| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 26 | 37 | 50 | 63 |
HL Paper 1
Common SL material was handled well and fewer candidates struggled badly, but the later calculus, complex number and statistics questions separated the cohort sharply.
Found difficult
- related rates of change
- differential equations
- integration techniques
- complex numbers
- type i and type ii errors
- conditional probability
- rounding and accuracy
- use of technology
- time management
- reading the question
Well prepared
- quadratic equations
- simultaneous linear equations
- geometric sequences and series
- logarithms and indices
- basic probability
- normal distribution
- basic differentiation
- vector equation of a line
- eigenvalues and eigenvectors
- product rule
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | solving a quadratic and stating an inequality | Answered well | solved the quadratic by formula instead of with the GDC; wrote the inequality in x rather than t; faulty interval notation and roundingTip: Let the GDC solve routine quadratics and state the final interval in the variable the question uses. |
| 2 | forming and solving three simultaneous equations | Mixed | translated a ratio condition the wrong way round (2x = y instead of x = 2y); used elimination by hand and made errorsTip: Check each translated equation against the words, then solve the system with technology. |
| 3 | chi-squared goodness of fit test | Answered well | gave a p-value outside the interval from 0 to 1Tip: Practise running goodness of fit tests on your GDC and sanity-check that a p-value lies between 0 and 1. |
| 4 | probabilities including a conditional probability | Mixed | could not set up the conditional probability in part (c); fraction arithmetic errorsTip: Write the conditional probability as a ratio of two probabilities and let the calculator handle the fractions. |
| 5 | geometric sequence of bounce heights | Mixed | mixed up n and n - 1 in the formulas; confused metres and centimetres; forgot that every distance after the first is travelled twiceTip: Sketch the motion before summing so you see which distances are covered up and down. |
| 6 | vectors and an angle in a triangle | Mixed | read the vector notation as its magnitude; reversed the vector direction; assumed a right angle or found the wrong angle; took the obtuse angle without its supplementTip: Learn the notation list in the guide and keep full accuracy until the final answer. |
| 7 | slope field and stationary points of a differential equation | Most struggled | did not link dy/dx = 0 to maxima and minima; drew the solution curve not through the given initial pointTip: Remember that turning points of solution curves lie where the derivative from the differential equation equals zero. |
| 8 | product rule and point of inflexion | Most struggled | misapplied the product rule for the second derivative; set the function or first derivative to zero to find the inflexionTip: A point of inflexion comes from the second derivative, so find it carefully and set it to zero. |
| 9 | normal probability and distribution of the sample mean | Mixed | wrote GDC syntax instead of mathematical notation; rounding errors; could not find the distribution of the sample meanTip: Use the central limit theorem to get the mean and variance of a sample mean, and write proper notation. |
| 10 | complex numbers in Euler form on an Argand diagram | Most struggled | left the question blank or scored nothing; did not label plotted points; confused by the parameter appearing in modulus and argumentTip: Convert Euler form to Cartesian values with the calculator to picture the points before answering. |
| 11 | eigenvectors and steady state of a transition matrix | Mixed | ignored that integer eigenvector entries were required; gave a decimal steady state when an exact fraction was asked forTip: When an exact answer is required, find the steady state algebraically rather than from a high matrix power. |
| 12 | logs and indices then a Poisson probability | Mixed | typed values into the Poisson function without defining the random variable; relied on calculator notationTip: Define the random variable and its distribution with parameter before calculating any probability. |
| 13 | vector equation of motion and a bearing | Mixed | used a parameter other than t; missed that a 045 bearing means equal east and north components; found t but not the actual clock timeTip: Use the variable the question names and convert your parameter value into the quantity asked for. |
| 14 | integration by substitution leading to a definite integral | Most struggled | missed the link between parts; could not integrate without technology; used the GDC where an exact form was requiredTip: Look for how earlier parts set up later ones and practise indefinite integration by hand. |
| 15 | binomial hypothesis test with type I and II errors | Most struggled | did not state the distribution; did not know the meaning of type I and type II errors; mishandled P(X > 300) on the GDCTip: Learn the definitions of the two error types and convert strict inequalities correctly for discrete distributions. |
| 16 | related rates of change | Most struggled | did not recognise a related rates problem; confused about rate of change and unitsTip: Write the chain rule linking the given rate to the required one and track the units. |
| 17 | fitting a curve through points and differentiating | Most struggled | got no further than substituting the given pointsTip: On the last question, collect method marks by setting up every equation the information gives you. |
What to practise
- Place candidates in the course and level that fits their ability; HL is unfair for those without the background.
- Train students to use the GDC fully while still learning the methods behind it.
- Insist from the start on exact or three significant figure answers.
- Teach students to write clear, concise solutions and model this in class.
HL Paper 2
Where the syllabus had been covered the opening questions went well, but large content gaps and imprecise rounding cost many candidates, and unstructured parts were rarely completed.
