IB Maths AI SL: the mistakes examiners report most often

Students often do not recognise a binomial situation at all, and when they do they confuse the pdf with the cdf or use the wrong boundary for strict inequalities such as fewer than 7 or more than 72. With the normal distribution the wrong tail is shaded, symmetry is ignored and a right-tail area is entered into inverse normal as if it were a left-tail one.

Why it happens. The calculator does the arithmetic, so the whole question is in translating words into a probability statement, and that step is usually skipped. Discrete and continuous variables are also treated the same way, although only the discrete one changes when the inequality is strict.

How to fix it. Before touching the calculator, write the probability statement, for example P(X <= 6) or P(X > k) = 0.15, and for the normal distribution draw a quick labelled sketch with the region shaded. Learn the four conditions for a binomial model so you can state them and spot them. Practise a set of inequality phrases (at least, fewer than, more than, at most) and convert each one for a discrete variable.

Bounds of a rounded measurement are found with plus or minus 0.1 instead of half the unit, and then the rounded value is used in place of the bound. Percentage error is divided by the approximate value, answers are truncated or rounded to two significant figures, intermediate values are rounded too early, and instructions for two decimal places, exact answers or standard form are ignored. Unit conversions, especially for area and volume, are missed.

Why it happens. Accuracy feels like a detail, so students do not read the instruction or check the final line. Early rounding is a habit from copying short decimals off the calculator.

How to fix it. Store full values on the GDC and round only at the end, to three significant figures unless the question says otherwise. Underline every accuracy or unit instruction and check it before moving on. For bounds, write the interval as value minus half a unit to value plus half a unit. Remember that percentage error always divides by the exact value.

To find an inverse value, students compute f(a) instead of solving f(x) = a, or waste time finding an inverse expression algebraically. Ranges are written with the inequality reversed or as a closed interval, asymptotes are given as a number instead of an equation with the right variable, and sketches do not approach the asymptote or ignore the domain.

Why it happens. In AI the inverse is mostly needed as a value, but students learn the algebraic method from other courses and apply it automatically. Notation for domain, range and asymptotes is rarely practised as a skill on its own.

How to fix it. Read f inverse of a as the x that gives f(x) = a, and solve it on the GDC. Write ranges as inequalities in the output variable, and asymptotes as equations such as y = 3 or T = 20. When sketching, mark the domain endpoints and any asymptote first, then draw a smooth curve that respects both.

Students cannot say what a parameter means in context, for example the initial value of an exponential model or the rate in a linear one, and they take a power of zero as zero. Logarithmic models fail when the base is treated as part of the argument or the equation is not rewritten in exponential form. Comments on whether a model is suitable are vague or missing.

Why it happens. Models are learnt as function families, while the questions ask what the numbers mean for the situation. Logarithms are rarely used outside these questions, so the rules are weak.

How to fix it. For every model you meet, write one sentence on the meaning of each parameter, with units. Substitute t = 0 to find initial values. For a log model, practise switching between log form and exponential form before solving, and use the GDC when an exact answer is not required. When asked about suitability, refer to a specific value or behaviour of the model, such as a negative output or growth without limit.

Students add probabilities along branches that should be multiplied, forget to reduce the sample space for a conditional probability, and treat dependent selections as independent. In probability distribution tables they assume outcomes are equally likely or let the total exceed 1, and for a fair game they set the expected value to 1 instead of 0.

Why it happens. Probability questions are short and wordy, and students start calculating before they have decided which events are involved and whether a condition is given. Expected value is remembered as a formula without its meaning.

How to fix it. Draw the tree, Venn diagram or table first, and mark the event asked for on it. For any question with given, if or knowing that, write the denominator before the numerator. In every distribution table check that the probabilities add up to 1, and remember that fair means the expected gain is zero.

Students assume a right angle or an isosceles triangle that is not given, pair the wrong side and angle in the sine or cosine rule, leave the calculator in radians, and measure angles of depression or bearings from the wrong line. With sectors and solids they use the wrong radius, miss faces of a surface area, and treat a 3D situation as a flat triangle.

