Substitution — single variable
Given a formula like \(y=3x-2\), find \(y\) when \(x\) is a given number. The skill: replace the letter with the number and compute.
① Substitution — two or more variables
Formulae like \(A=lw\), \(P=2(l+w)\) and \(C=2\pi r\). Substitute each value carefully and follow BIDMAS.
② Substitution into real formulae
Physics, finance and everyday formulae: \(v=u+at\), \(F=ma\), \(s=\dfrac{d}{t}\). Negatives and decimals included.
③ Changing the subject — one or two steps
Rearrange a formula so a different letter is the subject. Use inverse operations in the right order.
④ Changing the subject — multi-step
Harder rearrangements involving brackets, division, or the new subject appearing in more than one place.
Key ideas
Substitution: replace each letter with the given value (use brackets, especially for negatives), then evaluate using BIDMAS.
Changing the subject: do the same operation to both sides at every step. Aim to isolate the new subject. Reverse the order of operations: undo addition before division, division before squaring, etc.
Watch your signs: when moving a term across the \(=\), its sign changes. When multiplying or dividing both sides by a negative, every term changes sign.
Check your rearrangement: pick any sensible value, plug it into both the original and the rearranged form — the answers should match.