IB Math AI HL common mistakes
IB Math AI HL · Understand the traps and how to avoid them.
When a GDC gives a root or intersection, the candidate copies the rounded on-screen value (e.g. x = 1.23) straight into the final answer and into later working, rather than storing the exact value or a full-precision variable.
The screen shows a fixed number of significant figures, and under time pressure the visible digits feel like 'the' answer. Students also forget that AI HL mark schemes award accuracy marks on the unrounded value and penalise premature rounding in multi-step problems.
What to do instead
Store results in calculator memory or use the exact-value/Ans feature, and only round at the very end. Practise a routine: solve, store, then write the full-precision value in working and the rounded value as the final statement. When a question specifies 3 s.f., keep at least 6 s.f. through the calculation.
In arithmetic and geometric sequences, the candidate substitutes n instead of n − 1 (or vice versa) into the general term, and misidentifies whether a real-world model is arithmetic (constant difference) or geometric (constant ratio) before applying a formula.
Textbook formulas are memorised as u_n = u_1 + (n−1)d without connecting the index to what is being counted. Word problems about salaries, depreciation, or savings hide the structure, so students pattern-match on keywords like 'increase' rather than checking whether the increment is additive or multiplicative.
What to do instead
Always write out the first three terms explicitly before choosing a formula, and label what term 1 represents in the context (year 0 or year 1?). For models, compute the difference and the ratio between consecutive given values and let that decide. Check by substituting n = 1 and confirming you recover the first term.
The candidate answers a 'show that' or 'hence' question by jumping to the printed result, or ignores the 'hence' instruction and starts a fresh independent method that does not use the previous part.
Students treat the given answer as a check rather than a target, and 'hence' is read as 'therefore' rather than 'using your previous answer'. Under exam pressure, restarting feels safer than building on a result they are unsure of.
What to do instead
For 'show that', work forward from the given information and only reference the target at the end; never start from the answer. For 'hence', explicitly write 'Using part (a), ...' and substitute the earlier expression. If you cannot see the link, re-read part (a) - the needed form is almost always there.
When finding inverse functions or composite functions, the candidate swaps x and y but then fails to make y the subject, or writes f⁻¹(x) = 1/f(x), and does not restrict the domain of the inverse to the range of the original.
The algebra of rearranging is rushed, and the notation f⁻¹ is confused with a reciprocal. Domain and range are treated as optional decoration rather than part of the function's definition, so the restriction step is skipped entirely.
What to do instead
Follow a fixed three-step routine: write y = f(x), swap x and y, solve for y, then state domain of f⁻¹ = range of f. Explicitly write 'f⁻¹(x) ≠ 1/f(x)' in your notes. Verify by checking f(f⁻¹(x)) = x for a sample value.
In triangle problems, the candidate applies the sine rule when the given information is two sides and the included angle (SAS) or three sides (SSS), where the cosine rule is required, and does not handle the ambiguous case of the sine rule.
Both rules look similar and students select by the word 'triangle' rather than by auditing which quantities are known. The ambiguous case (two possible triangles) is often not taught deeply, so the second solution is missed.
What to do instead
Before computing, list what is known: if you have a matching side-and-opposite-angle pair use the sine rule; if you have SAS or SSS use the cosine rule. For the sine rule, check whether the angle found could also be 180° − θ and whether that is geometrically possible given the angle sum.
The candidate computes a probability or a binomial/ normal result but never states whether events are independent, mutually exclusive, or conditional, and confuses P(A|B) with P(A∩B) or with P(B|A).
The notation is visually similar and the conditional formula is memorised without the meaning of 'given that'. In word problems, the conditioning information is buried in a clause the student skims.
What to do instead
For every probability question, first write the events in words and identify the conditioning event. Use the definition P(A|B) = P(A∩B)/P(B) and rearrange rather than guessing. Test independence with P(A∩B) = P(A)P(B) and mutual exclusivity with P(A∩B) = 0 - these cannot both hold for non-zero probabilities.
In hypothesis testing, the candidate states the conclusion as 'accept H₀' or reports only the p-value without comparing it to the significance level, and mixes up one-tailed and two-tailed critical regions.
Everyday language ('the data supports H₀') leaks into the formal conclusion, and the mechanics of choosing the tail based on the direction of the alternative hypothesis are under-practised. Students also forget that the p-value is compared to α, not to the test statistic.
What to do instead
Use the fixed phrasing: 'Since p < α, reject H₀; there is sufficient evidence for H₁' or 'Since p > α, do not reject H₀; there is insufficient evidence.' Decide the tail by reading H₁ ('greater than' → upper tail, 'different from' → two tails) before touching the calculator. Always state α and the p-value explicitly.
When differentiating or integrating, the candidate drops the chain rule on composite functions, forgets the product or quotient rule, or omits the constant of integration and the limits substitution in definite integrals.
Rules are applied one at a time and the inner derivative is skipped when the expression looks simple. Indefinite and definite integrals are treated as the same procedure, so '+ C' and the evaluation step are lost.
What to do instead
Annotate each step: identify the outer and inner function and write the inner derivative before simplifying. For integrals, write 'let u = ...' when substituting, and for definite integrals always show the bracket with limits before substituting. Make '+ C' a reflex by writing it the moment you integrate.
The candidate finds stationary points but does not classify them, or uses the first derivative alone to claim a maximum/minimum without checking the sign change or the second derivative.
Setting f′(x) = 0 feels like the finish line, and the classification step is treated as optional. The second-derivative test is memorised but its meaning (concavity) is not, so it is applied without checking f″(x) ≠ 0.
What to do instead
After solving f′(x) = 0, always classify: compute f″(x) at each point and state 'f″ > 0 → local minimum'. If f″ = 0, fall back to a sign table of f′. In optimisation word problems, also confirm the answer is within the physical domain of the variables.
The candidate uses a normal distribution or a regression line without checking that the model is appropriate - no check of the correlation coefficient, no comment on extrapolation, and no interpretation of the gradient or intercept in context.
The calculator produces r and a line so readily that students treat the output as the answer. The AI HL emphasis on interpreting models in context is underestimated, and 'r = 0.95' is reported without saying what it means for the data.
What to do instead
For regression, always report r (or r²), state the strength and direction in words, and note whether the prediction is interpolation or extrapolation. Interpret the gradient as 'the predicted change in y per unit increase in x' and the intercept only if x = 0 is meaningful. For normal models, state the mean and standard deviation and justify the normality assumption.