| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 32 | 44 | 57 | 68 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 31 | 44 | 57 | 70 |
| Paper 2 | 110 | 36 | 50 | 65 | 79 |
| Paper 3 | 55 | 15 | 21 | 26 | 32 |
HL Paper 1
GDC-driven statistics, 3D solids, directed graphs and standard distributions went well, but simple probability with Venn diagrams, bearings, transformations, volumes about the y-axis and differential equations were weak, and accuracy rules were often ignored.
Found difficult
- basic probability
- financial mathematics
- spearman's rank correlation
- complex numbers
- matrix transformations
- bearings
- volumes of revolution
- separable differential equations
- rounding and accuracy
Well prepared
- use of technology
- hypothesis testing
- volume and surface area
- graph theory
- normal distribution
- binomial distribution
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | reading features from the graph of a height function | Answered well | gave no acceptable reason in the final partTip: Graph the function once on the GDC and read all the required features from it. |
| 2 | chi-squared test with a given critical value | Answered well | used the p-value even though the statistic and critical value were asked forTip: When a critical value is supplied, compare the test statistic with it as the question intends. |
| 3 | Venn diagram with independent events | Most struggled | set up the independence equation wrongly so probabilities summed above one; did not use P(R | S) = P(R) for independent eventsTip: Check that all regions of a Venn diagram add to one, and use independence to simplify conditional probabilities. |
| 4 | compound interest or finance solver problem | Answered well | did not round money to two decimal places as instructedTip: Money answers usually need two decimal places; read the accuracy instruction in each question. |
| 5 | short question with an inequality slip (topic not named in report) | Mixed | used a strict inequality where a non-strict one was needed; struggled with part (c) |
| 6 | measurement of a 3D solid | Answered well | omitted units; did not round to the nearest square centimetre as askedTip: Include units and follow any specific rounding requested in the question. |
| 7 | binomial probabilities and finding a required number of trials | Mixed | without an inverse binomial function, had to scan tables by trial and errorTip: Know how to use a table of cumulative binomial values on your GDC to find a minimum n or k. |
| 8 | directed graph and routes | Mixed | gave routes with too few steps in part (c)Tip: Check that each listed route meets the required number of steps before writing it. |
| 9 | Spearman's rank with ties and coefficient of determination | Mixed | did not average tied ranks; interpretation not in context; odd reasons for avoiding Pearson's coefficient; did not know what R squared meansTip: Give tied values the mean of their ranks and learn what the coefficient of determination tells you. |
| 10 | hypothesis test with a given critical value | Mixed | reversed or incorrect hypotheses; used the p-value instead of the given critical valueTip: Write the null as no effect or equality and use the method the question sets up. |
| 11 | sum of two sinusoids, maximum and phase | Most struggled | had no strategy to find the maximum; did not graph V1 + V2 on the GDCTip: When asked to use technology, graph the combined function and read off amplitude and phase. |
| 12 | related rates of change for a volume | Mixed | chose a chain rule form needing the harder derivative dr/dVTip: Write the chain rule using the derivative that is easiest to compute, such as dV/dr. |
| 13 | matrix transformations and area scale factor | Most struggled | left the question blank; multiplied matrices in the wrong order; used the determinant as a multiplier where division was neededTip: Apply the first transformation on the right of the product and use the determinant to scale areas both ways. |
| 14 | boat motion with bearings and vectors | Most struggled | could not identify the direction of travel; unfamiliar with bearings clockwise from north; set up wrong equations for timesTip: Draw a diagram with a north line and measure bearings clockwise before writing the velocity vector. |
| 15 | interval limits to given accuracy and a justification | Mixed | did not give limits to four significant figures; gave strange reasons in part (b)Tip: Follow the requested number of significant figures and base any reason on the statistics in front of you. |
| 16 | intersection of curves and volume of revolution about the y-axis | Most struggled | left the GDC in degree mode; did not rewrite the curves as x in terms of yTip: For rotation about the y-axis, express x in terms of y and integrate pi x squared dy. |
| 17 | separable differential equation | Most struggled | could not integrate x over x squared plus 1 after separatingTip: Recognise that f'(x)/f(x) integrates to ln|f(x)| plus a constant. |
What to practise
- Make the exact or three significant figure rule a habit from the start of the course.
- Teach students what conclusion follows from comparing a p-value or statistic with the threshold, and to state it in context.
- Check the GDC angle mode for each question, as both radians and degrees were needed.
