Equations, Inequalities & Formulae
Equations, inequalities, and formulae are really the same skill wearing three different hats — you're always isolating an unknown using balanced, reversible operations. The exam only starts biting when the reasoning matters more than the arithmetic: why a circle is open or closed, why a real-world limit isn't as sharp as its equation suggests, why 'decreased by' can flip an expression if you're not careful. That's what this chapter actually tests.
Overview: What This Chapter Is Really Testing
An equation () claims two expressions are exactly equal. An inequality () claims one is bigger, smaller, or not equal — and hands you infinitely many solutions instead of one. A formula () is a reusable rule linking several variables, one you substitute into rather than 'solve' once and forget.
- All three are manipulated with identical balancing rules — whatever operation you do to one side, you do to the other, in exactly the same order.
- Inequalities carry ONE extra rule that equations and formulae don't: multiplying or dividing both sides by a negative number flips the direction of the sign.
- A formula isn't solved for a single number — it's rearranged to change which letter is the 'subject', then values are substituted in.
- Word problems and real-world contexts test whether you can translate language into the correct symbol BEFORE any algebra even starts.
The shape of the chapter
Command terms that actually appear on this topic
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give a fact, symbol, or short answer with no justification required. | Knowing & Understanding | One correct word/symbol/value earns the mark — no working expected. |
| Explain | Give reasons that connect the maths to the specific value or context. | Knowing & Understanding / Communicating | A bare restatement of the symbol's name scores 0 — reference the actual value, e.g. 'because 4 itself is a solution'. |
| Identify | Select or name the correct item(s) from given information. | Knowing & Understanding | Must name the exact value(s) asked for — vague answers lose the mark. |
| Describe | Give a full account of a set, pattern, or process in words. | Knowing & Understanding | For an infinite solution set, state it's ALL numbers beyond the boundary, not just a few examples. |
| Calculate | Obtain a numerical answer, showing the working that produced it. | Knowing & Understanding | Method marks are awarded per correct balancing step, even before the final value appears. |
| Compare | Identify similarities and differences between two situations or models. | Critical thinking / Communicating | Needs BOTH models discussed relative to each other — describing only one loses half the marks. |
| Solve | Find the value(s) of the unknown that satisfy an equation or inequality. | Knowing & Understanding | Show every inverse-operation step; the final line must fully isolate the variable. |
Equation vs Inequality vs Formula
| Feature | Equation | Inequality | Formula |
|---|---|---|---|
| What it claims | Two expressions are exactly equal | One expression is bigger/smaller/not equal to another | A rule relating two or more variables |
| Typical solution | One value (or a small finite set) | A whole range — infinitely many values | No single 'solution' — you substitute values in |
| Example | |||
| How you work with it | Solve for the unknown | Solve, then show the range on a number line | Rearrange (change the subject) or substitute values |
Key point
Overview