Mastering Mathematics Smartly
by Wee Wen Shih

A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.

Substitutions in H2 Mathematics

When we study the various topics in H2 Mathematics, it is useful and practical to find a unifying link between them, to achieve effective and efficient learning.

In this short article, I will highlight the role of substitutions in H2 Mathematics through a few concrete examples below.

  1. We use substitutions in inequalities, when we wish to deduce the solution of a new inequality based on a previously solved one.

  2. We use substitutions in integration, so that a complex expression may become easier to integrate.

  3. We use substitutions in solving some differential equations, when the original DE looks daunting.

  4. We use substitutions when finding the areas and volumes of curves defined parametrically.

  5. We use substitutions to understand the behaviour of curves that have undergone transformations, e.g. the relationship between the graphs of y = \text{f}(x) and y = \text{f}(ax).

  6. We use substitutions in series expansions, e.g. we may obtain the series expansion of \text{ln}\:(1 - 2x) from the standard series expansion of \text{ln}\:(1 + x).

  7. We use substitutions in sequences and series, e.g. \text{T}_{n - 1} and \text{S}_{2n} can be obtained easily from \text{T}_{r} (the r th term in the sequence) and \text{S}_{r} (the sum of the first r terms of a sequence).

  8. We use substitutions in solving a system of equations.