The Words That Control Your Marks
Every IGCSE Maths question begins with a command word — an instruction that tells you exactly what to do. These words might seem interchangeable to the casual reader, but to an examiner, each one has a precise meaning. Responding to the wrong command word is like answering a different question entirely, and it costs marks every single year.
The frustrating thing is that students who make command word mistakes often know the maths perfectly well. They simply misinterpret what is being asked. This is entirely preventable with a clear understanding of what each command word requires.
”Simplify” vs “Factorise” vs “Expand”
These three command words are confused more than any others in algebra.
Simplify means to reduce an expression to its simplest form by collecting like terms, cancelling common factors, or reducing fractions. The answer should be a single, clean expression.
Example: Simplify 3x + 5x − 2x. Answer: 6x.
Factorise means to express as a product of factors. The answer should contain brackets.
Example: Factorise 6x + 9. Answer: 3(2x + 3).
Expand means to remove brackets by multiplying out.
Example: Expand 3(2x + 5). Answer: 6x + 15.
The classic mistake is factorising when asked to simplify, or simplifying when asked to factorise. These are opposite operations, and doing the wrong one earns zero marks regardless of how well you perform the operation.
”Solve” vs “Simplify”
Solve means to find the value(s) of the unknown variable that make an equation true. Your answer should be in the form “x = …” (or equivalent).
Example: Solve 3x + 7 = 22. Answer: x = 5.
Students sometimes simplify an expression when asked to solve an equation, or try to solve something that is not an equation. Remember: you can only solve an equation (with an equals sign). You simplify expressions (without an equals sign).
”Show That” vs “Prove” vs “Verify”
These words all involve demonstrating that something is true, but with different nuances.
Show that requires you to work from the given information to arrive at the stated result. You must present every step of the logic. The answer is given — your job is to provide the complete argument.
Prove is similar to “show that” but is typically used for more formal mathematical arguments, such as geometric proofs or algebraic identities. The expectation for rigour is slightly higher.
Verify means to check that a given statement is true by substituting values or testing conditions. Unlike “show that,” you can use the given answer as a starting point.
Example of verify: Verify that x = 3 is a solution of 2x² − 5x − 3 = 0. Answer: 2(3)² − 5(3) − 3 = 18 − 15 − 3 = 0. Since the result is 0, x = 3 is a solution.
”Calculate” vs “Estimate” vs “Write Down”
Calculate means to work out the answer using mathematical operations. Show your working.
Estimate means to find an approximate answer, usually by rounding each number to one significant figure first and then calculating. You must show the rounded values.
Example: Estimate 4.87 × 21.3. Working: 5 × 20 = 100. Answer: 100.
A common mistake is giving the exact answer when asked to estimate. This will earn zero marks even though the exact answer is more accurate. The question is testing whether you know how to estimate, not whether you can use a calculator.
Write down means the answer should be obvious and requires minimal or no working. These are typically 1-mark questions where the answer can be stated directly.
”Give Your Answer in the Form…”
When a question says “give your answer in the form a/b where a and b are integers” or “in the form a × 10ⁿ,” you must follow this instruction exactly. A correct numerical answer in the wrong form will lose the accuracy mark.
Common form requirements:
- As a fraction — do not give a decimal. Simplify if the question says “in its simplest form.”
- In standard form — must be a × 10ⁿ where 1 ≤ a < 10 and n is an integer.
- In terms of π — do not evaluate π. Leave it as a symbol.
- As an exact value — do not round. Leave surds, fractions, or π in your answer.
- Correct to 3 significant figures — round only the final answer and give exactly 3 significant figures.
”Describe” in Transformation Questions
Describe in the context of transformations means to state the transformation fully. Each transformation type requires specific information:
- Translation: state the translation vector
- Rotation: state the centre, angle, and direction (clockwise/anticlockwise)
- Reflection: state the equation of the mirror line
- Enlargement: state the centre and the scale factor
Missing any element costs marks. One of the most common errors is describing a rotation without stating the direction, or describing an enlargement without giving the centre.
”Hence” vs “Otherwise”
Hence means you must use the result from the previous part of the question. You are not allowed to use a completely different method. The word “hence” connects the current part to the previous one.
Hence or otherwise means you are encouraged to use the previous result but are allowed to use a different method if you prefer. The “otherwise” gives you freedom, but the intended (and usually faster) approach is the one connected to the previous part.
Students who ignore “hence” and use an independent method may not earn full marks, even if their answer is correct. The question is testing your ability to make connections between mathematical results.
”Explain” and “Give a Reason”
Explain requires a written explanation, not just a calculation. You need to describe the mathematical logic in words (or a combination of words and mathematical notation).
Give a reason requires you to state the mathematical principle, theorem, or property that justifies your answer. In geometry, this means naming the relevant angle fact or theorem.
Example: Angle ABC = 90°. Give a reason. Answer: “Angle in a semicircle” (not just “90 degrees” — the examiner wants to know why).
”Express in Terms of…”
Express in terms of means to rearrange or simplify so that your answer only contains the specified variable(s). Remove all other variables from the expression.
Example: Express y in terms of x, given that 3x + 2y = 12. Answer: y = (12 − 3x)/2, or equivalently y = 6 − 1.5x.
A Quick Reference Table
Here is a summary to review before every exam:
- Calculate — work it out, show steps
- Simplify — reduce to simplest form
- Factorise — write as a product with brackets
- Expand — multiply out brackets
- Solve — find the value of the variable
- Show that — prove the given result step by step
- Estimate — round first, then calculate
- Write down — state the answer with minimal working
- Describe fully — give all required details of a transformation
- Hence — use the previous result
- Explain/Give a reason — provide mathematical justification in words
Practice Exercise
Take a past paper and, before solving any question, underline the command word and write a one-sentence plan for what you need to do. This trains your brain to process the instruction before diving into the maths.
Summary
Command words are not optional suggestions — they are precise instructions that determine how you should answer. Misinterpreting them costs marks that are easy to keep. Learn the meaning of each command word, underline them during the exam, and make sure your response matches the instruction exactly. This is one of the simplest and most effective exam technique improvements you can make.
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