Patterns and relationships
You are expected to be able to recognise patterns and be able to use tables and graphs to represent and analyse them. As part of the analysis you need to be able to explain the pattern not only in words but also in numbers and then use this pattern to make predictions based on a table, graph or formula. It is necessary to be able to calculate the rate of change and y-intercept and put these into the context of the question. For two intersecting linear relations you may need to find a common value, in other words their intersection point either graphically (read from graph - make sure to mark on the graph) or algebraically (simultaneous equations).
The first three stages of a pattern are shown below. Each stage is made up of a certain number of shaded discs and a certain number of white discs.
(i)Shade in the appropriate discs below to show the 4th stage of the pattern.
(ii)Complete the table below to show how the pattern continues.
(iii)In a particular stage of the pattern, there are 21 white discs. How many shaded discs are there in this stage of the pattern?
(iv)Write down the relation between the number of shaded discs and the number of white discs in each stage of the pattern. State clearly the meaning of any letters you use.
There are two extra white discs for each extra shaded disc. There is one shaded disc and 5 white discs at the start.
shaded discs = n white discs = 3 + 2n