| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 33 | 45 | 56 | 66 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 28 | 39 | 50 | 61 |
| Paper 2 | 110 | 36 | 47 | 58 | 69 |
| Paper 3 | 55 | 21 | 28 | 34 | 41 |
HL Paper 1
Students found this paper tougher than usual because it leaned on conceptual understanding and traditional skills in algebra, coordinate geometry and calculus; many lacked these basics.
Found difficult
- coordinate geometry
- product rule
- integration techniques
- confidence intervals
- summary statistics
- binomial distribution
- complex numbers
- logarithms and indices
- mathematical notation
Well prepared
- graph theory
- voronoi diagrams
- poisson distribution
- financial mathematics
- use of technology
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | compound interest with the finance solver | Mixed | did not round to two decimal places as required; mismatched N with P/Y and C/Y; did not subtract the 100 000 from the earlier future value; misread quarterly compoundingTip: Write down every solver entry and give money answers to exactly two decimal places. |
| 2 | lengths and lines in coordinate geometry | Mixed | read the length notation AB as a vector; used position vectors instead of vectors between points; weak algebraTip: AB without an arrow means a length; draw a clear diagram before setting up the algebra. |
| 3 | Spearman's rank correlation of two judges | Mixed | ranked the dogs by their letter labels instead of the judges' order; correlated rankings with the labelsTip: Rank data by the order the judges gave, not by how the items happen to be named. |
| 4 | Voronoi diagram and perpendicular bisector | Mixed | gave the wrong value requested in part (a); disorganised working for the perpendicular bisector; rounded to 3 sf without first showing the exact valueTip: When an exact value is asked for, write it before any decimal approximation. |
| 5 | bounds of a measured time and a speed limit | Most struggled | argued using only the rounded value 1.2 s; used 1.24 or 1.249 as the upper boundTip: A value given to the nearest 0.1 lies within 0.05 either side; test a value in that range. |
| 6 | unbiased variance estimate and a t confidence interval | Mixed | did not use the booklet formula for the unbiased variance; gave s instead of its square; used a z-interval although sigma was unknown; found a single value instead of an intervalTip: When the population standard deviation is unknown, build the interval with the t-distribution. |
| 7 | integration by substitution | Most struggled | confused integrating with differentiating; applied substitution incorrectly; left out the constant of integrationTip: Practise substitution by hand and always add the constant to an indefinite integral. |
| 8 | directed graph and walks from a matrix power | Answered well | drew edges in both directions or crossing edges; did not sum the diagonal of the fourth power; listed routes by handTip: Closed walks of length k are counted by adding the diagonal entries of the k-th matrix power. |
| 9 | rate of change of an area using the product rule | Most struggled | substituted t = 0 values before differentiating; did not apply the product rule; errors expanding bracketsTip: Build a general expression in t first, then differentiate it, then substitute values. |
| 10 | discrete functions given as mappings, inverses and composites | Most struggled | tried to fit a model or plot points; wrote answers in a meaningless equation form; confused inverse, derivative and reciprocal notationTip: Treat a function as a set of input-output pairs and read inverses and composites from the table. |
| 11 | roots of a polynomial and a range for a horizontal line | Mixed | found only two of the three roots; gave the inequality in x rather than y; used the wrong inequality signTip: Sketch the graph to see which values of y give the required number of intersections. |
| 12 | forming and solving a separable differential equation | Most struggled | omitted the proportionality constant; dropped the constant of integration; missing integral signs; could not simplify the final expression for vTip: Translate proportionality with a constant k, then keep both constants until the initial conditions fix them. |
| 13 | Poisson and binomial probabilities | Mixed | used binomial in (c) and Poisson in later parts wrongly; left out the binomial coefficient; wrote only a number with no parametersTip: State the distribution and its parameters so method marks are available even if the number is wrong. |
| 14 | choosing a log-log graph and a power model | Mixed | put w rather than ln w as the left-hand side; could not use log laws to make w the subjectTip: Exponentiate both sides and apply log laws to turn a log-log line into a power model. |
| 15 | normal to a curve and the angle between two lines | Mixed | did not differentiate to get the tangent gradient; did not use gradient equals tangent of the angleTip: Use the arctangent of each gradient to find each line's angle, then subtract. |
| 16 | complex roots and conjugates of a quadratic | Most struggled | skipped showing the conjugate being eliminated; reused the z from part (a) in part (b)Tip: Recall that a complex root times its conjugate gives the squared modulus, a quick route for such problems. |
What to practise
- Avoid premature rounding and carry full calculator values through extended work.
- Use mock exams marked to examiner conventions and let mark allocations guide how much to write.
- Build conceptual foundations in calculus and modelling rather than reducing the course to calculator use.
- Guide students towards the course and level that suits them.
