Calculate, Work Out & Evaluate
The Calculation Commands
These three command words all ask you to find a numerical answer, but there are subtle differences in what's expected.
Quick Reference
| Command | What It Emphasises | Working Expected |
|---|---|---|
| Calculate | Precise numerical answer | Full working required |
| Work out | Find the answer | Method should be shown |
| Evaluate | Find the value (often algebra) | Substitute and simplify |
"Calculate" — Precision Required
When you see "Calculate", the examiner wants:
- A precise numerical answer (not a description or estimate)
- Clear working showing your method
- Appropriate rounding if specified
- Units in your final answer if relevant
Example: Calculate the area of a circle with radius 5 cm. Give your answer to 2 decimal places.
$A = \pi r^2$ $A = \pi \times 5^2$ $A = 25\pi$ $A = 78.54$ cm² (2 d.p.)
Note: Write $25\pi$ as an intermediate step — this shows you know the exact answer and earns method marks even if you make a calculator error.
"Work Out" — Show Your Method
"Work out" is the most common command word. It simply means find the answer, but you should always show how you got there.
Example: Work out $\frac{3}{4} + \frac{2}{5}$
$= \frac{15}{20} + \frac{8}{20}$ (common denominator) $= \frac{23}{20}$ $= 1\frac{3}{20}$
"Evaluate" — Substitution Questions
"Evaluate" typically appears with algebraic expressions where you substitute values.
Example: Evaluate $3x^2 - 2y$ when $x = 4$ and $y = -3$
$= 3(4)^2 - 2(-3)$ $= 3 \times 16 - (-6)$ $= 48 + 6$ $= 54$
Common Errors to Avoid
With negative numbers:
- $(-3)^2 = 9$ ✓
- $-3^2 = -9$ ✓ (these are different!)
With order of operations: Always follow BIDMAS:
- Brackets
- Indices
- Division and Multiplication (left to right)
- Addition and Subtraction (left to right)
With units:
- Convert units before calculating if they don't match
- Include units in your final answer
- Check if the question asks for a specific unit
Calculator vs Non-Calculator
On non-calculator papers:
- Leave answers as fractions or in terms of $\pi$ where sensible
- Show every step of arithmetic
- Use estimation to check your answer makes sense
On calculator papers:
- Still write down what you're calculating
- Don't round intermediate answers
- Give your answer to the accuracy requested