| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 38 | 51 | 64 | 76 |
| Internal assessment | 20 | 9 | 12 | 15 | 17 |
| Paper 1 | 110 | 31 | 44 | 57 | 70 |
| Paper 2 | 110 | 43 | 57 | 71 | 85 |
| Paper 3 | 55 | 27 | 34 | 41 | 48 |
HL Paper 1
Some topics looked unprepared, notably normal probabilities and volumes about the y-axis, and disorderly work in multi-stage questions caused many avoidable errors.
Found difficult
- normal distribution
- volumes of revolution
- graph sketching
- presentation of working
Well prepared
- l'hopital's rule
- laws of logarithms
- vectors, lines and planes
- trigonometric identities
- differentiation rules
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | logarithms and change of base | Answered well | did not know the change of base formula; worked backwards unsuccessfullyTip: Learn the change of base rule and use it to put all logs in one base. |
| 2 | functions and their inverse | Answered well | confused the inverse function with the reciprocalTip: f^-1(x) is the inverse function, not 1/f(x). |
| 3 | trigonometric equation leading to a quadratic in cos θ | Mixed | ignored the given interval; kept an impossible solution with cos θ = 5/4; divided by cos θ and lost solutionsTip: Factorise instead of dividing by cos θ, and reject values outside [-1, 1]. |
| 4 | tangent line condition | Mixed | did not use the discriminant; found the derivative but did not set it equal to mTip: A tangent touches once: set the derivative equal to the gradient or the discriminant equal to zero. |
| 5 | normal distribution probabilities and symmetry | Most struggled | left blank; misread the normal distribution notation; could not use symmetryTip: Sketch the bell curve, mark the mean and use symmetry to split the probabilities. |
| 6 | sketching a related graph without its equation | Mixed | asymptotes not shownTip: Always draw and label asymptotes on a sketch. |
| 7 | solid rotated about the y-axis | Most struggled | wrong or missing limits; treated the constant r as a variableTip: Identify which letters are constants before setting up the integral in y. |
| 8 | modulus and argument of a complex number | Mixed | got only one of modulus and argument right; unclear working in (b) |
| 9 | limit by L'Hopital's rule | Answered well | did not check the indeterminate form firstTip: State that the limit is of the form 0/0 before applying L'Hopital's rule. |
| 10 | multi-part question | Mixed | difficulties in (c)(i) and (c)(iii) |
| 11 | multi-part question | Mixed | untidy work full of errors; part (f) found hardestTip: Neat, ordered working prevents most careless slips in long questions. |
| 12 | final long question | Most struggled | ran out of time after earlier partsTip: Budget time so the last section B question gets a fair attempt. |
What to practise
- Practise keeping work tidy and orderly; many scripts were unreadable.
- Give more practice with long multi-stage questions.
- Show students that a given answer lets them enter later parts even if they are stuck.
HL Paper 2
Standard trigonometry, probability and calculus went well, but many lost time and accuracy by solving analytically what the calculator could do, and rounding was poor.
Found difficult
- tangents and normals
- extended binomial theorem
- counting principles
- inverse trigonometric functions
- related rates
- conditional probability
- differential equations
- calculator use
Well prepared
- trigonometry in triangles
- discrete random variables
- arcs and sectors
- differentiation rules
- scalar and vector products
- kinematics
- binomial distribution
- tree diagrams
- integration by parts
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | cosine and sine rule | Answered well | gave BC squared instead of BC; calculator in radians; used right-angle methods |
| 2 | remainder theorem with two unknowns | Mixed | errors in synthetic or long division; did not finish the division to get the remainder; poorly organised workTip: Use the remainder theorem directly: substitute the root into the polynomial. |
| 3 | discrete distribution: mode, mean and sampling | Mixed | gave the mode as a probability; divided the mean by n; named quota sampling wronglyTip: E(X) = Σ x P(X = x) with no division; enter it as a list on the calculator. |
| 4 | triangle area, radius and major arc length | Mixed | used the wrong sides in the area formula or a sector area; found only the minor arcTip: For a major arc, use the reflex angle in s = rθ. |
| 5 | quotient rule and gradient from an angle | Most struggled | swapped numerator terms in the quotient rule; equated f'(1) to 70 or to sin/cos of 70 degrees; gave a value outside the domainTip: The gradient of a line at angle θ to the horizontal is tan θ. |
| 6 | scalar product and an equation in p | Answered well | sign errors; answer given as a vector; solved the equation by long algebra instead of the calculatorTip: Once you have one equation in one unknown, let the calculator solve it. |
