Equations, Inequalities and Formulae
MYP Year 5 Mathematics — Equations, Inequalities and Formulae (Algebra strand)
This whole topic is really one skill wearing six different costumes: isolate the unknown, correctly, every time — whether that unknown is in a quadratic, in a formula, or the number of gigabytes a student can afford this month. The bit that separates a top grade from a middling one is almost never the algebra itself; it's the small procedural habits examiners build entire mark schemes around — flipping an inequality sign, checking a solution in the original equation, rounding sensibly once the answer means something real.
Overview — The Shape of the Chapter
An equation says two expressions are equal and asks you to find the exact value(s) that make that true. An inequality says one expression is not necessarily equal to another — bigger, smaller, or bounded between two values — so its solution is a whole range, not a single number. A formula (literal equation) is a relationship between several letters where nothing has been solved yet; you're usually asked to rearrange it so a different letter becomes the subject. All three are attacked with the same core move: do the same thing to both sides — or, for compound inequalities, to all parts — until the unknown you want stands alone.
- Equation → finite solution set (one value for linear, up to two for quadratic).
- Inequality → infinite solution set, written as an interval or shown on a number line with open/closed circles.
- Formula → no numbers to solve for; you're rearranging the relationship itself, so the 'answer' is another formula.
- Simultaneous equations → two conditions must hold at once, so the solution is a single pair, not two independently chosen values.
The shape of the chapter
Command terms this topic tests
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Solve | Find the value(s) of the unknown that make the equation/inequality true, showing method. | Knowing & applying | Method mark awarded for correct rearrangement step even with a follow-through error in the final answer. |
| Deduce | Draw a short, logical conclusion directly from the given model — minimal extra working. | — | Usually 1 mark; the conclusion must follow straight from the given equation, not from a fresh derivation. |
| Interpret | Explain what a numeric or algebraic result means back in the original real-world scenario. | — | A bare number scores 0 — you must reference what x represents and its units. |
| Justify | Give a reasoned argument, typically by substituting a specific value and comparing it explicitly. | — | Requires the explicit numeric check written down — 'yes because...' with no number shown scores 0. |
| Advise | State a clear recommendation for the person in the scenario, backed by your working. | — | Needs both the working AND a directional statement, e.g. 'the driver did not comply for the first 15 hours'. |
| Represent | Show the solution in the specified format (number line, graph, list). | — | Marked on correct notation — open vs closed circle, correct scale/arrow direction. |
| List | Write out every element of a finite solution set explicitly. | — | Missing a boundary integer, or including an excluded one, loses the mark even if the inequality was solved correctly. |
| State | Give a fact or rule directly — no working required. | — | Must be the general symbolic rule when asked for a 'property', not just a worked numeric instance. |
Key point
Overview