Throughout the whole of Year Three we solved equations and inequalities of many “kinds”: quadratic, fractional, irrational, with absolute value, exponential, logarithmic. At first sight each type had its own dedicated method. But if one looks carefully, behind all these methods there hides a small number of general ideas that work everywhere. This chapter gathers them together: it introduces nothing new, but it offers a way of reading that makes it easier to recognise the right strategy when faced with a “mixed” exercise. The unifying ideas are four — substitution, the application of an injective function, the application of a monotonic function and the study of the sign — and the section closes with a checklist for the oral exam and a group of exercises on recognising the strategy.
Sections
- Idea 1: substitution
- Idea 2: applying an injective function
- Idea 3: applying a monotonic function
- Idea 4: study of the sign
- A checklist for the oral exam