y is directly proportional to the square root of x. Complete the table.

These graphs represent four different types of proportionality. Match each type of proportionality to the correct graph.

In a spring, the tension (T newtons) is directly proportional to the extension of the spring (y cm). When the tension is 180 newtons, the extension is 4cm.

y is directly proportional to the cube root of x When y = 7600, x = 4096 (a) Find an equation connecting y and x. (b) Calculate the value of y when x = 125 (c) Calculate the value of x when y = 9975

A is directly proportional to B². When A = 50, B = 5. (a) Find a formula for A in terms of B. (b) Find the value of A when B = 3. (c) Find the value of B when A = 200.

y is inversely proportional to the square of x. When y = 200, x = 2. (a) Find an equation connecting y and x. (b) Work out the value of y when x = 5. (c) Work out the value of x when y = 50.

The number of days, D, to complete research is inversely proportional to the number of researchers, R, who are working. The research takes 125 days to complete when 24 people work on it. Find out how many people are needed to complete the r

q is inversely proportional to the square of t. When q = 7.5, t = 1.6. (a) Calculate the value of q when t = 8. (b) Calculate the value of t when q = 1.875.