| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 26 | 37 | 49 | 62 |
HL Paper 1
Most short opening questions went smoothly, but finance, error types, the trapezoidal rule used for a volume and the final vector and kinematics questions defeated the majority.
Found difficult
- conditional probability
- algebraic manipulation
- percentage error
- financial mathematics
- type i and type ii errors
- trapezoidal rule
Well prepared
- use of technology
- trigonometry
- graph theory
- t-test
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | probabilities from a two-way table | Mixed | treated a selection without replacement as one with replacementTip: Check whether items are put back before multiplying probabilities for successive picks. |
| 2 | angle of depression in right-angled trigonometry | Mixed | took the complement of the angle of depression; carried that wrong angle into a later partTip: The angle of depression is measured down from the horizontal; draw it on the diagram first. |
| 3 | normal distribution probabilities and expected count | Answered well | phrased an expected value as an exact count of people; mixed up the pdf and cdf functionsTip: Use the cumulative function on the GDC for probabilities over an interval. |
| 4 | calculating areas | Answered well | Nothing specific reported. |
| 5 | fitting a cubic model and finding where it is negative | Mixed | missed that the curve is also negative from 0 up to the first rootTip: Sketch the whole curve over the domain before listing where it is below the axis. |
| 6 | adjacency matrix and number of walks | Answered well | Nothing specific reported. |
| 7 | geometric series from sum to infinity and term conditions | Most struggled | read four more as four times; could not form or solve the second equation; did not reject the invalid solutionTip: Translate each condition into an equation carefully and test every solution against the convergence condition. |
| 8 | sector area with bounds and percentage error | Mixed | gave 4 decimal places instead of 4 significant figures; used wrong upper and lower bounds for radius and angle; divided by the estimate rather than the correct boundTip: Write out the bounds of each measurement explicitly before combining them in the area formula. |
| 9 | estimates of mean and variance and a test on the mean | Mixed | left out the frequency list in 1-Var StatsTip: Enter both values and frequencies on the GDC, and notice the test output also gives the estimates. |
| 10 | directed network problem | Answered well | Nothing specific reported. |
| 11 | investment with interest and inflation | Most struggled | misused the GDC finance solver; left the question blank; could not handle the extra condition in part (b)Tip: Study real interest rates; dividing the growth factors gives the exact combined rate, subtracting is only an approximation. |
| 12 | probabilities of type I and type II errors | Most struggled | could not set up the error probability calculationsTip: Learn that a type I error rejects a true null and a type II error keeps a false one. |
| 13 | adding sinusoids using complex exponentials | Most struggled | did not combine the real parts into a single real partTip: The sum of real parts equals the real part of the sum, so add the complex exponentials first. |
| 14 | trapezoidal rule to estimate a volume | Most struggled | did not see that the rule can approximate the integral of y squaredTip: The trapezoidal rule approximates any definite integral, including the one in the volume of revolution formula. |
| 15 | vector form of a line and a determinant problem | Most struggled | could not turn a Cartesian line into vector form; found no strategy for the final partTip: Practise converting between Cartesian and vector forms of a line by choosing a point and a direction. |
| 16 | velocity and acceleration vectors with parallel check | Mixed | applied the product rule wrongly for acceleration; set a vector equal to a multiple of itself without progressTip: Differentiate each component carefully with the product rule before comparing directions. |
| 17 | kinematics with horizontal and vertical components | Most struggled | could not find the horizontal velocity componentTip: Resolve the motion into horizontal and vertical parts and treat each one separately. |
What to practise
- Make sure students know the accuracy rules: final answers exact or to three significant figures, with full accuracy kept in between.
- Teach financial problems involving both interest and inflation, as many seemed never to have met them.
HL Paper 2
Accuracy improved and sequences, trigonometry, matrices and Voronoi diagrams went well, but simple differentiation, linearizing data and the kinematics modelling question caused heavy losses.
