| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 34 | 47 | 61 | 78 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 37 | 48 | 64 | 86 |
| Paper 2 | 110 | 39 | 51 | 64 | 85 |
| Paper 3 | 55 | 15 | 24 | 34 | 42 |
HL Paper 1
Routine questions were answered confidently, but induction, complex equations and limits caused trouble and presentation was often scattered across the page.
Found difficult
- proof by induction
- complex numbers
- trigonometric identities
Well prepared
- laws of logarithms
- differentiation rules
- sequences and series
- integration by parts
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | straightforward opening question | Answered well | occasional arithmetic slip in (b) |
| 2 | probability of a union of events | Answered well | Nothing specific reported. |
| 3 | arithmetic sequence from two linear equations | Answered well | work scattered around the page; basic subtraction slip in (b)Tip: Keep each line of working in order so you can check your own results. |
| 4 | area of a triangle using sin of an angle | Mixed | could not find sin BAC or did not think to; error-prone use of half base times heightTip: Find sin of the angle from cos via a right triangle or identity, then use (1/2)ab sin C. |
| 5 | binomial expansion to find n and k | Answered well | did not cancel powers of x before forming equations |
| 6 | proof by induction for divisibility | Most struggled | stalled after writing P(k+1); unclear about what is assumed and what is provedTip: Rewrite the k+1 expression so the assumed multiple appears, then factor out the divisor. |
| 7 | complex equation by equating real and imaginary parts | Mixed | squared 5 + qi incorrectly; did not equate real and imaginary partsTip: Expand carefully remembering i^2 = -1, then match real and imaginary parts. |
| 8 | repeated integration by parts | Answered well | sign slip on one term; unclear derivation of the given answer involving ln 4 |
| 9 | even function and a trigonometric limit | Mixed | claimed f(-x) = f(x) without intermediate steps; omitted limit notationTip: Show f(-x) step by step and keep writing 'lim' until the limit is taken. |
| 10 | logarithms, discriminant and sequences | Answered well | did not reject the d < 0 solutionTip: Check each solution against the conditions in the question. |
| 11 | stationary points, sketch and Maclaurin series | Mixed | gave x-values instead of full coordinates; sketches too small with wrong concavity at endpoints; differentiated cos 2x repeatedly instead of using the known series; did not see that the last part only needed multiplying by eTip: Build new Maclaurin series from booklet ones by substitution rather than differentiating. |
| 12 | De Moivre expansion and roots of a trig polynomial | Most struggled | did not collect real and imaginary terms; equated imaginary parts and stopped; could not explain why roots of sin 5θ give roots of the quarticTip: Link the trig equation to the polynomial explicitly and justify which roots carry over. |
What to practise
- Practise induction proofs for divisibility.
- Keep diagrams a reasonable size and sketch graphs with care.
- Present arguments line by line in a consistent sequence.
HL Paper 2
Generally well done with improving calculator use and broad HL knowledge, although some still used unsuitable algebra and lost accuracy through rounded intermediate values.
Found difficult
- kinematics
- inequalities
- vectors, lines and planes
- linear transformation of random variables
- normal distribution
Well prepared
- arcs and sectors
- scalar and vector products
- rational functions
- counting principles
- discrete random variables
- normal distribution
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | length and angle in a 3D solid | Mixed | gave a vector instead of a length; used position vectors instead of edge vectors; found an area instead of the angle; premature roundingTip: Notation like BV means a length, so give a number, not a vector. |
| 2 | graph sketch and parameter value | Mixed | endpoints poorly positioned; gave k as 2 instead of 1/2 |
| 3 | area and perimeter from circles and sectors | Answered well | missed some lengths in the perimeterTip: List every boundary piece before adding up a perimeter. |
| 4 | particle motion and distance travelled | Most struggled | differentiated by hand before integrating the modulusTip: Distance travelled is the integral of |velocity|; let the calculator do it. |
| 5 | discrete distribution with unknowns | Mixed | found k but did not go on to a; forgot that probabilities sum to 1Tip: Use both conditions: probabilities total 1 and the given expected value. |
| 6 | binomial mean and variance | Answered well | used the general variance formula instead of np(1-p) |
| 7 | counting arrangements and selections | Most struggled | added where they should multiply or vice versa; used permutations instead of combinationsTip: Multiply for successive choices, add for separate cases. |
| 8 | minimising a distance with a parameter | Mixed | expanded the squared magnitude and made errors; gave the minimising p but not the minimum value; assumed p was an integerTip: Answer what is asked: the minimum value, not just where it occurs. |