Found difficult
- hypothesis testing
- second order differential equations
- euler's method
- spearman's rank correlation
- expected value
- transformations of functions
- affine transformations
Well prepared
- trigonometry
- summary statistics
- eigenvalues and eigenvectors
- binomial distribution
- matrix transformations
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | quartiles, outliers, regression and Spearman's rank | Mixed | used formulas for quartiles instead of technology; used a non-standard outlier rule; did not handle tied ranksTip: Use the 1.5 IQR outlier rule and practise averaging tied ranks before computing Spearman's coefficient. |
| 2 | trigonometry of a grazing area and integration | Mixed | doubled a rounded intermediate angle and lost accuracy; assumed the whole circle could be grazed; tried to integrate by handTip: Carry full calculator values forward and look for how part (a) feeds the next part. |
| 3 | sampling methods and a one-sample test on the mean | Mixed | named convenience rather than quota sampling; wrote the null hypothesis as an inequality; omitted parts of the test; recalculated data instead of transforming mean and SDTip: For a full test state both hypotheses, the p-value, the comparison and a conclusion in context. |
| 4 | second order differential equation and Euler's method | Most struggled | topic not taught; tried to solve the system when only a statement was requiredTip: Learn to rewrite a second order equation as a coupled system and apply Euler's method to it. |
| 5 | binomial model of overbooking and expected cost | Mixed | used calculator notation; could not compute the expected compensation as a sum of x times P(X = x)Tip: For expected payouts build a table of outcomes, values and probabilities and sum the products. |
| 6 | derivative, transformations of a curve and area | Mixed | quoted calculator output for a show that; mishandled horizontal transformations when finding h; no diagram to see which areas to subtractTip: Remember horizontal stretches and shifts act on x in the opposite sense, and sketch areas before integrating. |
| 7 | matrix transformations and invariant points | Mixed | started a show that from the given matrix; did not spot that a point was invariantTip: In a show that, work towards the given result, never start from it. |
What to practise
- Teach the full syllabus so every question is accessible.
- Make sure students can set up and complete a hypothesis test with all its parts.
- Encourage quick calculator solutions, especially in calculus.
- Penalise premature rounding in mocks so students learn to avoid it.
HL Paper 3
Candidates were comfortable with procedural parts but weak at interpretation, communication and problem solving; Voronoi diagrams seemed untaught at some schools.
Found difficult
- separable differential equations
- problem solving
Well prepared
- use of technology
- voronoi diagrams
- adjacency matrices
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | modelling growth with regression, differential equations and half-life | Most struggled | used variables interchangeably; did not know the assumptions for testing a correlation coefficient; could not solve a separable equation with parameters; compared an R squared with an r valueTip: Practise differential equations containing letters as parameters and quote the actual figures you compare. |
| 2 | Voronoi diagrams and adjacency matrices | Mixed | found the wrong perpendicular line; ignored symmetry; did not know the toxic waste site is at a vertex; could not interpret zeros in matrix powersTip: Build intuition for how Voronoi cells change, and try later parts even if earlier ones fail. |
What to practise
- Practise interpreting results, not only running standard methods.
- Teach the assumptions and limits of each hypothesis test, not just how to get a p-value.
- Develop geometric intuition for Voronoi diagrams and their applications.
- Include parameters in modelling equations during lessons.
- Let students compare sample solutions to learn what makes working easy to follow.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. aims lacked focus, explanations were thin and inefficient routes such as hand integration made work less concise
- B. unlabelled diagrams, uncorrected computer notation and needless tables of trivial calculations
- C. effort alone or data copied from the internet does not show personal engagement
- D. reflection left to a closing summary of limitations instead of evaluating methods and results along the way
- E. software outputs such as p-values quoted without stating the test or hypotheses
- E. regression outliers checked per variable rather than looking for influential points on the scatter plot
- E. statistical tests run without checking their conditions or continued after they were shown unsuitable
About this summary
After every session the IB sends schools a subject report: how candidates did on each paper and question, and what teachers should work on. This page is my reading of the Maths AI HL report for May 2022 TZ1, in my own words. No text from the report or from the exam questions is reproduced, and it is not endorsed by the International Baccalaureate.
Session codes: TZ is the time zone variant of the papers. Other variants of the same session:
Frequently asked questions
Which questions were hardest in Maths AI HL May 2022 TZ1?
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The questions most candidates struggled with were on slope field and stationary points of a differential equation, product rule and point of inflexion, complex numbers in Euler form on an Argand diagram and integration by substitution leading to a definite integral. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2022 TZ1?
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Across the papers the examiners listed related rates of change, differential equations, integration techniques, complex numbers, type i and type ii errors, conditional probability, rounding and accuracy and use of technology, among others.
What were the grade boundaries for Maths AI HL May 2022 TZ1?
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Maths AI HL: a 7 from 63 out of 100 overall in May 2022 TZ1. The component boundaries are in the table on this page.
Is this the official IB subject report?
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No. It is my summary of the report the IB issues to schools after each session, rewritten in my own words with a teacher's reading of it. No text from the report or from exam questions is reproduced. Your school's IB coordinator can access the original.