Why it happens. Diagrams in context are often not drawn, or are drawn without the given information, so students guess the shape. Right-angled trigonometry is the most practised, and it gets used where it does not apply.

How to fix it. Always draw or redraw the diagram and label every given length and angle, including north lines for bearings. Use right-angled ratios only when a right angle is given or proved, and otherwise choose sine or cosine rule from what is known. Check degree mode before the paper. For solids, list each face or part and its formula before adding.

In show that questions students start from the given answer or verify it instead of deriving it, and in justify or explain questions they give a one-word conclusion or never make the comparison explicit. Long or unfamiliar questions are left blank. Many solve by hand what the GDC does at once, while others write calculator notation such as E-notation as the answer.

Why it happens. AI SL questions are long and set in context, and weaker students lose the thread after the first part. Work that the GDC does feels like it needs no explanation, so the method is not written.

How to fix it. In a show that question, never use the given value until the final line. When asked to justify, state the values you compare and write a full sentence that answers the question. Attempt every part of a long question, since later parts often do not depend on earlier answers. Use the GDC for solving, graphing and statistics, and write down what you entered in standard notation.

Terms like k/x are not rewritten as a negative power, so they are differentiated wrongly. The y-coordinate is substituted into the derivative or the function is evaluated instead of the gradient, the normal gradient is not the negative reciprocal, and the line is not given in the requested form. In optimisation, students give the maximum value when x is asked or the reverse, do not set the derivative to zero, and keep answers that make no sense in context.

Why it happens. The power rule is practised on positive powers, and the steps for a tangent or normal are learnt as a recipe without a picture of what each number is. Optimisation needs a function built from the context first, which many students skip.

How to fix it. Rewrite every fraction with x in the denominator as a power before differentiating. For tangents and normals write three labelled lines: the point, the gradient from f'(x), then the line. In optimisation, write the function of one variable, set the derivative to zero, check the domain, and answer exactly what was asked.

Outliers are argued in words instead of with the 1.5 IQR fences, quartiles are read from the wrong axis of a cumulative frequency graph, and frequencies are left out of the mean of a table. With correlation, students give r squared instead of r, use raw data instead of ranks for Spearman's coefficient, mishandle tied ranks and describe strength without context.

Why it happens. These are seen as easy marks, so the definitions are never learnt precisely. The GDC is often not set up to use a frequency list, and students who compute by hand run out of time.

How to fix it. Learn the outlier test as a calculation: find Q1 and Q3, compute both fences, and compare the actual data value with the fence. Practise entering data with frequencies on the GDC. For any coefficient, state its value, its direction, its strength and what it says about the two named variables, and know why Spearman's coefficient is used when the relationship is not linear.

In the trapezoidal rule students substitute x-values instead of y-values, use the wrong strip width, or drop the brackets around the middle terms. Integrals are written without dx or with wrong limits, an evaluated number is given when the integral itself was asked, and in indefinite integration the constant is omitted or not found from the given condition. Some do not see that a rate given as a derivative must be integrated.

Why it happens. The trapezoidal formula is in the booklet, so its meaning is not learnt, and the notation for integrals is treated as optional. Questions that give a rate of change rarely say integrate.

How to fix it. Before using the trapezoidal rule, write h and list the y-values in a table. Always write the full integral with limits and dx, then evaluate it on the GDC. When you integrate without limits, add + c at once and use the given point to find it. If a question gives a rate such as dP/dx and asks for P, integrate.

The most frequent error is using the compound interest formula from the booklet when there are regular payments. In the solver, PV, PMT and FV are given the same sign, the number of periods or the compounding frequency is wrong, FV is not set to zero for a loan that is paid off, and the rounding to the nearest cent or whole month is ignored.

Why it happens. Students learn the finance app as a list of boxes to fill without a picture of where the money flows. The formula feels safer because it is printed in the booklet, even when it does not apply.

How to fix it. Ask one question first: are there regular payments? If yes, use the solver. Decide the sign of each amount from the point of view of the person, money in positive and money out negative, and write the solver entries in your answer. Practise loans, savings with deposits, depreciation and real return with inflation until the set-up is automatic, then check that the answer makes sense in context.

