# five topics for early success

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## Curve Sketching - Introduction

In this introduction, we will introduce the key features of a curve to help sketching and look at the simple case of quadratic curves in relation to these properties. ## Introductory Trigonometry

In this section we will recap the basics of trigonometry from GCSE, recall the graphs of sin, cos and tan and make note of the multiple solutions that can arise from deceptively simple equations such as $\sin(x) = k$ ## Gradient of a line

This topic has made it into the five early topics list as it is one of the fundamental tools required for the ideas of calculus to be introduced. ## surds and indices

There are number of quotable rules that allow for the manipulations of indices and surds, all of which can be justified with a little work. ## Completing the square

This topic is significant because it is the first example of pure algebraic manipulation!

The process is probably the first regular encounter with algebra in which an equation is not directly solved, but rather expressions are just manipulated into different forms to reveal information which needs further manipulation or interpretation 