Why Derivations Show the Depth of Your Mathematical Understanding
In the IB Math IA, derivations prove that you’re not just applying formulas — you’re understanding where they come from.
Examiners look closely at how you build your math, not just the final answer.
A clear derivation tells a story: how you moved from a principle or assumption to a precise result.
It’s one of the clearest indicators of a top-tier IA in Criterion C: Communication and Criterion D: Use of Mathematics.
With RevisionDojo’s IA/EE Guide, Exemplars, and Derivation Builder, you’ll learn how to write derivations that are elegant, logical, and examiner-ready.
Quick-Start Checklist
Before writing a derivation:
- Start with a known formula, theorem, or principle.
- Define every variable used.
- Explain each transformation logically.
- Link algebraic steps to real meaning.
- Review a similar example in RevisionDojo’s Exemplars Library.
Step 1: Start From Fundamental Principles
Always begin your derivation with something recognized — a definition, law, or identity.
Example:
“Starting from Newton’s second law, F = ma, we can derive the velocity-time relationship for uniformly accelerated motion.”
RevisionDojo’s Derivation Builder helps you identify appropriate mathematical starting points for your topic.
Step 2: Define All Variables and Constants
Every symbol should be clear before it’s used.
Define variables in context, even if they seem obvious.
Example:
“Let v represent velocity (m/s), a represent acceleration (m/s²), and t represent time (s).”
RevisionDojo’s Symbol Reference Tool keeps variable definitions consistent throughout your IA.
Step 3: Write Each Step on a New Line
Mathematical clarity depends on structure.
Place each major step on its own line, and include short justifications where necessary.
Example:
- F = ma (Newton’s Second Law)
- a = dv/dt (Definition of acceleration)
- F = m(dv/dt) (Substitution)
RevisionDojo’s Equation Formatter ensures clean spacing and professional alignment for multi-step derivations.
Step 4: Explain the Reasoning Behind Each Step
Don’t just show transformations — explain why they make sense.
Example:
“Since acceleration is the rate of change of velocity, substituting a = dv/dt connects force directly to velocity change.”
RevisionDojo’s Step Annotation Prompts help you describe transitions without over-explaining.
Step 5: Keep Algebraic Flow Logical
Examiners love smooth, logical flow.
Avoid large jumps that skip reasoning. If you must skip steps, summarize the logic briefly.
Example:
“After integrating both sides with respect to t, we obtain the velocity equation v = u + at.”
RevisionDojo’s Flow Checker identifies sections that might need additional explanation for clarity.
Step 6: Include Units Where Relevant
Showing units reinforces understanding of physical or applied contexts.
Example:
“Since acceleration (m/s²) multiplied by time (s) gives velocity (m/s), the result’s units are consistent.”
RevisionDojo’s Unit Consistency Checker confirms dimensional accuracy across steps.
Step 7: Use Diagrams to Support Derivations
A simple sketch or labeled diagram can make abstract derivations easier to follow.
For instance, when deriving projectile motion or optimization problems, a clear geometric illustration helps.
RevisionDojo’s Diagram Assistant integrates labeled figures with equations for visual learners and examiners alike.
Step 8: Summarize the Final Result Clearly
End with a concise statement of what you derived.
Example:
“Therefore, the displacement function for uniformly accelerated motion can be expressed as s = ut + ½at².”
RevisionDojo’s Derivation Summary Template helps you conclude each proof in a way that reinforces mathematical insight.
Step 9: Reflect Briefly on What the Derivation Shows
IB rewards students who connect derivations to meaning.
Example:
“This derivation demonstrates how motion under constant acceleration arises directly from the relationship between force and time, linking calculus with physics.”
RevisionDojo’s Reflection Prompts guide you in writing one-sentence reflections after complex derivations.
Step 10: Keep Formatting Clean and Consistent
Presentation matters.
Use the same equation style, numbering system, and font throughout.
Avoid mixing inline and display math unless necessary.
RevisionDojo’s IA Formatting Template ensures that every derivation looks professional and readable.
Frequently Asked Questions
1. How many derivations should my IA include?
Typically 2–4 major derivations are sufficient — focus on clarity and relevance, not quantity.
2. Should I include derivations for standard formulas?
Only if they’re central to your argument or show understanding beyond simple application.
3. How detailed should I be?
Include enough steps for a reader to follow your logic without filling pages with algebraic repetition.
Final Thoughts
Mathematical derivations are your opportunity to show genuine understanding — not just competence.
They transform your IA from a project into a proof of mastery.
With RevisionDojo’s IA/EE Guide, Derivation Builder, and Exemplars, you’ll write derivations that are not just correct but beautifully explained and logically complete.
Call to Action
Master the art of mathematical reasoning.
Use RevisionDojo’s Derivation Builder and IA/EE Guide to create clear, elegant derivations that impress every IB examiner.