- Practise concise justifications and accurate notation.
HL Paper 2
Marks spanned almost the whole range; prepared candidates did well, but some left whole questions blank and many lacked basic algebra, matrix methods for differential equations and the test for a proportion.
Found difficult
- algebraic manipulation
- modelling with functions
- minimum spanning trees
- hypothesis testing
- second order differential equations
- eigenvalues and eigenvectors
Well prepared
- use of technology
- basic differentiation
- travelling salesman problem
- chi-squared test for independence
- markov chains
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | sequence model of a cushion design | Answered well | misread the first term in part (b); did not simplify algebraic termsTip: Check which term is the first one before building the sequence formula. |
| 2 | functions, integrals and equal derivatives | Answered well | gave coordinate pairs instead of solutions; added a modulus where none was needed; avoided the GDC when equating derivativesTip: Give exactly what is asked, and use the GDC when an analytic method is not demanded. |
| 3 | container volume and optimization | Most struggled | could not handle area and volume formulas of simple shapes; poor algebraic simplification; question left blankTip: Revise mensuration formulas and practise simplifying expressions before differentiating them. |
| 4 | Prim's algorithm and bounds for the TSP | Mixed | applied Prim by eye with no method shown; used nearest neighbour instead of Prim; picked the wrong upper and lower bounds; could not convert minutes to hoursTip: Show each step of an algorithm, including when it stops. |
| 5 | mean, probability, chi-squared independence and binomial test of proportion | Mixed | miscalculated the mean or confused it with the mode; ignored replacement in a compound probability; incomplete hypothesis test write-up; could not do the binomial proportion testTip: For every test write the test name, hypotheses, p-value, comparison and conclusion in context. |
| 6 | second order differential equation via eigenvalues and Euler's method | Most struggled | many did not attempt; eigenvector errors carried forward; gave the Euler answer with little working; used GDC default variables without stating the changeTip: Write Euler iterations in the question's variables and show at least the first step. |
| 7 | Markov chain probabilities and long-term behaviour | Mixed | miscounted days; jumped to a matrix method too early; little clear method shownTip: Count the transitions carefully and show the method behind each probability. |
What to practise
- Teach the whole syllabus, including prior knowledge and simple topics such as the mean.
- Set out algorithms and iterative methods in a clear logical sequence.
- Develop basic algebraic skills alongside GDC use.
- Show all relevant working so follow-through marks are possible.
- Use full calculator values in later parts and round final answers to 3 sf.
HL Paper 3
Most students could attempt most parts of both questions; the main losses came from not reading the guidance given in the stem and from poorly stated hypotheses.
Found difficult
- hypothesis testing
- reading the question
Well prepared
- use of technology
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | hypothesis tests on a population mean and correlation | Mixed | could not answer 1(d)(i) and so lost 1(d)(ii); wrote hypotheses in words mixing sample and populationTip: Write hypotheses with symbols for the population mean or correlation, not in loose words. |
| 2 | distances and bearings on the Earth's surface | Mixed | chose the wrong angle for the bearing; gave far too many significant figures; did not show the angle beyond 3 sf for a given answer; gave a decimal where an exact value was required; forced working to match the given answerTip: Use the hints in the stem, round sensibly, and show more precision than a given answer. |
What to practise
- Practise reading questions carefully and using the hints placed before parts.
- Write hypotheses with the proper population symbols.
- Round final answers sensibly for the context rather than copying the full display.
- When an answer is given, show it to greater accuracy and treat it as help for later parts.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. unclear or drifting aims break the logical development; on-syllabus methods over-explained and repetitive work
- B. calculator notation, small or unclear diagrams, large tables in the body and no equation editor
- C. topics chosen without room for independent thinking; small personal twists to standard problems help
- D. long descriptive reflections and generic AI-produced lists of limitations not tied to the mathematics
- E. procedural work without justifying method choice; complex mathematics preferred over appropriate mathematics
- E. test conditions ignored and chi-squared misused to judge how well a curve fits data
- E. nearest neighbour run from only one start vertex and Voronoi diagrams used where the context does not suit them
- E. template-driven Voronoi or TSP explorations that do not respond to intermediate results
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 TZ2, 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 TZ2?
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The questions most candidates struggled with were on bounds of a measured time and a speed limit, integration by substitution, rate of change of an area using the product rule and discrete functions given as mappings, inverses and composites. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2025 TZ2?
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Across the papers the examiners listed coordinate geometry, product rule, integration techniques, confidence intervals, summary statistics, binomial distribution, complex numbers and logarithms and indices, among others.
What were the grade boundaries for Maths AI HL May 2025 TZ2?
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Maths AI HL: a 7 from 66 out of 100 overall in May 2025 TZ2. 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.