Equations Inequalities and Formulae
Every equation you meet this year hides a number, and your algebra is the interrogation. Inequalities do the same job but for a whole range of numbers, and formulae are just equations with more than one letter waiting to be rearranged. Examiners don't reward you for landing on the right number — they reward you for showing the legal, reversible moves that got you there, one line at a time.
Overview — How This Topic Fits Together
Four ideas run through this whole topic: an equation pins down one exact value (or a small fixed set of values), an inequality describes a whole range, a formula links several letters together, and simultaneous equations need two independent pieces of information before either unknown can be pinned down. Every worked question you'll see this year — a mobile data plan, a food truck's legal distance from a hydrant, a candle business's break-even point — is just one of these four skeletons wearing real-world clothing.
- Solving is always a balancing act: whatever legal operation you apply, apply it to BOTH sides (or all parts of a compound inequality) without exception.
- The one rule that has no equation equivalent: multiply or divide an inequality by a negative number and the direction flips.
- Context questions are marked as much on interpretation as on algebra — a correct value with no units or explanation regularly drops a mark.
The shape of the chapter
Command terms that control the marks
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Solve | Find the value(s) of the unknown that make the equation/inequality true, showing algebraic steps. | Applying | Mark given for a correct method line AND the correct final value with correct sign/inequality — a bare correct answer with no working forfeits the method mark. |
| Justify | Give a mathematical reason, usually by substituting a specific value and comparing it to the boundary. | Communicating | A bare 'yes'/'no' scores zero — you must reference the actual number and state which inequality symbol applies. |
| Represent | Show the solution set correctly, e.g. on a number line with the correct type of circle and shading. | Communicating | Open vs closed circle is the mark itself — correct algebra with the wrong circle still loses the representation mark. |
| Interpret | Translate the mathematical answer back into the real-world context, with units. | Applying / Communicating | Repeating the inequality (e.g. '') is NOT interpretation — must state what 11 means in the story. |
| Rearrange / Show that | Manipulate a formula to make a different variable the subject, or prove a given result. | Applying | Each correctly reversed operation scores; skipping straight to the final line forfeits method marks if that line contains an error. |
| State | Give a fact, property or rule directly — no working required. | Knowing & Understanding | Must name the exact property (e.g. 'the addition property of inequalities') rather than describe it vaguely. |
Key point
Overview