IB Math AI SL common mistakes
IB Math AI SL · Understand the traps and how to avoid them.
Rounding intermediate values (e.g., a z-score, a partial sum, or an intermediate probability) to 2 or 3 significant figures and then carrying that rounded number into the final calculation, producing a final answer that differs from the mark-scheme value.
Candidates copy intermediate calculator displays into their written work and then re-enter the rounded value, because the paper looks neater and the AI SL formula booklet encourages writing values step by step. The habit is inherited from earlier courses where rounding was tolerated.
What to do instead
Store every intermediate result in a calculator variable (e.g., STO on a GDC) and reference the variable, not the displayed digits. Only round at the point of writing the final answer, and round to 3 significant figures unless the question specifies otherwise. Do one timed set of past-paper questions where you deliberately keep full precision and compare your answer with the mark scheme.
Applying a percentage change to the wrong base or reversing the direction: for example, computing a 15% increase as x × 0.15, or treating a 20% decrease followed by a 20% increase as no net change.
Percentages are learned as 'multiply by the percentage', and successive percentage changes look additive because the numbers are the same magnitude. Candidates also forget that the multiplier for an increase is 1 + r and for a decrease is 1 − r.
What to do instead
Always write the multiplier explicitly before calculating: increase by r% is ×(1 + r/100), decrease is ×(1 − r/100). For successive changes, multiply the multipliers (0.8 × 1.2 = 0.96, a 4% net decrease). Practise by converting ten everyday statements into multipliers until it is automatic.
Confusing arithmetic and geometric sequences: using the arithmetic formula u_n = u_1 + (n − 1)d for a geometric sequence, or misidentifying the common difference versus the common ratio when the sequence is given in context (e.g., a salary rising by 3% each year versus by a fixed amount).
The two formula-booklet entries look structurally similar, and word problems hide whether the growth is additive or multiplicative. Candidates also mis-index, using n instead of n − 1 for the first term.
What to do instead
Before choosing a formula, compute the first two differences and the first two ratios from the given terms; whichever is constant tells you the type. Write down u_1 and either d or r explicitly, then substitute. Check by computing u_2 from your formula and confirming it matches the given second term.
Reading a graph or a function's behaviour incorrectly: stating the domain or range from the visible window rather than from the function itself, or misidentifying the axis of symmetry and vertex of a quadratic given in completed-square or factorised form.
The GDC window becomes the de facto definition of the function, and candidates do not distinguish what is shown from what is true. For quadratics, the sign inside the bracket (x − h)² is frequently mishandled.
What to do instead
For domain and range, reason from the algebraic form first (denominators, square roots, the squared term), then use the graph only to confirm. For y = a(x − h)² + k, state the vertex as (h, k) and check the sign of a to decide maximum or minimum. For factorised form, the axis of symmetry is the midpoint of the roots.
Solving an equation graphically or with the GDC and reporting only one intersection or one root when the equation has several, or reporting a solution outside the stated domain.
Candidates graph the two sides, see one obvious intersection in the default window, and stop. The default window may not show all intersections, and the question's stated interval is often ignored.
What to do instead
Set the window deliberately from the question's domain before graphing, then use the GDC's intersection tool repeatedly (or the polynomial root tool) and count the solutions you find. Write each solution with its context and check it lies in the required interval. If the question says 'hence' or 'exact', decide whether an algebraic method is expected instead.
Using the sine rule in a triangle where it does not apply (no matching side–angle pair), or using the cosine rule with the wrong included angle, and forgetting to check the ambiguous case for the sine rule.
Both rules are in the formula booklet and look interchangeable; candidates pattern-match on 'triangle with an angle' rather than checking which data are given. The ambiguous case is rarely practised.
What to do instead
Classify the triangle first: if you have a side opposite a known angle, use the sine rule; if you have two sides and the included angle, or three sides, use the cosine rule. State the pairing (a/sin A = b/sin B) before substituting. When finding an angle with the sine rule, check whether the obtuse supplement also fits the given data.
Mixing up surface area and volume formulas, or applying a scale factor to area or volume without squaring or cubing it (e.g., doubling the radius and expecting the volume to double).
The formulas for cones, spheres and pyramids are visually similar in the booklet, and similarity scaling is taught as a single ratio rather than as a ratio raised to a power.
What to do instead
Write the formula with its name before substituting, and label units (cm² versus cm³) as a check. For similar figures, record the linear ratio k, then area ratio k² and volume ratio k³ explicitly. Do a quick dimensional check: an area answer must involve two lengths multiplied.
Confusing correlation with causation, or reporting r and the regression line as if they prove a relationship, and extrapolating a regression line well beyond the data range.
The GDC produces r and a line of best fit automatically, so candidates treat the output as a conclusion rather than a description. The AI SL syllabus emphasises interpretation, but practice tends to focus on computation.
What to do instead
After computing r, write one sentence on strength and direction and one sentence on what it does not show (causation, or prediction outside the observed range). Check r against the scatter plot before commenting. When asked to interpret the gradient or intercept, do so in the units of the context.
Computing a probability for 'at least one' or a conditional probability by adding or multiplying raw probabilities instead of using the complement or the conditional formula, and failing to distinguish independent from mutually exclusive events.
The phrases 'at least', 'given that' and 'or' are read quickly, and the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B) is applied without the subtraction, or applied when events are mutually exclusive and the subtraction is unnecessary.
What to do instead
Translate the wording before calculating: 'at least one' means 1 − P(none); 'given that' signals P(A|B) = P(A ∩ B)/P(B); 'mutually exclusive' means P(A ∩ B) = 0; 'independent' means P(A ∩ B) = P(A)P(B). Draw a Venn diagram or tree diagram for every multi-stage problem and label the branches with probabilities.
Differentiating or integrating a term and losing the coefficient or exponent, or omitting the constant of integration, and misinterpreting the derivative as the value of the function rather than its rate of change.
The power rule is applied mechanically under time pressure, and the constant of integration is treated as optional notation. In context questions, candidates compute f′(x) and then answer as if they had computed f(x).
What to do instead
Write the rule beside each term before applying it (d/dx of axⁿ is anxⁿ⁻¹; ∫axⁿ dx is axⁿ⁺¹/(n + 1) + c). Always include + c for indefinite integrals. For context questions, state in words what the derivative or integral represents (rate of change, accumulated total) before substituting a value, and check units.