IB Numeric Calculation Exam Technique | Step-by-Step Guide to Units, Sig Figs & Partial Credit
Lost marks on a calculation you almost got right? In IB exams, showing your working clearly is the key to maximising partial credit—and a consistent step-by-step routine can make it automatic.
The Bottom Line: One Routine to Rule Every Calculation Question
IB calculation questions reward clarity of process, not just a correct final answer. If you walk into every exam with the same five-step routine—set up → formulate → calculate → check units → verify significant figures—you give examiners a clear trail of reasoning to award marks along the way. This guide breaks down each step, explains the most common traps students fall into, and gives you subject-specific checklists you can use immediately.
Why Does Having a Fixed Routine Matter in IB Exams?
Many students treat calculation questions as a race to the final number. That instinct is understandable, but it costs marks in two specific ways.
First, IB markschemes frequently award method marks (M marks) and error-carried-forward marks (ECF) independently of the final answer. A student who writes a correct formula and substitutes numbers logically—even if they make an arithmetic slip—can still receive most of the available credit. A student who writes only a final answer with no working receives nothing if that answer is wrong.
Second, under time pressure, the most common errors are not conceptual—they are procedural. Forgetting to convert centimetres to metres, dropping a negative sign in an equilibrium expression, or rounding too early: these are routine-failure errors, not understanding-failure errors. A fixed checklist catches them before they reach the answer line.
What Are the Five Steps of a Reliable IB Calculation Routine?
Step 1 — Set Up: Identify What You Know and What You Need
Read the question twice. On the second read, extract and list:
- Given quantities with their units exactly as stated
- The target quantity (what you are solving for) and the unit the question expects
- Any constraints (e.g., assume ideal gas behaviour, ignore air resistance)
Write these in a brief column before touching any formula. This prevents the single most common error in IB Science: substituting numbers in the wrong units.
Step 2 — Formulate: Write the Equation Before Substituting
Write the symbolic equation first, with all variables clearly labelled. Do not write numbers yet. This keeps your logic visible to the examiner and forces you to confirm you have chosen the right relationship.
If you are unsure which formula to use, check your data booklet. IB Physics, Chemistry, and Mathematics all provide approved formula sheets or data booklets; knowing what is in them and where to find it quickly is itself an exam skill.
Step 3 — Calculate: Convert Units, Then Substitute
This is where most marks are lost unnecessarily. The golden rule is:
Convert all units immediately after writing your formula and before substituting numbers.
Do not convert "in your head." Write the conversion explicitly:
v = 72 km h⁻¹ = 72 × (1000 / 3600) m s⁻¹ = 20 m s⁻¹Only after every quantity is in consistent units should you substitute and compute. Keep intermediate values to at least one extra significant figure during calculation; round only at the final step.
Step 4 — Check Units: Use Dimensional Analysis
After substituting but before writing your final answer, verify that the units cancel to give what the question requires. Treat units exactly like algebraic quantities—multiply, divide, and cancel them.
| Calculation type | Unit check example |
|---|---|
| Kinetic energy: ½mv² | kg × (m s⁻¹)² → kg m² s⁻² = J ✓ |
| Molar concentration | mol ÷ dm³ → mol dm⁻³ ✓ |
| Acceleration from F = ma | N ÷ kg → kg m s⁻² ÷ kg → m s⁻² ✓ |
If the units do not cancel correctly, you have either used the wrong formula or made a conversion error. Catching this before the answer line is far better than losing marks after it.
Step 5 — Verify Significant Figures and Reasonableness
Round your answer to the appropriate number of significant figures. Then ask: Is this physically or contextually reasonable?
- A calculated molar mass of 580 g mol⁻¹ for a small organic molecule is a red flag.
- A velocity greater than the speed of light is a red flag.
- A negative absolute temperature is a red flag.
These sanity checks take ten seconds and catch arithmetic errors that dimensional analysis cannot.
How Do Significant Figures Work Across IB Subjects?
Significant figures (sig figs) are one of the most inconsistently applied skills in IB exam scripts—and one of the most reliably penalised.
The core rules are stable across subjects:
| Operation | Sig fig rule |
|---|---|
| Multiplication / Division | Answer has the same number of sig figs as the least precise input |
| Addition / Subtraction | Answer has the same number of decimal places as the least precise input |
| Exact numbers (e.g., stoichiometric coefficients) | Do not limit sig figs |
| Logarithms (pH, pKa) | Number of decimal places in result = number of sig figs in the argument |
However, the number of sig figs expected in a final answer varies by subject, question type, and even markscheme year. Do not memorise a fixed universal rule. Instead:
For a deeper look at Mathematics calculation expectations, see our IB数学 AA/AI HL 完全ガイド.
How Do I Earn Partial Credit Even When I Cannot Finish the Question?
Partial credit—often called error-carried-forward (ECF) or consequential marking in IB markschemes—is one of the most student-friendly features of IB external assessment. Understanding how it works changes your exam strategy significantly.
