| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 38 | 52 | 65 | 77 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 37 | 50 | 64 | 77 |
| Paper 2 | 110 | 38 | 53 | 68 | 83 |
| Paper 3 | 55 | 27 | 34 | 40 | 47 |
HL Paper 1
Common material was handled confidently, but HL-specific topics gave consistently low scores, suggesting some were barely taught, and basic algebra and rounding were weak.
Found difficult
- summary statistics
- chain rule
- product rule
- markov chains
- eigenvalues and eigenvectors
- separable differential equations
- type i and type ii errors
- kinematics
- volumes of revolution
- linearizing data
- matrix transformations
- coordinate geometry
- sampling methods
Well prepared
- chi-squared test for independence
- linear regression
- sine and cosine rules
- logarithms and indices
- financial mathematics
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | sine and cosine rules and shortest distance to a line | Mixed | calculator left in radian mode; measured to a median or angle bisector instead of the perpendicularTip: Check the angle mode after a reset, and remember the shortest distance is perpendicular. |
| 2 | exponential model solved with logs or the solver | Answered well | did not write the solution in the form requestedTip: Rewrite your answer in exactly the form the question asks for. |
| 3 | chi-squared test for independence | Answered well | wrong rule for rejecting or accepting the null hypothesisTip: Reject the null hypothesis only when the p-value is below the significance level. |
| 4 | reading and drawing box plots with outliers | Mixed | did not see that each quarter holds 25% of data; misread Q1 by one grid division; did not mark outliers on the drawn box plotTip: Read scales carefully and show outliers as separate points with the whisker ending before them. |
| 5 | loan repayments and early settlement with the finance solver | Mixed | could not assign solver values for an early repaymentTip: Sketch a timeline of the loan to decide which values go into each solver field. |
| 6 | geometric probability with an arithmetic series and a binomial model | Mixed | did not recognise a binomial situation; misinterpreted the binomial resultTip: Check for a fixed number of independent trials with constant probability to spot a binomial model. |
| 7 | sampling methods and linear regression | Answered well | could not name the sampling techniqueTip: Learn the names and features of each sampling method in the guide. |
| 8 | matrix transformations and reversing them | Most struggled | often left blank; multiplied matrices in the wrong order or incompatible sizes; could not find the original point from its imageTip: Use the inverse matrix to undo a transformation, and check matrix order before multiplying. |
| 9 | product and chain rule and the tangent slope | Most struggled | forgot to multiply by the inner derivative; skipped part (b) after struggling in (a)Tip: With the chain rule, never forget the factor coming from differentiating the inside function. |
| 10 | inverse square variation and linearizing with logs | Most struggled | guessed the wrong proportionality; did not see that F against d to the minus 2 is a line through the originTip: Plotting against the transformed variable turns variation into a line whose gradient is the constant. |
| 11 | coupled differential equations, eigenvalues and Euler's method | Mixed | solved the characteristic equation when not needed; could not run the booklet iteration on the GDC to fill the tableTip: Practise setting up Euler's method for a coupled system on your own GDC before the exam. |
| 12 | type I error with a Poisson distribution | Mixed | defined a type I error but could not calculate it; chose the wrong Poisson parameter; did not relate Poisson assumptions to the contextTip: A type I error probability is the chance of landing in the critical region when the null is true. |
| 13 | separable differential equation for a proportion | Most struggled | did not know separation of variables; missed the factor of minus one when integrating; substituted 90 instead of 90 percentTip: Watch the sign from the inner derivative when integrating 1 over (1 minus P). |
| 14 | vector kinematics by integration | Most struggled | left out the constant of integration; could not interpret the physical contextTip: Use initial conditions to find the constant whenever you integrate velocity or acceleration. |
| 15 | eigenvectors and steady state of a Markov chain | Most struggled | could not find the eigenvector for eigenvalue 1; could not get the steady state with a non-numeric matrixTip: The steady state is the eigenvector for eigenvalue 1 scaled so its entries add to 1. |
| 16 | translating a curve and the volume of a half revolution | Most struggled | did not bracket x + 0.3; applied the shift to the wrong component; did not subtract two volumes; ignored that only half a revolution was madeTip: Draw the region and decide whether the volume is a difference of two solids before integrating. |
What to practise
- Explain the reasons behind methods, notably for Markov chain eigenvectors, motion problems and solids of revolution.
- Build fluency in differentiation, separation of variables and integration through varied practice.
- Focus on interpreting statistics, including error types, assumptions and sampling.
- Practise geometric reasoning with distances, box plots and forward and reverse matrix mappings.
- Check angle mode after calculator resets and practise timed exam questions.
HL Paper 2
Routine mensuration, differentiation and GDC work went well and presentation was often good, but complex numbers, vectors in context and show that reasoning caused trouble.
