| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 24 | 39 | 52 | 64 |
HL Paper 1
Well-prepared candidates did well, but too many were under-prepared, with weak calculus and whole topics missing even at a basic level.
Found difficult
- basic differentiation
- chain rule
- product rule
- integration techniques
- complex numbers
- matrix transformations
- second order differential equations
- matrices
- transformations of functions
- phase portraits
Well prepared
- hypothesis testing
- non-linear regression
- logarithms and indices
- inverse functions
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | chi-squared test with a given critical value | Mixed | imprecise wording of hypotheses; used the p-value when a critical value was given; no conclusion in context; muddled conclusion about rejecting H0Tip: If a critical value is given, compare the test statistic with it and conclude in context. |
| 2 | inverse function of a model | Answered well | treated inverse notation as a reciprocal; could not rearrange the equationTip: Read an inverse value as solving the original function equal to that number, perhaps graphically. |
| 3 | right-angled trigonometry in three dimensions | Mixed | used cosine instead of sine; used the sine rule unnecessarily; could not find the right angle; rounded too early in long answersTip: Identify a right-angled triangle containing the required angle and keep full accuracy. |
| 4 | adjacency matrix and counting walks | Most struggled | missed that two edges joined S and D; counted walks of exactly 4 edges rather than up to 4; listed walks unsystematicallyTip: Sum the relevant matrix powers when walks of up to a given length are needed. |
| 5 | probability of successive outcomes and expectation | Most struggled | treated outcomes in different orders as the sameTip: Draw a tree diagram so that different orderings appear as separate branches. |
| 6 | trigonometric model of a rotating wheel | Mixed | could not relate the function to the wheel; used 8 for the period when it should be 16Tip: Link the period to one full rotation of the wheel before writing the model. |
| 7 | savings and interest with the finance app | Most struggled | relied on the compound interest formula rather than the TVM app; wrong signs for PMT, PV and FV; rounded k down instead of up; could not compute the interest earnedTip: Money paid out and money received need opposite signs in the finance solver. |
| 8 | intersection of lines and angle between them | Mixed | found p and q but not the point; solved simultaneous equations by long algebra; used position expressions instead of direction vectors for the angleTip: The angle between lines uses their direction vectors only. |
| 9 | determinant as area scale factor and an inverse matrix equation | Most struggled | did not know the determinant gives the area factor; multiplied in the wrong order or treated a column as squareTip: Write the matrix equation and multiply both sides by the inverse on the left. |
| 10 | logarithmic magnitude scale | Mixed | could not evaluate a correct log expression on the calculator; did not combine a difference of logs into a quotientTip: Use the quotient law to turn a difference of magnitudes into a brightness ratio. |
| 11 | cubic regression and stretching a graph | Mixed | rounded the coefficients badly; ignored or misapplied the horizontal stretch; tried matrix multiplicationTip: A horizontal stretch by factor a replaces x with x divided by a. |
| 12 | phase portraits of coupled equations with complex eigenvalues | Most struggled | guessed matches between portraits and eigenvectors; copied a portrait instead of drawing a spiralTip: Learn how real, repeated and complex eigenvalues shape phase portraits, including spirals. |
| 13 | log-linear model and choosing axes | Most struggled | dropped log Q from the equation; could not make P the subject; could not say what to plot on each axisTip: Keep the logarithm on the variable the stem specifies and plot the transformed variables. |
| 14 | kinematics with product, chain rule and substitution | Most struggled | divided velocity by time to get acceleration; no product or chain rule; evaluated at t = 8 instead of maximising; calculator in degreesTip: Differentiate velocity for acceleration and use a graph on the interval to find its maximum. |
| 15 | second order differential equation solved numerically | Most struggled | little progress made; answers given without the methodTip: Show the iterative expressions entered in the GDC and a few rows of the table. |
| 16 | binomial hypothesis test with type I and type II errors | Mixed | hypotheses not in terms of p or reversed; wrong inequality endpoints; did not state distribution parametersTip: State hypotheses about p and write the distribution with its parameters before using technology. |
| 17 | adding sinusoids using complex exponentials | Most struggled | did not link trigonometric terms to complex exponentials; could not combine the two exponential termsTip: Turn each sinusoid into a complex exponential, add them, then read off amplitude and phase. |
What to practise
- Guide students to the appropriate course and level.
- Teach the whole syllabus and fill gaps for students taught alongside other programmes.
- Keep full accuracy, check degree or radian mode and support GDC answers with evidence.
- State distributions with parameters and give conclusions of tests in context.
- Teach analytic calculus alongside technology so students can choose the best approach.
