IB command term
Derive in IB exams: what the command term means
By Michael Thompson - Head of Teaching Excellence; 15 years as an IB Coordinator
In IB exams, derive means you rearrange or manipulate a mathematical relationship to arrive at a new equation or relationship. You start from accepted definitions or laws and show every algebraic step that leads to the result.
Paraphrased from the command-term definitions in the IB Diploma Programme subject guides (International Baccalaureate Organization).
At a glance
Data, working and diagrams
Answer shape: Visible working, read data or a labelled diagram
What derive asks you to do
Derive asks you to take a mathematical relationship and rearrange or manipulate it until you reach a new equation or relationship. The work is the point. You build the target relationship from accepted starting points, and the reader should be able to follow each algebraic step you show.
How to set out a derivation
Open by naming the definitions or laws you are allowed to assume and are starting from. Then work forward one operation at a time, so that every line is something the reader can verify. Skipped steps are where derivation marks disappear. Keep your symbols consistent from start to finish, and define any new symbol the moment you introduce it.
Checking your result
Once you reach the final expression, check its units or dimensions. A mismatch is the fastest way to catch an error, and it is a quick check to do before you move on. If the units do not agree, go back through your steps and look for a slip in the algebra.
Telling derive apart from nearby terms
Derive is easy to confuse with other command terms. Calculate, deduce and construct are the three we pair it with. Each has its own page, and reading them side by side helps you see what the examiner wants from each. With derive, the answer is a relationship reached by visible algebra from accepted starting points.
Where it appears
Physics
In physics, derive means starting from the laws or definitions you may assume and rearranging them into the new relationship. Name your starting points first, show each step, and check the units of the final expression.
Physics tutoringMathematics AA
In Mathematics AA, derive means manipulating a mathematical relationship into a new equation or relationship. Show every algebraic step so that each line can be verified, and keep your symbols consistent and defined.
Mathematics AA tutoringMathematics AI
In Mathematics AI, derive again means rearranging a relationship to reach a new one. State what you are starting from, lay out the algebra line by line, and define any symbol you introduce along the way.
Mathematics AI tutoringCommon mistakes
- Skipping algebraic steps because the jump looks obvious to you; the reader cannot verify a step that is not on the page.
- Starting without saying which definitions or laws you are assuming.
- Changing or reusing symbols mid-derivation, or introducing a new symbol without defining it.
- Stating the final relationship and working backwards to fit it, rather than building it forward from accepted starting points.
- Not checking the units or dimensions of the final expression, which would have exposed the error.
Frequently asked questions
- What does derive mean in IB exams?
- It means rearranging or manipulating a mathematical relationship to arrive at a new equation or relationship. You build the target from accepted starting points and show each algebraic step.
- Do I need to state my starting point?
- Yes. Open by naming the definitions or laws you are allowed to assume and are starting from. That tells the reader what your derivation rests on.
- How many steps should I show?
- Show enough that every step is an operation the reader can verify. Skipped steps are where derivation marks disappear, so err on the side of writing a step down.
- How can I check a derivation quickly?
- Check the units or dimensions of your final expression. A mismatch is the fastest way to catch an error, and it tells you to re-check your algebra.
Related command terms
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