The key principle: if you make an error in an early part of a multi-part question and carry that incorrect value forward, many markschemes award full credit for subsequent parts provided your method is correct given your earlier answer.
This means:
- Never leave a calculation blank. Even if you know you cannot reach the right answer, write the formula, show partial substitution, and state what you would do next. Examiners can only award marks for what they can see.
- If you get stuck on Part (b), attempt Part (c) anyway using your Part (b) answer, even if you are uncertain about (b). ECF often applies.
- Box or underline your answer to each sub-part clearly. Examiners follow your work linearly; a clearly marked answer helps them apply ECF correctly.
- State any assumptions you make if you cannot derive an intermediate value. Writing "Assuming the pressure in Part (a) is 1.5 × 10⁵ Pa…" and proceeding correctly can still earn method marks.
What Are the Most Common Calculation Pitfalls in Each IB Science and Social Science Subject?
Every subject has recurring errors that appear year after year. Build a personal checklist based on the ones relevant to your subjects.
IB Physics
| Pitfall | Prevention |
|---|---|
| Mixing SI and non-SI units (km vs m, °C vs K) | Always convert in Step 3 before substituting |
| Using degrees instead of radians in circular motion or wave problems | Check whether your calculator is in the correct mode |
| Forgetting vector direction (sign errors in momentum, field direction) | Draw a diagram and define positive direction explicitly |
| Misreading a graph gradient (wrong units for slope) | Label axes and gradient units before calculating |
For a complete overview of Physics HL demands, see our IB物理 HL 完全ガイド.
IB Chemistry
| Pitfall | Prevention |
|---|---|
| Using mass instead of moles (or vice versa) in stoichiometry | Write the mole ratio from the balanced equation before calculating |
| Forgetting to divide by the equation coefficient when calculating moles of reaction | Check the stoichiometric coefficients in your balanced equation |
| pH / pKa logarithm errors (decimal places ≠ sig figs) | Apply the log sig fig rule explicitly |
| Enthalpy sign errors (exothermic vs endothermic) | Define system and surroundings at the start of every thermodynamics problem |
See our IB化学 HL 完全ガイド for deeper coverage of Chemistry-specific exam technique.
IB Mathematics AA / AI
| Pitfall | Prevention |
|---|---|
| Not reading "exact answer" vs "3 significant figures" instructions | Circle the instruction word when reading the question |
| Calculator in wrong mode (degrees vs radians) | Standardise your calculator setup at the start of each paper |
| Premature rounding of intermediate values | Keep at least one extra digit until the final step |
| Forgetting domain restrictions (e.g., ln only defined for positive values) | State domain when writing any logarithmic or inverse trig expression |
IB Economics
| Pitfall | Prevention |
|---|---|
| Calculating percentage change incorrectly (change ÷ original, not change ÷ new) | Write the formula before substituting |
| Inconsistency between a diagram and a written calculation | Draw the diagram first; ensure calculated values match what is labelled |
| Misidentifying base year in index calculations | Underline the base year in the question before starting |
How Should I Build and Use a Personal Calculation Checklist?
A generic checklist is less useful than one tailored to your specific weak points. Here is how to build yours:
Step 1: After each practice paper, record every calculation error in a logbook—not just whether you got the answer right, but where in the process you went wrong. Unit conversion? Formula selection? Sig fig rounding?
Step 2: After four or five papers, patterns will emerge. Group your errors into categories (e.g., "always drop the negative in ΔH," "never convert dm³ to m³ correctly").
Step 3: Write a checklist of no more than eight items—brief, specific, actionable. Laminate it or keep it in your data booklet.
Step 4: Run through the checklist during the review stage of every calculation (after Step 5 above), not before you start. Reviewing before tends to interrupt your thinking; reviewing after catches what you missed.
Time management across multiple subjects and assessments is always a challenge; if you want a framework for balancing exam preparation with Internal Assessments, our IB Diploma の時間管理術 covers practical scheduling strategies.
Putting It All Together: A Pre-Submission Checklist for Calculation Questions
Before moving on from any calculation question in an IB exam, take thirty seconds to run through this:
| Check | Question to ask yourself |
|---|---|
| Formula visible? | Did I write the symbolic equation before substituting? |
| Units converted? | Are all quantities in consistent, appropriate units? |
| Dimensional analysis done? | Do the units cancel to give the correct unit for my answer? |
| Sig figs applied? | Have I rounded at the final step, not before? |
| Answer reasonable? | Is the magnitude physically or contextually plausible? |
| Working shown? | Would an examiner be able to award ECF if I made one error? |
| Answer boxed? | Is my final answer clearly marked? |
This routine does not require extra time—it replaces the unfocused re-reading that most students do anyway. With practice, it becomes automatic.
Developing reliable calculation technique is exactly the kind of skill that benefits from working with someone who has navigated IB exams themselves. At Quick IB, our tutors are IB graduates who can identify the specific procedural gaps in your working and help you build habits that hold up under exam pressure.