The calculation is usually done on the GDC, and the marks go in the words around it: hypotheses that do not mention population means or do not name the variables, a p-value read from scientific notation as greater than 1, the wrong comparison with the significance level, and conclusions with no context. In t-tests the pooled option is left off and one-tailed and two-tailed tests are confused.

Why it happens. Students treat a test as a button to press and learn the output, not the logic. The hypotheses and the final sentence look like formalities, yet they carry a large share of the marks.

How to fix it. Learn a fixed template: H0 and H1 in terms of the population parameter or of independence between the two named variables, the test statistic or p-value with its value, the comparison with the significance level, and a conclusion in the words of the question. Check every p-value is between 0 and 1 before you use it. Do the pooled setting and the one-tailed or two-tailed choice deliberately each time, from the wording of H1.

Statements such as twice as many adults are written the wrong way round, every equation in a system is set equal to the same total, and variation is written without a constant of proportionality or ignores the square or cube. Once the equations are set up, students solve them by hand over many lines instead of with the GDC, and brackets go missing when expressions are multiplied.

Why it happens. Translating words into algebra is a separate skill from solving, and it gets little practice. Students who struggle with algebra then avoid the GDC solver, which is exactly what makes it quick.

How to fix it. Define each variable in words before writing any equation, and test a statement like y = 2x with small numbers to see if it says what the question says. For variation, always start from y = kx^n with n read from the wording, find k, then use it. Solve linear systems with the GDC and show the equations you entered.

The b parameter is the most common failure: students do not find the period first, or estimate it from the graph instead of using the given times. Amplitude and principal axis are found with flawed methods, a negative amplitude is given, the principal axis is written as a function instead of a line, and answers are read off the diagram instead of solved on the GDC.

Why it happens. Sinusoidal models appear almost every session but usually in a context, so students have to build the model from a description, which is harder than recognising a function from its equation.

How to fix it. Follow the same order every time: maximum and minimum, then amplitude as half their difference, principal axis as their mean, period, then b as 360 divided by the period in degrees. Check the starting point to decide between sine, cosine and negative cosine. Solve any equation with the model by intersecting graphs on the GDC and read all solutions in the domain.

Students use the sum formula when a single term is asked, or the other way round, apply arithmetic formulas to a geometric sequence, take the wrong common ratio from a percentage change, and round n the wrong way so that a total falls short. In context the first term and what is being counted are often misread.

Why it happens. The formulas are easy to find in the booklet, so the real decision, which quantity and which type, is made in a hurry. Percentage growth is turned into a ratio by habit rather than by reasoning.

How to fix it. Before choosing a formula, write whether the sequence is arithmetic or geometric, what u1 represents and whether you need a term or a sum. Turn a percentage change into a multiplier explicitly, for example an increase of 5 per cent gives 1.05. When solving for n, check the value either side in a GDC table and decide in context whether to round up or down.

Students draw the line through two sites instead of their perpendicular bisector, use an endpoint instead of the midpoint, forget the negative reciprocal gradient, and give a vertex or midpoint without coordinates. When interpreting the diagram they compare distances from only one site or misunderstand what an edge or a larger cell means.

Why it happens. Voronoi diagrams are new to most students and are often taught as a drawing exercise, so the link with the perpendicular bisector and equal distance is not secure.

How to fix it. Learn the three steps for a bisector: midpoint, perpendicular gradient, equation through the midpoint, and show all three. Remember that every point on an edge is equally far from two sites and a vertex is equally far from three. In interpretation questions compute the distance to every relevant site and compare them explicitly.

Each report lists, paper by paper, the areas candidates found difficult. Every item was assigned to one of the areas above, with its session and paper recorded. An area counts once per report, however many papers mention it; each time zone has its own report.

The count says how often examiners raise something, not how many marks it costs. The explanations and the advice are mine, from teaching the course, and no wording from the reports or from exam questions is reproduced. Session by session summaries are in the examiner reports. This is independent work and is not endorsed by the International Baccalaureate. Session codes: M is May, N is November. Corrections: pietro@pietromeloni.com.