IB Maths AA HL Curriculum: Papers, Marks and Timing

The IB Maths AA HL curriculum contains five topics: Number and Algebra, Functions, Geometry and Trigonometry, Statistics and Probability, and Calculus. It is taught over 240 hours, about 30 of which are the mathematics toolkit and the Exploration. Assessment is three written papers plus the internally assessed Exploration.

AA HL is AA SL plus a second layer.

Analysis and Approaches HL contains the entire SL syllabus and then extends every topic. The HL additions are the ones that decide grades: proof by induction and proof by contradiction, complex numbers in Cartesian, modulus argument and Euler form, vectors with lines and planes, the binomial expansion with fractional and negative indices, Maclaurin series, implicit differentiation, integration by parts and by substitution, volumes of revolution, differential equations (separation of variables and Euler's method), Bayes' theorem and continuous random variables.

Why a content list is not a revision plan.

Each topic is examined with its own question grammar, and that is what exam technique means here. A complex numbers question usually rewards converting to exponential form before anything else, because then $\left(re^{i\theta}\right)^{n} = r^{n}e^{in\theta}$ collapses several lines of algebra into one. A calculus question usually rewards naming the rule you are about to use. A statistics question on Paper 2 usually rewards defining the distribution in words before touching the calculator.

The formula booklet is issued with every paper.

It supplies standard results, never the method, so the marks live in how you deploy them. If you want the topic by topic breakdown of content, the complete AA HL syllabus guide covers it; this article is about what the examiner does with that content under the clock.

In IB Maths AA HL the command word fixes how much working the examiner expects. "Write down" and "state" want the answer with no method. "Show that" and "prove" want every step to a result that is already printed. "Hence" forces you to use the previous part. "Sketch" wants shape and key features, not plotted points.

The two words that cost the most marks are "hence" and "show that".

When a part begins with "hence", the mark scheme is written around the result of the part before it. A student who abandons that result and restarts with a longer method can reach the correct answer and still lose the method mark, because the mark was allocated to the link, not to the arithmetic. "Hence or otherwise" is the opposite signal: any valid route is acceptable, including a graphical or numerical one on the calculator papers.

"Show that" questions are a gift, not a trap.

The answer is printed, so you already know where you are going, and the marks are all in the chain. Two rules protect them. Work forwards from the given expression towards the printed result, never backwards from the result, and finish with a line that states the conclusion explicitly. If you cannot complete part (a) of a "show that", you may still quote the printed result in part (b) and earn those marks in full.

"Justify" and "give a reason" are reasoning marks.

They are coded R1 in the mark scheme and they need a sentence, for example that $f'(x)$ changes sign from negative to positive, not just a number.

IB Maths AA HL Paper 1 and Paper 2 each last 2 hours and carry 110 marks, which gives a budget of roughly 1.1 minutes per mark. Each paper has a Section A of short response questions and a Section B of extended response questions, and each paper is worth 30% of the final grade.

Turn the budget into a clock, not a feeling.

A 6 mark question deserves about seven minutes. If you are at ten minutes with no route, the question has already cost you another question, so mark it, leave a gap on the page and move on. The realistic target is to finish Section A with at least half the time still available, because Section B questions are long and their later parts carry the marks that separate a 6 from a 7.

Paper 1 is the exact answer paper.

With no calculator, AA HL expects answers such as $\frac{\sqrt{3}}{2}$, $\ln 2$ or $\frac{\pi}{6}$, and the algebra is always designed to be doable by hand. If your working produces an ugly decimal on Paper 1, that is usually the signal that you have made an error, not that the question is hard.

Paper 2 is the paper where the calculator changes the timing.

A question that asks you to solve $e^{x} = 3 - x^{2}$ is a thirty second graphical intersection on Paper 2 and a completely different task on Paper 1. Store intermediate values in the calculator memory instead of retyping rounded decimals, and give final answers to three significant figures unless an exact answer is requested. For a full revision structure across the two years, see our IB exam preparation strategy.

Method marks in IB Maths AA HL are awarded for the correct process, independently of the final answer. Write the rule, the substitution or the set up line before you compute, and an arithmetic slip or an unfinished question still earns M1 and any follow through marks that depend on it. A bare answer earns nothing if the method mark came first.

