A familiar solution can make sense when you read it. Mastery means knowing how to begin when the question changes. That’s the skill to build, whether you’re strengthening the basics or tackling Extended Mathematics.
- 01
Find the missing step.
Start with a question you found difficult and explain your thinking. Is the obstacle the concept, the algebra or choosing a method? A problem about a straight-line graph may reveal a gap in equations or fractions. Working on that specific gap makes the next lesson more useful.
- 02
Connect the method to the meaning.
Move between equations, graphs and explanations. Don’t only rearrange an equation: explain what its gradient tells you about a straight-line graph. Your tutor can vary one part of a question at a time, helping you recognise which ideas stay the same.
- 03
Make the thinking your own.
Try a related question independently, then mix topics and add timed practice. Review where marks were lost: method, notation, calculation or interpretation. In Extended Mathematics, build towards longer problems that combine ideas and require you to decide the next step.
A SMALL EXAMPLE. A BIG CONNECTION.
From a pattern to a rule.
3, 5, 7, 9, … → an = 2n + 1
The sequence increases by 2 each time. How can you find the twentieth term without listing every term? Connect the pattern to a rule you can explain and test.
See the reasoning +
Twice the position gives 2, 4, 6, 8, … . Adding 1 gives the original sequence, so an = 2n + 1. Check the first few terms, then substitute n = 20: a20 = 41.