Equations, Inequalities & Formulae
An equation, an inequality and a formula all look like symbols glued together with an equals or inequality sign — but they're answering three completely different questions. Most marks lost in this unit aren't lost to weak algebra; they're lost because a student solved the wrong kind of question, or forgot the one extra rule inequalities carry that equations don't.
Overview: What This Chapter Really Tests
Three symbols, three different jobs
An equation asks 'what single value (or few values) of x makes this true?' An inequality asks 'what whole range of values works?' A formula is a rule connecting several variables permanently — you substitute into it for a number, or rearrange it for a new formula, but you never 'solve' it the way you solve an equation. Confusing these three is the single biggest reason for lost marks in this unit.
- Equations → a point (or points) on the number line.
- Inequalities → a region on the number line, shown with open or closed circles.
- Formulae → a rule linking two or more variables, like or .
- All three use the same balance-method rules — with exactly one extra rule for inequalities: flip the sign when multiplying or dividing by a negative number.
The shape of the chapter
Command terms that drive the mark scheme
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Solve | Find the value(s) of the unknown that make the equation/inequality true — show algebraic working, not just the answer. | Knowing & applying | Marks are awarded for each correct line of working — a bald final answer with no steps typically scores under half the marks. |
| Represent | Show the solution set on a number line (or other specified form) with correct open/closed endpoint notation. | Communicating | Getting the inequality right but drawing the wrong circle type still loses the representation mark. |
| Justify / Explain why | Give a mathematical reason tied to the actual numbers in the question, not a restated rule. | Reasoning | 'Because that's the rule' scores zero — you must say why the rule applies to these specific numbers. |
| Describe | State a pattern or relationship in words, referencing the actual values given. | Investigating patterns | A description that never mentions the actual numbers in the sequence loses the mark. |
| Apply | Use a given rule or conjecture on new values and show working for each case. | Applying | Each case/row is usually worth its own mark — skipping one loses that mark specifically. |
Key point
Overview