| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 31 | 44 | 56 | 70 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 31 | 46 | 59 | 75 |
| Paper 2 | 110 | 29 | 44 | 57 | 73 |
| Paper 3 | 55 | 17 | 23 | 29 | 36 |
HL Paper 1
Presentation was better than in recent sessions, but many candidates who were secure on SL ideas could not access the HL questions, and vectors remained a weak spot.
Found difficult
- equations reducible to quadratics
- polynomial roots and factors
- graph transformations
- volumes of revolution
- vectors, lines and planes
Well prepared
- rational functions
- discrete random variables
- graph transformations
- differentiation rules
- sequences and series
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | rational function: intercepts, asymptotes and inverse | Answered well | evaluated f(0) when the zero of the function was asked for; wrote the horizontal asymptote as a number rather than an equation y = ...; read the inverse notation as a reciprocalTip: An asymptote is a line, so always state it as an equation such as y = k. |
| 2 | expected value and estimating a count | Answered well | used the single probability instead of the expected value from the first partTip: When a later part says 'hence', reuse the quantity you just found rather than restarting from raw data. |
| 3 | trigonometric equation as a quadratic in sin x | Mixed | relied on trial and error and found only some solutions; errors solving the quadratic or converting to exact anglesTip: Spot the hidden quadratic, solve it carefully, then list every angle in the given domain. |
| 4 | exponential equation as a quadratic in e^x and the discriminant | Most struggled | did not see the quadratic in e^x; required a strictly positive discriminant for at least one real root; tried to isolate ln k and lost the threadTip: Substitute u = e^x, then remember u must be positive when you interpret the roots. |
| 5 | period of a sine function and sketching it | Mixed | found the period but did not set it equal to 2π/q; substituted a point instead of using the periodTip: Link the period to the coefficient directly: period = 2π divided by the coefficient of x. |
| 6 | related rates for an equilateral triangle | Most struggled | substituted the given side length before differentiating; wrong expression for area or height in terms of the side; wrong exact value of sin(π/3)Tip: Write the area as a function of the changing variable first; substitute numbers only after differentiating. |
| 7 | complex roots of a cubic with unknown coefficients | Most struggled | treated factors as if they were roots; did not identify 3i and -3i as the roots; messy incorrect sum or product of rootsTip: Keep factors and roots distinct: z - a is a factor exactly when a is a root. |
| 8 | sketching a graph after two reflections | Mixed | applied only the reflection in the x-axis and missed the second oneTip: Break a composite transformation into single steps and sketch each one in order. |
| 9 | volume of a ring about the y-axis between curves | Most struggled | assumed the cylinder and sphere had the same radius; wrong limits of integrationTip: Draw the cross-section and label each radius before you set up the volume integral. |
| 10 | multi-part algebra question | Answered well | gave only the positive value in (d) and so could not continue to (e)Tip: Check whether both signs of a square root are valid before discarding one. |
| 11 | trigonometric derivatives and minimising a length | Mixed | could not rearrange the derivative to the required form; could not find the other trigonometric ratio needed for the show-that; found the second derivative test but not the minimum value; weak numerical evidence in the justificationTip: After confirming a minimum with the second derivative, also evaluate the function to state the minimum value. |
| 12 | 3D vectors: scalar product, shortest distance, cone vertex | Most struggled | used magnitudes or the cross product instead of the scalar product formula; did not use the perpendicular as the minimum distance; no attempt at the final partTip: The closest approach of a point to a line is measured along the perpendicular; sketch it first. |
What to practise
- Cover every syllabus topic thoroughly; many blank responses suggested topics were never taught.
- Practise rewriting exponential, trigonometric and surd equations as quadratics.
- Use correct language for polynomials and never call a factor a root.
- Encourage labelled diagrams for volumes of revolution and 3D vector problems.
- Give regular practice on unfamiliar, applied problems and on solving trig equations over restricted domains.
HL Paper 2
Candidates attempted a wider range of SL and HL questions and used the graphing calculator more effectively, though many still did unnecessary algebra where technology would do.
