Toolkits
Deep dives on the ideas that show up everywhere. Each one starts with why the idea exists at all — the problem it was invented to solve, what it actually does, and where it turns up outside a classroom — and then goes through it properly: the full explanation, the table you actually need, worked examples, and the mistakes that cost marks.
Number
Negative numbers without the guesswork
The sign rules are one idea, not five. Subtracting as adding the opposite, counting negatives, (−2)⁴ against −2⁴, subtracting a polynomial, and reversing an inequality.
Open the toolkit
Patterns and relations
Keep it balanced
An equation is a balance: do the same to both sides and check by substitution. Then the two places the rule breaks — inequalities with negatives, and dividing by a variable.
Open the toolkit
How to use these
- Wondering why any of this is a thing? Read the opening section. It is the part a textbook usually skips.
- Stuck on a question type? Open the toolkit for that idea and find the worked example closest to it.
- Revising? Read the tables and try the checks, then go to practice questions to see whether it stuck.
- Getting ready for the achievement test? Every Grade 9 student writes it in June. The printable worksheets and a mixed quiz are the closest thing here to sitting it.