| 7 | extended binomial expansion with a parameter | Most struggled | wrong generalised binomial coefficient; sign errors; forgot the factor of q to a negative power; attempted a Maclaurin seriesTip: Factor the constant out first so the bracket starts with 1, then apply the formula carefully. |
| 8 | counting games in a tournament | Most struggled | expressions in n given without explanation; miscounted the total number of gamesTip: Explain in words what each counting expression represents. |
| 9 | related rates with arctan | Most struggled | differentiated with respect to x instead of t; omitted the factor 1/6 from the arctan derivative; did not use the calculatorTip: For a rate in time, use the chain rule: dθ/dt = dθ/dx × dx/dt. |
| 10 | kinematics of a race | Mixed | differentiated by hand instead of using the calculator; used L'Hopital and got 0 or infinity for a limit; omitted the constant of integration; premature roundingTip: Use the calculator's derivative and integral tools on kinematics questions. |
| 11 | binomial distribution and conditional probability | Mixed | assumed independence for the intersection; left the unknown n part blank; recalculated a probability already found; did not multiply by 100 at the endTip: Find an unknown n with a table of binomial cdf values. |
| 12 | integration by parts, integrating factor and sketching solutions | Most struggled | sign and bracket errors in repeated parts; used y = vx or separation instead of an integrating factor; poor sketches ignoring the Ce^-x term; did not see each solution has its own constantTip: Draw axes with a ruler and scale, and keep the domain and constant term in mind when sketching. |
What to practise
- Teach calculator skills explicitly: solving equations, graphing derivatives and evaluating integrals.
- After forming a single-variable equation, let the calculator solve it.
- Enforce correct rounding and teach students to recall unrounded values.
- Spend about half the time on each section.
- Make sure students can extend formula booklet results, such as further binomial terms.
HL Paper 3
Algebra was mostly sound and both questions were accessible, but induction write-ups, limits and rigorous justification separated candidates.
Found difficult
- proof by induction
- limits
- show that and proof reasoning
Well prepared
- algebraic manipulation
- composite functions
- quadratic functions
- differentiation rules
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | iterated linear functions, induction and limits | Mixed | extra term in the summation or wrong limits; vague induction statements and wrong base case; ignored -1 < m < 1 when finding the limit; missing brackets around -1 in (-1)^nTip: Write the inductive hypothesis precisely as 'assume P(k) is true', not 'assume n = k'. |
| 2 | maximising the volume of a box and integer conditions | Mixed | errors simplifying the discriminant; set the second derivative to zero instead of evaluating it; no argument that the local maximum is global; ignored the condition t > 2sTip: When dividing an inequality by a variable, state that the variable is positive. |
What to practise
- Develop rigour in written mathematics, including assumption and conclusion statements in induction.
- Use brackets and notation carefully.
- Practise limits at infinity of algebraic expressions.
- Stress that a show-that needs every step correct, ending at the stated result.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. poor flow, unnecessary methodology sections and evaluative comments added after the conclusion
- B. graphs with faint or missing labels, tables of variables at the start and broken layout
- B. approximation signs only at the end and no stated degree of accuracy
- C. heavily sourced work and extra irrelevant models showing little original thinking
- D. reflection given as a list of observations rather than ongoing critical review
- E. techniques beyond the course used without understanding, or work not going beyond SL
- E. technology results taken on trust without checks or interpretation
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 2025 TZ3, 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 2025 TZ3?
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The questions most candidates struggled with were on normal distribution probabilities and symmetry, solid rotated about the y-axis, final long question and quotient rule and gradient from an angle. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in May 2025 TZ3?
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Across the papers the examiners listed normal distribution, volumes of revolution, graph sketching, presentation of working, tangents and normals, extended binomial theorem, counting principles and inverse trigonometric functions, among others.
What were the grade boundaries for Maths AA HL May 2025 TZ3?
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Maths AA HL: a 7 from 76 out of 100 overall in May 2025 TZ3. 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 November 2024: the previous report IB Maths AA HL November 2025 TZ3: 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