Found difficult
- integration techniques
- differential equations
- discrete random variables
- binomial distribution
- counting principles
- continuous random variables
- normal distribution
- complex numbers
- proof by contradiction
- euler's method
Well prepared
- linear regression
- composite functions
- trigonometry in triangles
- arcs and sectors
- rates of change
- binomial theorem
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | bearings and non-right-angled triangles | Answered well | did not know what a bearing is; calculator left in radians; treated the triangle as right-angledTip: Check your calculator angle mode at the start of every paper. |
| 2 | composite function and sketching it | Mixed | key points (maximum, minimum, endpoints) not placed accurately; coordinates not given to 3 significant figures; calculator in degreesTip: On a sketch, mark and label the turning points and domain endpoints with their coordinates. |
| 3 | regression and prediction | Mixed | used y on x regression when x on y was needed; coefficients not to 3 significant figuresTip: To predict x from y, use the regression line of x on y. |
| 4 | unfamiliar statistics topic | Most struggled | treated 0.28 as a probability |
| 5 | general term of a binomial expansion | Mixed | dropped the nCr factor or the power of b; equated a term to a coefficient; added the parts of a term instead of multiplyingTip: Write the general term in full, coefficient times both powers, before matching coefficients. |
| 6 | powers of complex numbers and rotation in the Argand plane | Most struggled | did not add multiples of 2π to get an integer n; did not identify the transformation as a rotation or omitted its centreTip: When solving with arguments, include + 2kπ before choosing the value that fits. |
| 7 | tree diagram and Bayes' theorem | Mixed | struggled with the reverse conditional probabilityTip: For 'given that' questions, divide the favourable branch probability by the total probability of the condition. |
| 8 | angle between a line and a plane | Most struggled | missed that the angle with the normal is the complement of the angle with the plane; sign error in the z component of the direction vector; set up correct equations but did not solve them with the calculatorTip: The angle with a plane is 90 degrees minus the angle with its normal. |
| 9 | proof by contradiction with odd and even integers | Most struggled | did not start by assuming the statement is true; circular argument about a perfect square; used modular arithmetic results without proofTip: State the assumption clearly, then split into odd and even cases until a contradiction appears. |
| 10 | geometry of a gutter cross-section and area by integration | Mixed | verified the given answer instead of deriving it; invalid assumption about the position of a point; working hard to followTip: In a show-that, work forwards to the given result rather than substituting it back. |
| 11 | pdf expectation by substitution, binomial and counting | Mixed | used the calculator where an exact value was needed; found the median instead of the mean; used 1 - P(X <= 1) instead of 1 - P(X = 0); multiplied counts by combinations incorrectlyTip: 'At least one' means one minus the probability of none. |
| 12 | Euler's method, Maclaurin series and separable differential equation | Mixed | substituted x and y before differentiating; could not separate the variables or spot the standard integral; did not link the underestimate to tangents on a concave-up curveTip: Euler's method follows tangents, so concavity decides whether it under- or over-estimates. |
What to practise
- Teach students to read key points off the calculator and place them on sketches.
- Practise splitting long problems into steps and picking out the given information.
- Show how to run Euler's method with the calculator's recursive sequence tool and explain why it uses tangents.
- Remind students that exact answers usually need an analytic, not a calculator, method.
HL Paper 3
Integration and calculator graphing were reasonably strong, but many scripts were so disorganised that marks were lost and candidates lost track of their own reasoning.
Found difficult
- presentation of working
- proof by induction
Well prepared
- integration techniques
- graphing with the calculator
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | graph, integrals, sequence formula and proof by induction | Mixed | sketch drawn outside the given domain; skipped steps on a given answer; wrong upper limit of integration; gave a recursive formula instead of one in terms of nTip: When the answer is given, every step leading to it must be visible. |
| 2 | maximising a product with integer constraints | Mixed | argued only one side of a two-sided argument; accepted non-integer values of n; did not give both n and the requested values; differentiated directly instead of using implicit differentiationTip: If a variable counts things, check that your optimum is an integer and test neighbouring integers. |
What to practise
- Train students to lay out long answers clearly, labelling each part, especially where results are given.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. lengthy rationales, methodology sections and subtitles that break the flow
- A. aim missing or not linked to the mathematics; missing or bloated bibliographies and huge data appendices
- B. calculator or computer notation, unlabelled diagrams, and content split across lines or pages
- B. key tables and derivations pushed into the appendix to save pages
- C. reliance on textbook problems, historical reports or standard derivations leaves little room for ownership
- D. descriptions of results or lists of assumptions offered instead of critical reflection; models not tested for viability
- E. mathematics far beyond the course copied from sources without understanding
- E. models fitted to a few points and correlation treated 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 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 AA HL May 2023 TZ1?
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The questions most candidates struggled with were on exponential equation as a quadratic in e^x and the discriminant, related rates for an equilateral triangle, complex roots of a cubic with unknown coefficients and volume of a ring about the y-axis between curves. 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 equations reducible to quadratics, polynomial roots and factors, graph transformations, volumes of revolution, vectors, lines and planes, integration techniques, differential equations and discrete random variables, among others.
What were the grade boundaries for Maths AA HL May 2023 TZ1?
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Maths AA HL: a 7 from 70 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.