Found difficult
- basic differentiation
- linearizing data
- kinematics
- mathematical notation
- reading the question
- interpreting results in context
Well prepared
- rounding and accuracy
- trigonometry
- arithmetic sequences and series
- geometric sequences and series
- matrices
- eigenvalues and eigenvectors
- voronoi diagrams
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | sequences and series with interpretation | Mixed | lost marks on the interpretation parts; used a long method where a GDC sum was expectedTip: Use the GDC summation feature and spend the saved time on the interpretation. |
| 2 | differentiating a model with a parameter and graphing it | Mixed | could not differentiate the expression; treated the constant k as a variable; ignored the domain when drawing the graphTip: Expand products before differentiating and respect the given domain when sketching. |
| 3 | multi-part question needing an exact answer (topic not named in report) | Mixed | did not understand what exact means; weak answer to the last partTip: An exact answer means no decimal approximation; leave surds, fractions or pi in place. |
| 4 | differentiation and linearizing a data set | Most struggled | could not differentiate the given expression; did not understand how to linearize data; gave the final model in x and y instead of the original variablesTip: Practise transforming data with logarithms and write the final model in the variables the question uses. |
| 5 | transition matrix and Markov chain probabilities | Mixed | misread what the matrix entries represent; picked the wrong probabilities; diagonalized the matrix when it was not neededTip: Label rows and columns of a transition matrix with states before using its entries. |
| 6 | kinematics modelling with vectors | Most struggled | wrote answers with no working; confused the variables; made little progress in the final partsTip: Define every variable clearly and show your working even for quick early parts. |
| 7 | final long question (topic not named in report) | Mixed | did not reach the question, likely through lack of time; struggled with the last two partsTip: Manage time so that the final question gets a proper attempt. |
What to practise
- Make sure students and supervisors know the calculator rules and test-mode settings.
- Cover vector applications in a wider range of contexts.
- Do not neglect algebra; basic differentiation and logarithm skills need renewed attention.
HL Paper 3
Most candidates found entry points and scored steadily, but they stalled whenever no method was suggested and wrote hypothesis tests and graph algorithms imprecisely.
Found difficult
- hypothesis testing
- graph theory
- problem solving
- showing working
Well prepared
- summary statistics
- use of technology
- sine and cosine rules
- travelling salesman problem
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | Poisson model, goodness of fit test and critical value for sales | Most struggled | used the independence test rule for degrees of freedom; wrote hypotheses reversed or without the Poisson mean; merged columns needlessly; compared raw profit instead of the expected differenceTip: State full hypotheses naming the distribution and parameter, and write out the observed and expected values you enter. |
| 2 | cosine rule, minimum spanning tree and travelling salesman bounds | Mixed | calculator in radians or entry slips with the cosine rule; did not show the order edges were chosen; gave definitions instead of a reason; could not set up the binomial parametersTip: When applying a graph algorithm, list each edge in the order selected and the running total. |
What to practise
- Teach efficiency: know what working is needed and keep one-mark answers short.
- Use the GDC directly to solve equations rather than rearranging by hand.
- Give students problems where they must choose the method themselves.
- Make sure students can carry out a complete hypothesis test unprompted, including critical values.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. unfocused aims, weak explanations and inefficient routes such as integrating by hand made work less concise
- B. unlabelled diagrams, uncorrected computer notation and tables of trivial calculations in the main text
- C. effort or data taken from the internet is not enough; creative reaction to problems is needed
- D. reflection reduced to a closing summary of limitations instead of justified evaluation during the work
- E. software p-values quoted without naming the test or hypotheses
- E. regression outliers checked per variable instead of looking for influential points
- E. statistical analysis continued after earlier results showed it was not appropriate
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 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 2022 TZ2?
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The questions most candidates struggled with were on geometric series from sum to infinity and term conditions, investment with interest and inflation, probabilities of type I and type II errors and adding sinusoids using complex exponentials. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2022 TZ2?
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Across the papers the examiners listed conditional probability, algebraic manipulation, percentage error, financial mathematics, type i and type ii errors, trapezoidal rule, basic differentiation and linearizing data, among others.
What were the grade boundaries for Maths AI HL May 2022 TZ2?
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Maths AI HL: a 7 from 62 out of 100 overall in May 2022 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.