HL Paper 2
Marks were widely spread; some candidates were excellent while others seemed unprepared or better suited to SL, and analytic skills were often lacking.
Found difficult
- kinematics
- volumes of revolution
- linear combinations of random variables
Well prepared
- basic probability
- binomial distribution
- voronoi diagrams
- definite integrals
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | Venn diagram, conditional probability and binomial conditions | Mixed | wrong value for m; struggled with the conditional probability; used the wrong interval; did not discuss binomial conditionsTip: Know the conditions for a binomial model and judge them against the context. |
| 2 | Voronoi diagrams and perpendicular bisectors | Answered well | used a formula instead of seeing a horizontal bisector; did not use the meeting point of two bisectorsTip: Look at the diagram first; many bisectors can be found by inspection. |
| 3 | differentiation, area and an extended calculus problem | Mixed | could not differentiate accurately; confused derivative notation with the inverse; ignored an instruction in (a)(ii); poor integral notationTip: Practise differentiating by hand and write integrals with limits and dx. |
| 4 | graph theory algorithms and TSP lower bound | Mixed | guessed or left parts blank; thought a smaller lower bound is betterTip: The best lower bound is the largest one found by deleting different vertices. |
| 5 | volume of revolution about the y-axis | Most struggled | did not rearrange for x in terms of y; wrong lower bound; did the integral manually rather than on the GDCTip: For rotation about the y-axis, express x squared in terms of y and integrate in y. |
| 6 | linear combinations of normal variables and a test | Mixed | added standard deviations instead of variances; multiplied SD by 8 or variance by 64; misread GDC output; could not get the p-valueTip: Combine random variables by adding variances, never standard deviations. |
| 7 | motion of particles with vector velocity | Most struggled | ignored vector notation or treated it as complex; gave no reasoning for (b)(ii)Tip: Write displacement as a vector function of time and use the GDC to minimise distance. |
What to practise
- Use marks as a guide to how much work is needed.
- Stress correct reading and writing of notation.
- Teach the assumptions behind each probability distribution.
- Practise volumes about both axes and two-dimensional kinematics.
- Teach all of the syllabus and keep practising analytic skills.
HL Paper 3
Many had partial success, but knowledge gaps and difficulty reading the questions made it hard to complete problems; basic parts were sometimes missed while harder ones were done.
Found difficult
- basic probability
- binomial distribution
- chi-squared goodness of fit test
- geometric sequences and series
- logistic models
Well prepared
- markov chains
- eigenvalues and eigenvectors
- separable differential equations
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | frequency data, binomial goodness of fit and a transition matrix | Mixed | unable to compute the mean of tabulated frequency data; wrong degrees of freedom after estimating a parameter; skipped a straightforward part; did not see a known eigenvectorTip: Reduce the degrees of freedom by one for each parameter you estimate from the data. |
| 2 | differential equation model, geometric sums and limits | Most struggled | did not use t = 0 to fix the constant; could not construct a show that argument; did not handle a variable tending to infinity; left late parts blankTip: Build show that answers forward from the given information, using results such as a geometric sum. |
What to practise
- Link statistics, probability and hypothesis testing rather than treating them separately.
- Practise extracting key information and engaging with the model in long questions.
- Use the GDC more efficiently for statistics and graphing.
- Give students practice in building mathematical arguments.
- Compare sample solutions to learn clear, structured communication.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. plans laid out but not followed, statistics computed by hand and simple algebra over-explained
- B. undefined variables, unlabelled graph axes, no equation editor and wrong vector notation
- C. engagement must show in the mathematics, not only in a personally chosen topic
- D. reflection on outside factors instead of critical analysis of the model; errors named but not quantified
- D. R squared used to compare models when the aim is prediction
- E. SL-only mathematics or complex methods where simpler ones exist are not sophisticated
- E. statistical tests chosen or applied without meeting their conditions
- E. TSP lower bound treated as a possible tour, showing weak understanding of the algorithm
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 November 2022, 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. Corrections: pietro@pietromeloni.com.
Frequently asked questions
Which questions were hardest in Maths AI HL November 2022?
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The questions most candidates struggled with were on adjacency matrix and counting walks, probability of successive outcomes and expectation, savings and interest with the finance app and determinant as area scale factor and an inverse matrix equation. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in November 2022?
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Across the papers the examiners listed basic differentiation, chain rule, product rule, integration techniques, complex numbers, matrix transformations, second order differential equations and matrices, among others.
What were the grade boundaries for Maths AI HL November 2022?
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Maths AI HL: a 7 from 64 out of 100 overall in November 2022. 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.