| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 34 | 46 | 57 | 69 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 31 | 42 | 53 | 64 |
| Paper 2 | 110 | 37 | 50 | 62 | 75 |
| Paper 3 | 55 | 19 | 26 | 33 | 40 |
HL Paper 1
Several questions let candidates show solid knowledge, but inaccurate rounding was common and bearings, 3D problems, log-log graphs and the last few questions attracted very few correct answers.
Found difficult
- bearings
- trigonometry
- three-dimensional geometry
- linearizing data
- linear regression
- rounding and accuracy
Well prepared
- hypothesis testing
- trapezoidal rule
- vector product
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | loan with regular payments using the finance solver | Mixed | used the compound interest formula, which ignores regular payments; wrong signs for PV, FV and PMT; mixed up months and yearsTip: Use the GDC finance app for loans and keep money paid out and received with opposite signs. |
| 2 | one-tailed two-sample t-test | Mixed | reversed or mismatched inequality signs in hypotheses; left the GDC on the unpooled setting; concluded without reference to the contextTip: Select the pooled option for two-sample t-tests and phrase the conclusion in terms of the situation. |
| 3 | segment length and nearest neighbour interpolation | Mixed | confused segment length notation with a line or vector; took a mean or weighted average instead of the nearest valueTip: Learn the notation list in the guide so you know when AD means a length. |
| 4 | trapezoidal rule, integral and percentage error | Mixed | arithmetic slips adding single trapezoids; omitted dx in the integral; evaluated the integral without the GDCTip: Write integrals with dx and let the calculator evaluate definite integrals. |
| 5 | journey using three-figure bearings | Most struggled | unfamiliar with three-figure bearings; drew the second leg not starting where the first ended; missed the right angle in the diagramTip: Revise bearings from prior learning and draw each leg from the end of the previous one with a north line. |
| 6 | projectile height problem | Mixed | did not pick out the key information in part (a); rounded early to one or two significant figuresTip: Keep full calculator values through the working and round only the final answer. |
| 7 | vectors in 3D: triangle area and angle between planes | Most struggled | could not visualise the 3D situation; forgot to halve the cross product magnitude for triangle area; did not know how to find the angle between planesTip: Use normal vectors to find the angle between planes and recall the triangle area is half the cross product. |
| 8 | t-test for linear correlation | Mixed | wrote hypotheses about the p-value or non-linear correlation; reversed the hypotheses; used a one-sided alternative instead of rho not equal to 0; compared r with the significance levelTip: Write hypotheses about the population correlation rho and compare the p-value, not r, with the significance level. |
| 9 | normal distribution with an unknown parameter | Most struggled | was led by standard deviation wording into an unworkable approach; relied on a GDC model that only gave the lower tailTip: Practise inverse normal problems with unknown mean or standard deviation using standardisation. |
| 10 | fitting a curve with a condition on the gradient | Mixed | took many lines to find a simple line; assumed a minimum point read from the diagram; errors solving three simultaneous equationsTip: Use only the conditions the question gives, not features that merely appear in a diagram. |
| 11 | combined weights of independent random variables | Most struggled | did not consider the distribution of the combined weight; confused 2L with the sum of two independent L; mishandled the variance of a multipleTip: Distinguish Var(2L) = 4Var(L) from Var(L1 + L2) = 2Var(L) when variables are independent. |
| 12 | combining trigonometric functions using complex exponentials | Most struggled | tried to merge two trig functions without a valid method; weak algebra after converting to exponential form; confused degree and radian modesTip: Practise rewriting sinusoids as real parts of complex exponentials and check the calculator angle mode. |
| 13 | Euler's method for a second order differential equation | Mixed | could not generate the sequence values on the GDCTip: Set up the coupled recurrence and practise running it in a GDC table or sequence mode. |
| 14 | finding a model from a log-log graph | Most struggled | wrote y = mx + c with no logarithms; found the gradient without logs then added them laterTip: A straight log-log graph means a power model; write log y against log x and convert back. |
| 15 | volume of a solid formed by rotating a hexagon | Most struggled | confused rotation about the y-axis with a horizontal axis; found areas instead of volumes; struggled with truncated cone volumesTip: Sketch the 3D solid first, then use cylinder and cone formulae or volume of revolution. |
| 16 | hardest question on the paper | Most struggled | left blank by many |
| 17 | related rates using the chain rule | Most struggled | did not see that dividing the two given rates was enough; unfamiliar with function notation x(theta); ran out of timeTip: When two rates share a variable such as t, divide them using the chain rule. |
What to practise
- Work through past AI papers and their markschemes to learn the question style.
- Know where formulas sit in the formula booklet and learn the command terms and notation list.
- Practise core GDC skills for statistics, equations and graphs, and know when each applies.
- Avoid premature rounding, watch for question-specific accuracy, and check degree or radian mode.
