| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 30 | 43 | 57 | 70 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 30 | 44 | 60 | 76 |
| Paper 2 | 110 | 28 | 43 | 58 | 74 |
| Paper 3 | 55 | 17 | 23 | 30 | 36 |
HL Paper 1
Standard work was handled well, but harder complex numbers, scalar-product geometry and the last integration question separated the strongest candidates.
Found difficult
- complex numbers
- vectors, lines and planes
- continuous random variables
- answer form and notation
Well prepared
- arcs and sectors
- rational functions
- differentiation rules
- conditional probability
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | arc length and sector area | Answered well | worked in degrees instead of radiansTip: Sector formulas assume radians; convert any angle first. |
| 2 | rational function graph and its intercepts | Mixed | did not write intercepts as coordinate pairs; swapped the x- and y-interceptsTip: If coordinates are asked for, write the point as (x, y), not just one value. |
| 3 | conditional probability with simultaneous equations | Answered well | Nothing specific reported. |
| 4 | integration by substitution with logarithms | Mixed | wrong limits after the substitution; numerical slips in the final logarithmTip: State the substitution and change the limits explicitly before integrating. |
| 5 | unusual algebra question with a parameter | Answered well | overlooked the case a = -2; numerical slipsTip: Check every special value of a parameter, including those that make a term vanish. |
| 6 | mean and variance of a continuous random variable | Mixed | integrated for a mean that could be written down by symmetry; errors with limits and integration in the varianceTip: Use symmetry of the pdf to state the mean, then compute E(X^2) carefully for the variance. |
| 7 | proof by induction with algebraic fractions | Mixed | vague or inaccurate concluding statement; missing brackets in the inductive stepTip: End an induction proof with a full sentence linking the base case and inductive step to all n. |
| 8 | common tangent condition with trigonometric functions | Mixed | wrote full tangent equations instead of comparing gradientsTip: For curves touching, equate both the function values and the gradients. |
| 9 | scalar product in a geometric proof | Most struggled | rarely completed the scalar product OM.MC accurately; could not express cosine in terms of kTip: Write each vector in components first, then the dot product follows mechanically. |
| 10 | maximising an area using product and chain rules | Mixed | sign error giving 27/2 instead of -27/2Tip: Substitute your x back into the original function and check the sign of the result. |
| 11 | modulus-argument form and complex equations | Mixed | could not explain why the argument takes its value; unfamiliar with substituting w = 1/z; set z = a + bi but did not equate real and imaginary partsTip: After substituting z = a + bi, equate real and imaginary parts to get two equations. |
| 12 | integration by parts and sums of areas | Most struggled | could not handle the limits to reach the required 4nπ; ran out of time on the last partTip: With trig integrals over multiples of π, simplify sin(nπ) and cos(nπ) explicitly at each limit. |
What to practise
- Insist that every line of an induction proof is logically complete.
- Write requested coordinates as ordered pairs.
- Give more practice using the scalar product in geometric proofs and unfamiliar settings.
- Use the mark allocation to judge how much work a part needs.
HL Paper 2
Calculator use and accuracy improved, though many still did long hand calculations instead of using technology and found the unfamiliar counting and parameter questions very hard.