Read the mark scheme codes once and they stop being mysterious.

M1 is a method mark, A1 is accuracy, R1 is reasoning, AG means the answer was given in the question, and FT means the examiner follows through your earlier error so later parts can still score. In multi step questions the mark scheme also caps what a correct answer with no working can receive, which is the whole argument for writing the set up line even when you can see the answer.

A worked example, Paper 1 style.

(a) Show that $\frac{d}{dx}\left(x\ln x - x\right) = \ln x$. [2]

(b) Hence find $\int_{1}^{e} \ln x \, dx$. [3]

• Step 1. Name the rule before using it: product rule on $x\ln x$ gives $\frac{d}{dx}(x\ln x) = \ln x + x\cdot\frac{1}{x} = \ln x + 1$. That line is the M1.
• Step 2. Subtract the derivative of $x$: $\ln x + 1 - 1 = \ln x$, which is the printed result, so state it as reached (AG).
• Step 3. Obey "hence". Part (a) has handed you an antiderivative, so write $\int_{1}^{e}\ln x \, dx = \left[x\ln x - x\right]_{1}^{e}$. This single line is where the method mark of part (b) lives.
• Step 4. Evaluate the limits: at $x = e$, $e\ln e - e = e - e = 0$; at $x = 1$, $1\cdot\ln 1 - 1 = -1$.
• Step 5. Subtract: $0 - (-1) = 1$.

A student who writes only "$= 1$" risks the full three marks on one line of arithmetic. A student who writes step 3 and then mishandles $\ln e$ still banks the method mark. That asymmetry is the whole of exam technique in AA HL. The same habit is what breaks the common AA HL difficulties students bring to a first lesson.

IB Maths AA HL Paper 3 lasts one hour, carries 55 marks and is worth 20% of the final grade. It contains two extended response problem solving questions, each built as a long scaffolded investigation, and a graphic display calculator is required throughout. Paper 3 exists only at HL, in both Analysis and Approaches and Applications and Interpretation.

The skill being tested is reading, then generalising.

A Paper 3 question typically opens with a concrete case, asks you to compute or verify it, then widens the same structure towards a general result and often closes with a proof, a conjecture or a limiting behaviour. The stem carries definitions and notation that the later parts depend on, so the first three or four minutes should be spent reading the whole question before writing a single line. Students who start part (a) immediately frequently solve it in a way that does not generalise, and then have to redo the work at part (e).

Dependency is the real danger, and the cure is simple.

Because the parts build on one another, a missed early result can block three later parts. When a part asks you to show a general formula and you cannot derive it, write it down anyway as a quoted result and use it in the next part: the later method marks are awarded on their own terms. The same applies to a numerical answer you could not reach, which you can carry forward symbolically.

Timing on Paper 3 is unforgiving.

Fifty five marks in sixty minutes is about 1.1 minutes per mark again, but the marks come in two blocks, so leave the two questions roughly thirty minutes each and refuse to overrun the first one.

The Exploration is the internally assessed component of IB Maths AA HL, worth 20% of the final grade and marked out of 20 against five criteria: Presentation (4 marks), Mathematical communication (4), Personal engagement (3), Reflection (3) and Use of mathematics (6). The guide recommends roughly 12 to 20 pages with double line spacing.

Criterion E carries the most marks and is where HL candidates are separated.

Use of mathematics at HL requires mathematics commensurate with the HL course, relevant, correct and understood, and the top band asks for sophistication or rigour. An exploration that is beautifully written around SL level algebra caps itself in the criterion that matters most. Choosing a topic that genuinely needs an HL tool, for example a differential equation, a Maclaurin expansion or a continuous random variable, protects those six marks from the start.

Mathematical communication is a technique mark, not a styling mark.

Define every symbol before using it, keep one notation throughout, and write $\frac{dV}{dt} = -k\sqrt{h}$ rather than describing the relationship in words. Graphs need axis labels and units, and every table needs a caption explaining what it shows.

Reflection is the criterion students lose by accident.

It rewards commenting on results as you go, comparing approaches and recognising limitations, not a paragraph of conclusions bolted on at the end. Our IB internal assessment guide sets out how the criteria are applied across IB subjects, and the planning habits transfer directly to the maths Exploration.