Found difficult
- complex numbers
- linear combinations of random variables
- vector equation of a line
- vectors
- adjacency matrices
- modelling with functions
- optimization
- mathematical argument
Well prepared
- volume and surface area
- basic differentiation
- use of technology
- mathematical notation
- rounding and accuracy
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | volume and surface area of a prism and minimising area | Answered well | used the wrong base dimensions for the volume; missing or wrong units; skipped the minimisation part; could not justify that the second derivative is positiveTip: To confirm a minimum, explain why the second derivative is positive over the whole domain. |
| 2 | sinusoidal tide model and solving for times | Mixed | amplitude given as the full range or the maximum; used the wrong tide level or the earliest intersection; rounded t too early before converting to a time; solved analytically instead of with the GDCTip: Amplitude is half the difference between maximum and minimum; read which crossing the context wants. |
| 3 | trapezoidal rule and a bridge arch model | Mixed | wrong strip width or brackets in the trapezoidal formula; divided instead of multiplied by 0.3; gave x without the y-value; checked only the centre of the archTip: Use the mark allocation as a hint that a clearance problem needs more than one check. |
| 4 | adjacency matrix powers and minimum spanning tree | Mixed | ignored the instruction to compute M cubed; did not list every possible route; chose wrong shortest edges; left out the two smallest edges joined to A when finishingTip: Follow the instructed method, and finish the deleted-vertex bound by adding back two edges. |
| 5 | vectors for motion at constant velocity in three dimensions | Most struggled | confused the position of B with vector AB; squared a negative without brackets; used position vectors as direction vectors; set up the wrong position for P2Tip: Use differences of position vectors for directions and bracket negative values before squaring. |
| 6 | Poisson mean and a linear combination of normal variables | Mixed | did not see that the mean equals the given parameter; used binomial ideas wrongly; squared an earlier answer instead of combining variablesTip: When a total of several normal variables is needed, combine their means and variances directly. |
| 7 | complex numbers as rotations and a geometric series | Most struggled | confused the branch length with a coordinate; wrong argument; added ten terms by hand instead of using the sum function; used the wrong common ratioTip: Form an expression for the nth term and apply the GDC sigma tool or the geometric series formula. |
What to practise
- Keep more digits in working to avoid premature rounding.
- Show what was done on the GDC, such as the matrix computed or equation solved.
- Practise brief, clear written justifications.
- Practise interpreting position, direction and velocity vectors in context and learn the guide's vector notation.
- Cover every topic in the guide, including complex numbers and linear combinations of normal variables.
HL Paper 3
The paper was accessible and the extra time helped many reach the end of question 2, but full marks needed broad mastery and some untaught topics gave zeros.
Found difficult
- voronoi diagrams
- expected value
- algebraic manipulation
- use of technology
- summary statistics
Well prepared
- coordinate geometry
- hypothesis testing
- linear regression
- problem solving
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | Voronoi cells for air quality, triangle area and a test on a mean | Mixed | used long algebra where inspection sufficed; computed distances to every site; started a show that from the result; forgot to divide sigma by root n; treated the normal distribution as discreteTip: Look for the simplest method first, such as half base times height for a triangle. |
| 2 | logistic growth model, rearranging and rates of change | Mixed | missing brackets when rearranging; used t = 19 instead of 20; multiplied by only one factor; could not set up the charging point equationTip: If you cannot do a part, invent a value and use it to earn follow-through marks later. |
What to practise
- Cover the whole syllabus, especially hypothesis testing.
- Practise show that questions without working backwards from the given result.
- Encourage students to consider simpler techniques and use command terms and marks as guides.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. aims unclear or abandoned, too much explanation of on-syllabus methods and repetitive work
- B. calculator notation, unreadable diagrams, large tables in the body and no equation editor
- C. explorations that leave little scope for independent thinking
- D. lengthy descriptive reflections and generic AI-style lists of limitations
- E. procedural mathematics without explaining why techniques suit the task
- E. chi-squared used to assess curve fit and test conditions not checked
- E. nearest neighbour tried from a single start and Voronoi diagrams used in unsuitable contexts
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 2025 TZ3, 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 2025 TZ3?
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The questions most candidates struggled with were on matrix transformations and reversing them, product and chain rule and the tangent slope, inverse square variation and linearizing with logs and separable differential equation for a proportion. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2025 TZ3?
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Across the papers the examiners listed summary statistics, chain rule, product rule, markov chains, eigenvalues and eigenvectors, separable differential equations, type i and type ii errors and kinematics, among others.
What were the grade boundaries for Maths AI HL May 2025 TZ3?
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Maths AI HL: a 7 from 77 out of 100 overall in May 2025 TZ3. 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.