Found difficult
- counting principles
- differential equations
- domain and range
- inequalities
- kinematics
- calculator use
- derivative graphs
- polynomial roots and factors
- volumes of revolution
Well prepared
- linear regression
- trigonometry in triangles
- binomial theorem
- normal distribution
- binomial distribution
- vectors, lines and planes
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | linear regression | Answered well | did not know how to run regression on the calculator |
| 2 | standard SL question | Answered well | Nothing specific reported. |
| 3 | normal distribution followed by binomial | Answered well | could not read the answer from symmetry of the normal curveTip: Use the symmetry of the normal curve about the mean to deduce probabilities quickly. |
| 4 | binomial expansion terms forming a geometric sequence | Answered well | Nothing specific reported. |
| 5 | kinematics: velocity, time and distance | Most struggled | differentiated by hand instead of using the calculator; unsure how to find the required time; misapplied the distance formulaTip: Distance travelled is the integral of |v|; let the calculator evaluate it. |
| 6 | verifying a point lies on a plane and finding a closest point | Mixed | found a normal vector without completing the verification; reached correct coordinates from incorrect workingTip: To verify a point is on a plane, substitute it into the plane equation and show it holds. |
| 7 | volume of revolution about the y-axis | Most struggled | did not express x in terms of y or change the limits; expanded a binomial instead of using the calculator; calculator in degree modeTip: For rotation about the y-axis, integrate π x^2 dy with y-limits. |
| 8 | range of a function and a modulus equation with a parameter | Most struggled | poor notation for the range; did not find the maximum and minimum y-valuesTip: State a range as an interval using the minimum and maximum values of the function. |
| 9 | selections combined with divisibility | Most struggled | could not set up the cases from the divisibility conditionTip: Sort the numbers into classes by remainder first, then count selections from each class. |
| 10 | modelling with a trigonometric function | Mixed | gave a positive amplitude when the graph was reflected; solved by hand instead of with the calculator; tried integration where it was not neededTip: Check whether a cosine model starts at a maximum or a minimum; a minimum means a negative coefficient. |
| 11 | probability leading to a quadratic and integer solutions | Most struggled | could not solve a quadratic with letters as coefficients; did not see that the discriminant must be a perfect squareTip: For integer solutions of a quadratic, require the discriminant to be a perfect square. |
| 12 | Euler's method, homogeneous differential equation and inflection point | Mixed | could not form the iteration with numbers; tried an integrating factor on a homogeneous equation; differentiated instead of copying derivative graphs from the calculator; no justification for choosing the positive valueTip: If the equation is homogeneous, substitute y = vx before trying anything else. |
What to practise
- Give final answers to three significant figures and avoid rounding intermediate values.
- Model clear written justification for reasoning questions.
- Teach kinematics with technology and let students decide when the calculator is the efficient tool.
- Use proper interval notation, paying attention to open and closed ends.
- Follow instructions exactly, for example copying derivative graphs from the calculator when asked.
HL Paper 3
Many candidates made real progress on two unfamiliar investigations in the hour, but rigorous justification, exact logarithm work and general parameter reasoning were weak.
Found difficult
- optimisation
- show that and proof reasoning
- laws of logarithms
- algebraic manipulation
- quadratic functions
Well prepared
- logarithmic functions
- differentiation rules
- graphing with the calculator
- tangents and normals
- sequences and series
- polynomial roots and factors
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | logarithm graphs, x > ln x and tangency of exponential and log curves | Mixed | log graphs touching the axis or on separate axes; found where the minimum occurs but not its value; used a graph alone as justification of a minimum; treated the constant a as a variable when differentiatingTip: Justify a minimum with a derivative test, not a picture, and state the minimum value too. |
| 2 | linear and quadratic functions whose roots form arithmetic sequences | Most struggled | misread the definition of the new function type; checked numerically or worked back from the given result; unsystematic trial and error for integer cases; sign errors after substitutionTip: When several integer cases exist, build a table of values rather than guessing. |
What to practise
- Practise Paper 3 investigations, including parts with several answers best found by a table.
- Discuss what words like hence, deduce, justify and show that require.
- Stress that exact answers rarely come from the calculator and that working backwards from a given answer earns little.
- Use sliders to explore how parameters change a function's behaviour.
- Write legibly and avoid graph paper, which scans badly.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. unnecessary rationales, methodology overviews and subtitles that disrupt coherence
- A. aims that are too ambitious or unrelated to the mathematics used; poor bibliography practice
- B. computer notation, unlabelled diagrams, split equations or tables, and separated variables written without integral signs
- C. personal engagement mistaken for interest or effort rather than ownership of the mathematical process
- D. summaries and lists of assumptions offered in place of critical reflection on the mathematics
- E. advanced mathematics transcribed from sources without explanation a peer could follow
- E. modelling based on a handful of points and correlation taken as causation
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 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 AA HL May 2023 TZ2?
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The questions most candidates struggled with were on scalar product in a geometric proof, integration by parts and sums of areas, kinematics: velocity, time and distance and volume of revolution about the y-axis. 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 complex numbers, vectors, lines and planes, continuous random variables, answer form and notation, counting principles, differential equations, domain and range and inequalities, among others.
What were the grade boundaries for Maths AA HL May 2023 TZ2?
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Maths AA HL: a 7 from 70 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.