Unit 6

It takes a bee 300 000 km to produce 2 kg of honey. The distance (km) travelled is directly proportional to the mass (kg) of honey produced.

How many grams of honey can the bee produce by flying 45 000 km? (Give your answer in grams.)

The time, T seconds, for a chemical reaction is directly proportional to the square of the temperature, t °C. The reaction takes 32 seconds at 40°C.

a) Write down the formula for T in terms of t.

b) Calculate the time for the reaction at 70°C.

c) Find the temperature if the reaction takes 50 seconds.

The cost, C dollars, of producing a metal sphere varies as the cube of its radius, r cm. A sphere of radius 5 cm costs $120.

a) Find the formula for C in terms of r.

b) What is the cost of a sphere with a radius of 7 cm?

c) A company wants to make a sphere for $405. Work out the radius of this sphere.

The cost of producing a metal container varies as the square of its base diameter and is inversely proportional to its height . When cm and cm the cost is £64.

Simplify the following using the rules of indices. Write your answer with positive indices only:

Write down the second and third terms of the sequence that starts at 7 and increases by 5 each time.

The sequence starts 15, 30, 45, ... What is the common difference?

A sequence is defined by the nth term formula: . Find the first and fourth terms of the sequence.

Given the sequence 2, 5, 10, 17, 26, ... use the difference method to find the next two terms of the sequence.

The nth term of a sequence is given as . Calculate the value of the 8th term.