| 9 | Euler's method and solving a first-order differential equation | Answered well | calculated each Euler step separately; mishandled the constant of integration; gave percentage instead of absolute errorTip: Write the iteration formula and use the calculator's recursion to list values. |
| 10 | normal distribution: inverse normal, discrete counts and IQR | Mixed | substituted probabilities into the z formula; used at most 49 instead of fewer than 49; premature roundingTip: For a discrete count, 'fewer than 49' means at most 48. |
| 11 | rational function with an oblique asymptote and inequality | Mixed | drew only one branch; curves moving away from asymptotes; values not to 3 significant figures; algebraic attempts at the inequalityTip: Draw both branches approaching every asymptote, using a ruler for axes and asymptotes. |
| 12 | reflection in a plane and lines lying in a plane | Mixed | no reasoned argument that the point exists; checked only one point to show a line lies in the plane; algebraic slipsTip: A line lies in a plane only if a point is on it and its direction is perpendicular to the normal. |
What to practise
- Teach students when a calculator method is suitable and how to record it.
- Avoid rounding intermediate values; give answers exactly or to 3 significant figures.
- Practise clear sketches with endpoints and asymptotic behaviour.
- Teach the guide's notation for segments, angles, lines and interval sets.
- Build conceptual understanding in kinematics.
HL Paper 3
Most candidates attempted both investigations within the hour; cubic families with parameters, formal direct proof and the homogeneous differential equation were the hard parts.
Found difficult
- parameters in functions
- show that and proof reasoning
- graph sketching
- chain rule
- differential equations
- integration techniques
- limits
Well prepared
- graphing with the calculator
- stationary and inflexion points
- differentiation rules
- tangents and normals
- differential equations
- implicit differentiation
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | cubic graphs with parameters: intercepts, turning points and a proof | Mixed | integer sets instead of real inequalities for b; did not substitute x into y to complete a show-that; wrong conclusions about which turning point is above the axis; divided by b without checking b is non-zeroTip: Before dividing by an expression, state why it cannot be zero, or split into cases. |
| 2 | orthogonal families of curves and a homogeneous differential equation | Mixed | sketched only half of each curve or left them unlabelled; did not justify dividing by a + b; chain rule errors instead of implicit differentiation; could not integrate 1/x or the v-expression; misused L'Hopital for the final limitTip: Two curves meet at right angles when the product of their gradients there is -1. |
What to practise
- Practise Paper 3 style questions, including parts with several answers.
- Discuss command terms and exact-value requirements.
- Use sliders to show how parameters change graphs.
- Discourage working backwards from given answers and avoid graph paper.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. plans written in the introduction, aims too ambitious and tiny fonts or single spacing used to fit pages
- A. sources left out of the bibliography or padded bibliographies; AI use not acknowledged
- B. unlabelled diagrams, computer notation and unexplained terms from outside the syllabus
- C. hard work and effort mistaken for personal engagement; textbook or historical topics limit ownership
- D. visual readings of graphs and descriptions of results instead of evaluating strategies
- E. mathematics either too far beyond the course to explain or no deeper than SL
- E. correlation used without understanding causality or testing dependence
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 AA 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 AA HL November 2023?
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The questions most candidates struggled with were on proof by induction for divisibility, De Moivre expansion and roots of a trig polynomial, particle motion and distance travelled and counting arrangements and selections. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in November 2023?
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Across the papers the examiners listed proof by induction, complex numbers, trigonometric identities, kinematics, inequalities, vectors, lines and planes, linear transformation of random variables and normal distribution, among others.
What were the grade boundaries for Maths AA HL November 2023?
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Maths AA HL: a 7 from 78 out of 100 overall in November 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.
Related
IB examiner reports: every session, Maths and Physics IB Maths AA HL May 2023 TZ1: the previous report IB Maths AA HL May 2024 TZ1: the next report IB Maths AA HL: the mistakes examiners report most often IB Maths AA HL grade boundaries, every session IB Maths AA HL revision notes IB Maths and Physics topic tests, with markschemes