01 — Explanation
What's the difference between an expression and an equation?
An expression is a mathematical phrase with no equals sign, such as for "3 less than double a number". It has a value depending on , but there's nothing to solve. An equation contains an equals sign and asserts two expressions are equal, such as , which can be solved for .
Golden Rule
if there's no equals sign, don't try to solve it. The most common error at this level is forming a correct expression like and then setting it equal to zero out of habit.
02 — Explanation
How do I translate words into algebra?
Learn the keyword-to-operation links: "more than / sum / total" → add; "less than / difference" → subtract; "times / product / lots of" → multiply (write the number before the letter, e.g. not , to avoid confusion with ); "shared between / divided by" → divide.
Common Mistake
"less than" reverses the natural word order. " less than " means start with and take away , giving — not .
03 — Explanation
How do I combine several operations, and when do I need brackets?
Work through the sentence in the order the operations are described, but add brackets whenever a single operation must apply to an entire previous result.
- " add 2, then multiplied by 5" → the addition must happen first and the whole result gets multiplied: .
- Without brackets, would mean "multiply by 5, then add 2" — a different instruction entirely.
04 — Explanation
How do I form an expression from a worded problem with several quantities?
Identify the unknown, express every other quantity in terms of it, then combine and simplify as instructed.
Example: a rectangle has length and width . Find its perimeter in simplest form.
Grouping the -terms () and the numbers ():
05 — Worked example
Worked exam-style question
A child's cinema ticket costs . An adult's ticket costs more than a child's.
(a) Write an expression for the price of an adult's ticket.
(b) Write an expression, in its simplest form, for the cost of one adult's ticket and two child's tickets.
(a) "£5 more than " translates directly: .
(b) One adult plus two children: . Collecting like terms: .
Exam Tip
write the unsimplified expression first — — before collecting terms. This secures the method mark even if a slip occurs during simplification, and it also protects you from the most serious error on this topic: accidentally trying to "solve" the finished expression because it looks like an equation.
06 — Explanation
How do I avoid answering a different question from the one asked?
Before finalising an answer, re-read the question's exact final phrase. Examiner reports for this topic repeatedly note that students correctly translate most of a scenario but then answer, say, "the total number of boxes" when the question asked for "the total number of items inside the boxes". Underlining the command phrase on first reading — and checking your final expression against it — catches this reliably.