| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 35 | 50 | 62 | 77 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 37 | 53 | 65 | 83 |
| Paper 2 | 110 | 40 | 57 | 70 | 88 |
| Paper 3 | 55 | 17 | 24 | 31 | 40 |
HL Paper 1
Most candidates coped with a good share of the paper and used the GDC sensibly once a method was set up, but forming that set-up, and giving answers to three significant figures, often failed.
Found difficult
- upper and lower bounds
- complex numbers
- chain rule
- linearizing data
- definite integrals
- transformations of functions
- kinematics
- vector product
- markov chains
- conditional probability
- vector equation of a line
- rounding and accuracy
Well prepared
- simultaneous linear equations
- sine and cosine rules
- voronoi diagrams
- basic probability
- volumes of revolution
- slope fields
- eigenvalues and eigenvectors
- poisson distribution
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | geometric sequence terms, partial sum and infinite sum | Mixed | took the wrong value as the first term; used a large n in the partial sum instead of the sum to infinityTip: Identify the first term carefully and recognise when a question needs the infinite sum formula. |
| 2 | inverse function from a graph | Mixed | could not reflect the graph in y = x; did not understand how to obtain the inverseTip: The graph of an inverse is the mirror image in y = x; practise sketching it. |
| 3 | upper and lower bounds and volume of a pyramid | Most struggled | gave a rounded value as the upper bound; added the absolute error to the wrong quantities; misused the pyramid volume formula; used a linear rather than cubic unit conversion factorTip: For bounds, find each measurement's interval first, then combine; cube the conversion factor for volumes. |
| 4 | angles and the sine rule | Answered well | took the supplementary angle as the required angle; used long right-angled trigonometry instead of the sine ruleTip: In non-right triangles reach for the sine rule rather than splitting into right triangles. |
| 5 | quadratic model from three equations | Answered well | rounded the model coefficients too early; solved the system by hand and made errors; used quadratic regression against the instructionsTip: Solve the system with the GDC and follow the method the question specifies. |
| 6 | perpendicular bisector and Voronoi vertex distances | Mixed | wrong gradient of the perpendicular bisector; could not write the equation of a line; calculated only one distance or just read the furthest vertex from the diagramTip: Justify a toxic waste dump choice by computing the distance from each candidate vertex. |
| 7 | probabilities and a conditional probability | Mixed | did not see that the denominator was the complement found earlierTip: Look back at earlier parts; they often supply the denominator of a conditional probability. |
| 8 | complex numbers in Euler form and a sum of sinusoids | Most struggled | could not convert Cartesian form to Euler form on the GDC; worked in degrees despite the given range; could not factor out the t termTip: Practise converting complex numbers between forms on your GDC and keep angles in radians. |
| 9 | sinusoidal model, chain rule and rate of change | Mixed | could not identify amplitude and vertical shift; missed the chain rule in the derivative; chose the value giving a minimum rate of changeTip: Read amplitude and principal axis straight from the graph; a 2-mark part needs little working. |
| 10 | linearizing an exponential model with logarithms | Mixed | rounding errors; checked equivalence at one t value instead of using log laws; misapplied laws of logarithmsTip: Show equivalence of two models algebraically using log laws, not by testing a single value. |
| 11 | area by integration, transformations and volume of revolution | Most struggled | wrote an incorrect integral or accepted a zero area; ignored the x-axis scale and domain in the transformation; used 2 pi instead of pi in the volume formulaTip: For area below the x-axis take the absolute value, and copy the volume formula exactly from the booklet. |
| 12 | tangent from a differential equation and solution curve on a slope field | Mixed | did not see the equation gives the tangent gradient at the point; ignored the required form of the line; solution curve not through the given pointTip: Evaluate dy/dx at the point to get the tangent gradient, and start your sketch at the initial point. |
| 13 | kinematics with velocity and displacement | Most struggled | gave several or negative solutions; unclear final statement; did not set an integral equal to zero for return to startTip: Returning to the starting point means total displacement, an integral of velocity, equals zero. |
| 14 | shortest distance from a point to a line and vector product | Most struggled | did not write a general vector PQ in terms of lambda; gave coordinates as a position vector; did not use the cross product or used wrong vectorsTip: Write PQ with the parameter, set its dot product with the direction vector to zero, then solve. |
| 15 | transition matrix, eigenvalues and steady state | Answered well | poor determinant notation; did not set the characteristic equation to zero; no interpretation of the steady state in contextTip: After finding the steady state vector, explain what it means in the context of the question. |
| 16 | multi-step unstructured problem | Most struggled | very few complete solutions to part (b)Tip: Tackle unfamiliar problems systematically, rereading the question and listing what you know. |
What to practise
- Keep drilling three significant figure answers; one or two figures always loses marks.
- Use mathematical rather than calculator notation in written solutions.
