Unit 6

A 1.8 metre metal rod is to be cut into pieces, each measuring metres. How many full pieces can be cut from the rod, and what length of the rod will be left over? Give your answer as a mixed number where appropriate.

The number is such that .

A car travels s kilometres in t hours. It is known that s is directly proportional to t, and that when t = 2.5, s = 165.

a) Write down the formula connecting s and t.

b) What is the value of the constant of proportionality?

c) Calculate the value of s when t = 6.4.

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:

In a science experiment, Marta adds chemicals to a solution following this sequence: she adds 2 ml on the first day, 5 ml on the second day, 8 ml on the third day, and so on, increasing the amount by 3 ml each day.

On which day will she add exactly 44 ml to the solution?

The first term of an arithmetic sequence is 12. The common difference is 7. Calculate the sum of the first 30 terms of this sequence.

Sophie decides to save money for a holiday by following a plan: she saves $15 in the first week and then increases how much she saves by $4 each week. She needs to save at least $350. Explain how she can work out the minimum number of weeks needed to reach her goal. Show your reasoning clearly.