HL Paper 2
Candidates were broadly well prepared, kept to accuracy rules and coped with HL topics such as graph theory, Markov chains and coupled systems; gaps appeared mainly in SL trigonometry and optimization.
Found difficult
- trigonometry
- optimization
Well prepared
- graph theory
- markov chains
- eigenvalues and eigenvectors
- coupled differential equations
- rounding and accuracy
- use of technology
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | trigonometry in context with area and arc length | Mixed | lacked basic trigonometry knowledge; found the area without the area formula; calculated more sides than neededTip: Revise SL triangle trigonometry and pick the shortest route to the required length or area. |
| 2 | exponential model in context | Answered well | avoided technology when solving; gave three significant figures instead of the nearest minuteTip: Use the GDC to solve and give the answer in the unit and precision asked for. |
| 3 | optimization of dimensions | Most struggled | could not clearly show the given formula; reused a wrong formula from part (a); found only one of two sets of dimensionsTip: When solving with technology, look for every solution in the domain, not just the first one returned. |
| 4 | spanning trees and travelling salesman bounds | Mixed | missed that twice the MST gives an upper bound; started nearest neighbour from the wrong vertex; took the smaller value as the lower bound; did not return to the start vertexTip: Choose the larger lower bound and the smaller upper bound, and make tours start and finish at the given vertex. |
| 5 | Markov chain transition matrix and steady state | Mixed | worked with the transpose and premultiplied wrongly; used 30 instead of 6 from the context; could not set up the steady state equationsTip: Fix whether columns or rows sum to one and multiply the state vector on the matching side. |
| 6 | Poisson distribution, hypothesis test and type II error | Mixed | did not know the conditions for a Poisson model; wrote hypotheses about counts instead of the mean; could not write the critical region as an intervalTip: State hypotheses about the population mean and write the critical region as a clear set of values. |
| 7 | coupled differential equations and phase portrait | Answered well | unclear on what a ratio means; could not draw the particular solution curveTip: After sketching the general phase portrait, practise drawing the trajectory through a given starting point. |
What to practise
- Present organised, legible working with clear labelled diagrams.
- Use technology to avoid premature rounding and give answers to three significant figures.
- Do not neglect SL topics such as trigonometry and basic calculus.
- Write units in contextual answers and use technology to find all solutions in a domain.
HL Paper 3
Harder than intended because several standard techniques were not secure; candidates struggled to plan, to differentiate by hand and to understand and adapt statistical tests.
Found difficult
- chain rule
- problem solving
- t-test
- hypothesis testing
- interpreting results in context
Well prepared
- trigonometry
- use of technology
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | minimising journey time across two regions | Most struggled | assumed the rectangle diagonal makes 45 degrees; added speeds from the two regions; copied a given answer without justification; made invalid algebra while differentiatingTip: Plan the route on a diagram, show each step of a show that, and practise differentiating roots by hand. |
| 2 | paired t-test, regression and Kendall's tau | Most struggled | ran an unpaired test when a paired one was named; described the p-value as the probability the null is true; used the wrong regression line; misused critical regions for a new statisticTip: Learn what a p-value means and read new definitions slowly before applying them. |
What to practise
- Practise making a plan before starting an extended problem.
- Teach clear written communication of reasoning.
- Train students to read unfamiliar information calmly and use it.
- Integrate problem solving throughout instead of treating the syllabus as separate items.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. coherence slipped towards the end and topics beyond the syllabus were poorly explained
- A. repeated calculations and descriptions of syllabus methods reduced concision; teacher marks often too high
- B. undefined variables, graphs without labels, long data tables and unreferenced internet diagrams
- C. effort and presentation rewarded instead of independent or creative thinking
- D. results described rather than evaluated; little checking of test validity or residuals
- E. hand calculation of statistics and unexplained use of methods beyond the syllabus
- E. non-significant results treated as proving the null and outliers removed without context
- E. tests applied without checking normality or minimum expected frequencies
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 2023 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 2023 TZ2?
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The questions most candidates struggled with were on Venn diagram with independent events, sum of two sinusoids, maximum and phase, matrix transformations and area scale factor and boat motion with bearings and vectors. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2023 TZ2?
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Across the papers the examiners listed basic probability, financial mathematics, spearman's rank correlation, complex numbers, matrix transformations, bearings, volumes of revolution and separable differential equations, among others.
What were the grade boundaries for Maths AI HL May 2023 TZ2?
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Maths AI HL: a 7 from 68 out of 100 overall in May 2023 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.