HL Paper 2
Regression, tree diagrams and hypothesis conclusions were handled well, but many blank answers suggested untaught topics, and rounding, variance estimates, goodness of fit details and phase portraits cost heavily.
Found difficult
- rounding and accuracy
- summary statistics
- chi-squared goodness of fit test
- phase portraits
- matrix transformations
Well prepared
- basic probability
- linear regression
- hypothesis testing
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | linear model, rate of change and regression line | Answered well | rounded incorrectly; left a decimal inside a fraction; missed that the gradient is a change per year; gave the regression of x on yTip: Give units of a gradient as change per unit time and use the y on x regression line for predictions. |
| 2 | sinusoidal model | Mixed | tried to rearrange the equation; took d as the y-intercept; gave half the period; answered in radians when degrees were askedTip: Learn what each parameter in a sinusoidal model means: amplitude, period, phase and principal axis. |
| 3 | probability and binomial distribution | Mixed | used the wrong probability in the binomial model; found P(X >= 2) when P(X > 2) was asked; rounded incorrectlyTip: Translate strict and non-strict inequalities carefully before using the binomial cdf. |
| 4 | Eulerian circuits, spanning trees and TSP bounds | Mixed | explained odd vertices imprecisely; gave a path instead of a cycle; built the spanning tree on the wrong graph; added only one edge in the deleted vertex methodTip: In the deleted vertex algorithm add the two shortest edges back to the removed vertex. |
| 5 | Poisson model and goodness of fit test | Most struggled | computed the variance by formula instead of the GDC; forgot to multiply probabilities by the total to get expected values; used the contingency table rule for degrees of freedom; did not combine small cellsTip: For goodness of fit, combine cells with small expected values and subtract one extra degree of freedom per estimated parameter. |
| 6 | eigenvalues and phase portrait of a coupled system | Most struggled | sign errors in the characteristic equation; errors solving for the eigenvalues; did not know how to sketch the phase portraitTip: Link the signs of the eigenvalues to the shape of the phase portrait and practise sketching each case. |
| 7 | matrix transformations, powers and area by determinant | Most struggled | multiplied the matrix and coordinates in the wrong order; computed the determinant of a matrix power the long way; little attempt at the last partsTip: Image area equals the original area times the absolute determinant, and det of a power is the power of det. |
What to practise
- Insist on exact or three significant figure answers throughout the course.
- Cover the whole syllabus, including graph theory and phase portraits.
- Give more practice on trigonometric modelling.
- Make sure students can get unbiased variance estimates and run goodness of fit tests on the GDC.
- Give regular chances to interpret answers and justify methods.
HL Paper 3
The paper was more accessible and the mean rose slightly, but many schools had not prepared students for the vector kinematics question or unscaffolded parts.
Found difficult
- volumes of revolution
- kinematics
- scalar product
Well prepared
- modelling with functions
- algebraic manipulation
- vectors
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | modelling the volume of a barrel | Mixed | wrote 2r squared instead of (2r) squared; differentiated a constant d as if it were variable; used a rounded coordinate in later working; did not apply the volume of revolution formulaTip: Substitute given constants before differentiating and remember the volume of revolution formula is in the booklet. |
| 2 | aircraft motion with vectors, closest approach and circular motion | Most struggled | did not know speed is the magnitude of velocity; considered full distance instead of only z coordinates; did not recognise motion in a circle; could not compute a scalar product in unfamiliar formTip: Practise kinematics in 2D and 3D, including closest approach and circular motion, and draw a diagram. |
What to practise
- Give kinematics with vectors more focus.
- Start practising extended paper 3 style questions early in the course.
- Use past paper 3 questions right after the matching unit, for example motion in space.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. coherence faded towards the end, and topics beyond the syllabus led to unclear explanations
- A. repeated calculations and explanations of syllabus methods made work not concise; teachers often marked too high
- B. undefined variables, unlabelled axes, large data tables in the text and unreferenced internet diagrams
- C. teachers rewarded effort and presentation rather than independent or creative thinking
- D. reflection that only describes results; little reflection on validity of methods or on residuals
- E. statistics computed by hand, and work beyond the syllabus assumed to be sophisticated
- E. misunderstandings such as claiming the null is proved or removing outliers without a reason
- E. tests used without checking conditions such as 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 TZ1, 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 TZ1?
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The questions most candidates struggled with were on journey using three-figure bearings, vectors in 3D: triangle area and angle between planes, normal distribution with an unknown parameter and combined weights of independent random variables. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2023 TZ1?
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Across the papers the examiners listed bearings, trigonometry, three-dimensional geometry, linearizing data, linear regression, rounding and accuracy, summary statistics and chi-squared goodness of fit test, among others.
What were the grade boundaries for Maths AI HL May 2023 TZ1?
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Maths AI HL: a 7 from 69 out of 100 overall in May 2023 TZ1. 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.