Algebraic Expressions and Identities
MYP Mathematics Framework — Number & Algebra strand: Algebraic Expressions and Identities
This is the topic where algebra stops being 'follow the steps' and starts being 'spot the structure'. Every exam question in this bank — beam loads, drone fuel efficiency, filling tanks, chemical concentrations — is really the same handful of moves in disguise: factorise, cancel a genuine common factor, expand carefully, substitute in brackets. Examiners aren't testing whether you can do arithmetic; they're testing whether you cancel factors and not terms, and whether you can justify a 'show that' line by line instead of just writing the answer.
Overview
Identity vs equation — the distinction everything else rests on
An identity is true for every possible value of the variable — holds whether , , or . An equation like is only true for specific values of . Every 'simplify', 'expand', or 'factorise' instruction in this topic is manipulating an identity — you are never solving for , you're rewriting the same expression in a different, equally valid form.
- The six subtopics below aren't independent — exponent laws feed into fraction simplification, factorisation feeds into both fractions and identities, and everything eventually gets tested by substituting numbers in at the end.
- The exam bank for this topic is dominated by real-world 'show that' and 'hence' questions — engineering load ratios, chemical concentrations, filling rates — because these test whether you can carry algebra through a multi-step context, not just perform an isolated skill.
The shape of the chapter
Command terms this topic is actually examined on
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Simplify | Reduce an expression to its lowest equivalent form with no further cancelling possible. | Criterion A | Mark lost if a valid common factor remains, or if a term (not a factor) has been wrongly cancelled. |
| Factorise | Write as a product of factors; the highest common factor must be fully extracted. | Criterion A | No mark for a partial factorisation, e.g. stopping at instead of . |
| Show that | Derive the GIVEN result from the starting expression using visible, logical steps. | Criterion B | A correct final answer with no working scores zero — every line of method is what earns marks here. |
| Deduce | Use an established pattern or earlier result (without re-deriving from scratch) to state a new result. | Criterion B | Must reference the pattern explicitly, not just state the answer out of nowhere. |
| Hence | Use the result you just found — starting a completely fresh method forfeits the mark. | Criterion B | A correct answer via an independent method still loses the 'hence' mark. |
| Evaluate | Substitute given values and compute a single numerical answer. | Criterion A | An unsimplified fraction or leftover algebra in the final line loses the accuracy mark. |
| Justify / Interpret | Connect the algebraic result back to the real-world context in a full sentence. | Criterion D | A bare number with no linking sentence (guests, hours, kN, grams...) scores no communication mark. |
Key point
Overview