- Show formulas being applied with values substituted, not merely stated.
- Give more practice at problem solving in unfamiliar settings and at GDC work on complex numbers.
- Use mark allocations to judge how much work each part needs and simplify final answers.
HL Paper 2
Many candidates appeared to have covered only SL content with extras, and gaps in algebra and prior knowledge such as units, volumes and frequency table means cost heavily.
Found difficult
- algebraic manipulation
- linear combinations of random variables
- matrices
- summary statistics
- financial mathematics
Well prepared
- hypothesis testing
- trigonometry
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | sector area, arc length and units | Mixed | forgot to double the angle in the sector formula; used the wrong radius; wrong formulas or unit conversionTip: Label the diagram with radius and full angle before substituting into sector formulas. |
| 2 | mean from a frequency table, IQR, outliers and a t-test | Mixed | ignored frequencies when finding the mean; could not read the IQR from a cumulative frequency curve; did not know the upper fence; hypotheses without parameters or reversed, normality stated for the sampleTip: Enter frequency data in the GDC, and write hypotheses using population parameters. |
| 3 | loan repayment with the finance solver | Mixed | could not use the GDC finance solver; forgot the interest in the final monthTip: Practise the TVM solver thoroughly and think about what happens in a final partial payment. |
| 4 | model of height with asymptote and derivative | Most struggled | gave an answer to one significant figure; interpreted the height of the wrong object; wrong asymptote equation; could not differentiate, and found the gradient at an endpoint not the maximumTip: Practise differentiating rational and composite functions by hand, and check maxima across the whole interval. |
| 5 | graph theory: spanning tree and route problems | Mixed | topic not covered; found a circuit where a tree was needed; used the wrong shortest distance between two verticesTip: Know which algorithm answers which question: trees connect, circuits return to the start. |
| 6 | matrix transformations and equation of a line | Mixed | wrong form for the line; multiplied matrices in the wrong order for a composite transformationTip: For a composite transformation, the first transformation applied goes on the right. |
| 7 | normal and binomial combined, sums of random variables and a test | Most struggled | could not combine normal and binomial models; wrong variance of the sum; wrote standard deviation in the normal notation; gave only one assumption and wrong p-valueTip: Remember N(mean, variance) notation and that variances add for independent variables. |
What to practise
- Teach the full HL syllabus rather than SL plus extras.
- Make sure students arrive with secure algebra and basic statistics skills.
- Use correct IB notation throughout the course, as listed in the subject guide.
HL Paper 3
Candidates handled routine calculus and substitution, but separating variables, working with a formula defined in the question and giving answers in terms of a variable were weak.
Found difficult
- separable differential equations
- modelling with functions
- basic differentiation
- algebraic manipulation
Well prepared
- basic differentiation
- use of technology
- basic probability
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | motion modelled by differential equations, separation of variables and Euler's method | Most struggled | could not adapt the chain rule to v and t; dropped the constant of integration or square rooted terms separately; could not separate variables with a v squared term; ignored the four significant figure instruction and did not divide by v for Euler's methodTip: Practise separating variables in many forms and always include the constant of integration. |
| 2 | information gained model with probabilities | Mixed | sketched outside the domain or left intercepts and asymptotes unlabelled; found the derivative but did not state it is negative; used the wrong probability; gave numbers instead of an expression in pTip: To show a function decreases, state that its derivative is negative on the domain. |
What to practise
- Practise exploring unfamiliar models and making decisions from them.
- Solve a variety of separable differential equations including particular solutions.
- Give students chances to explain reasoning and justify conclusions.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. sections poorly linked, over-explained routine syllabus content and long end sections instead of reflecting along the way
- B. calculator style notation, long tables in the body, missing units and poorly labelled graphs
- C. textbook style tasks or simply researching new mathematics leave no room for independent thinking
- D. errors named but never quantified, and models validated on the same data used to build them
- E. work too routine for sophistication, or advanced methods used without showing understanding
- E. chi-squared tests applied to non-frequency data and test conditions not checked
- E. models chosen only by highest R squared without a contextual reason
- C. lists of limitations generated by AI tools count as superficial; AI use must be cited where used
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 2023, 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 2023?
+
The questions most candidates struggled with were on upper and lower bounds and volume of a pyramid, complex numbers in Euler form and a sum of sinusoids, area by integration, transformations and volume of revolution and kinematics with velocity and displacement. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in November 2023?
+
Across the papers the examiners listed upper and lower bounds, complex numbers, chain rule, linearizing data, definite integrals, transformations of functions, kinematics and vector product, among others.
What were the grade boundaries for Maths AI HL November 2023?
+
Maths AI HL: a 7 from 77 out of 100 overall in November 2023. The component boundaries are in the table on this page.
Is this the official IB subject report?
+
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.