Topic One (1.1): Prior Knowledge

Introduction

This topic revises key parts of the GCSE/IGCSE syllabus that are pre-requisites for the study of AS and A Level Mathematics.

Tasks

Complete the following:

A Level Maths builds upon the knowledge of all the algebra studied at GCSE/IGCSE level. If you haven’t studied maths for a while, you might like to watch and explore the following links first to remind you of the basics:

Surds

The CAIE A Level course assumes you can manipulate surds. This might have been covered in your Key Stage 3 course, but as this will have been a while ago, we suggest you refresh your knowledge by watching the following:

Graphs of the form $y=kx^n$

You are also expected to be familiar with the shapes of graphs of the form $y=kx^n$ , where $k$ is a constant and $n$ is an integer (positive or negative). Please study and make notes on the following video:

There are two other graphs to investigate, $LaTeX: y=kx^{\frac{1}{2}}$ $y=kx^{\frac{1}{2}}$ and $LaTeX: y=kx^{\frac{-1}{2}}$ $y=kx^{\frac{-1}{2}}$ . Work these out for yourself by visiting the following website and entering the equations. Remember that your indices should be in brackets, so you draw $LaTeX: f\left(x\right)=x^{\frac{1}{2}}$ $f\left(x\right)=x^{\frac{1}{2}}$ . Can you predict what the graph of $LaTeX: y=kx^{\frac{-1}{2}}$ $y=kx^{\frac{-1}{2}}$ will look like? Check by asking it to draw the graph of $LaTeX: f\left(x\right)=x^{\frac{-1}{2}}$ $f\left(x\right)=x^{\frac{-1}{2}}$ .
You can explore all of the different types of graph for yourself using Desmos Graphing Calculator. Try out all of the types of graph listed to see what they look like:

Note that there is a difference between plotting a graph, which we did at GCSE and sketching a graph, as required at A level. The following video helps you to see what is needed for a sketch graph:

An overview of all of the graphs and transformations can be found on the following playlist: