Equations, Inequalities & Formulae
This is the unit where algebra stops being abstract letters and starts being a tool — you'll turn sentences into equations, rearrange real formulas (speed, perimeter, cost), and handle inequalities where the answer isn't one number but a whole range. The single mark-losing habit examiners see over and over: forgetting the sign flips when you multiply or divide an inequality by a negative number. Get that automatic and this whole topic is straightforward marks.
Overview: What This Topic Actually Tests
Three ideas run through this whole unit and every question bank you'll see: an equation () has exactly one solution (or a fixed few), an inequality () has a whole range of solutions, and a formula () is a rule connecting two or more letters that you substitute into or rearrange. The skill being tested isn't just 'solve for x' — it's translating a real situation (a ride height rule, a taxi fare, a word problem about ages) into correct algebra first, then solving it.
- Equations answer 'what exact value makes this true?' — one point on a number line (or a small finite set).
- Inequalities answer 'what range of values makes this true?' — a ray or segment on a number line, shown with an open or closed circle.
- Formulae are equations with more than one letter that already mean something in context — you substitute known values in, or rearrange to make a different letter the subject.
The shape of the chapter
Command terms this topic actually uses
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | give a short answer, no justification needed | AO1 | Just write the inequality, e.g. — no working required, but the wrong symbol scores 0 even if the number is right. |
| Identify | pick out or name a feature already shown to you | AO1 | For an open circle you must say '3 is NOT included' — saying 'it shows an inequality' earns nothing. |
| Describe | a fuller account that explains, in more than one clause | AO2 | Asking why the sign flips needs the reasoning (order reverses on the number line) — 'it just flips' alone loses marks. |
| Calculate | produce a numerical answer with working shown | AO1 | Method mark for the correct operation, accuracy mark for the correct value — both are needed separately. |
| Compare | address similarities AND differences between two cases | AO2 | A 'compare' on positive vs negative multipliers needs both cases discussed — one-sided answers cap at half marks. |
| Construct | build an expression or equation from given information | AO2 | In word problems the mark is awarded for the correctly built equation, even before you solve it. |
| Solve | find the value(s) satisfying the equation/inequality with working shown | AO1 | A bare final answer with no working forfeits the method mark even if it's correct. |
Key point
Overview