How to Get a 7 in IB Maths AA HL: Grade Boundaries Paper by Paper

The short answer: in recent sessions a 7 in IB Maths Analysis and Approaches HL has needed between 71 and 79 marks out of 100 on the final weighted total. The figures below come from the IB documents "Grade boundaries for Diploma Programme coordinators", which we have read session by session and publish in full on the IB grade boundaries page for Maths AA HL.

The 7 is never a fixed percentage. The IB sets boundaries after each session by reviewing candidate work against the grade descriptors, so a harder paper usually comes with a lower boundary. In the sessions below, November has usually needed more marks than May, though November 2025 TZ3 (75) was below two May sessions.

What about May 2026?

At the time of writing we do not hold the IB coordinators' document for May 2026. Public compilations of the subject reports put the 7 at 72 or 73 out of 100 depending on the time zone, but we have not been able to confirm these figures against an IB document, so treat them as unconfirmed. The same applies to November 2026: its boundaries will only exist after results day.

If you take AA SL rather than HL, the logic is identical but the papers differ. The SL figures are on the Maths AA SL grade boundaries page, and the main grade boundaries page covers all six Maths and Physics courses.

The final mark out of 100 is not the sum of your raw marks. Each component is converted to its weighting from the IB Maths AA guide, and the weighted parts are added.

• Paper 1 (2 hours, no technology, 110 marks): 30%.
• Paper 2 (2 hours, technology required, 110 marks): 30%.
• Paper 3 (1 hour, technology required, 55 marks, two extended problem-solving questions): 20%.
• Exploration (internal assessment, 20 marks): 20%.

So one raw mark is worth different amounts in different places. A Paper 1 or Paper 2 mark is worth 30/110, about 0.27 of a final point. A Paper 3 mark is worth 20/55, about 0.36. An IA mark is worth a full point. One extra mark on the exploration is worth almost four marks on Paper 1.

A worked example.

Take the May 2025 TZ2 boundaries, where a 6 needed 59 and a 7 needed 71. A student scores 16/20 on the IA, 75/110 on Paper 1, 70/110 on Paper 2 and 35/55 on Paper 3. The weighted total is about 16 + 20.5 + 19.1 + 12.7 = 68.3, a 6. To reach 71 the student needs roughly 2.7 more weighted points: for example one more IA mark, four more marks on Paper 1 and three more on Paper 3.

This is a close approximation of how the IB combines components; the IA mark is also subject to moderation, which can move it up or down.

The component boundaries show where a 7 is decided. In every session where the IB document gives component data, these were the lowest marks for a 7. The November 2025 document gives only the final boundaries for AA HL, so that session is not in the table.

Three things stand out.

Paper 3 asks for the highest percentage.

A 7 on Paper 3 needed 41 to 48 out of 55, roughly 75% to 87%, more in percentage terms than either Paper 1 or Paper 2. Paper 3 has only two questions, so losing the thread of one extended question is expensive. The AA HL Paper 3 traps quick reference covers the patterns that cost the most.

Papers 1 and 2 swing the most.

The Paper 2 boundary for a 7 went from 67 in May 2025 TZ1 to 85 in May 2025 TZ3, in the same session. You cannot predict which way your paper will go, so build your margin on the first, more routine parts of every question.

The IA boundary is stable.

A 7 on the exploration needed 17 out of 20 in all six sessions with component data. It is the only component you control before the exam.

Most students sitting between a 6 and a 7 are not missing a topic. They are leaking marks in the same few places, and the weighting tells you which leaks to fix first.

1. The exploration.

Each IA mark is worth a full final point, and the draft feedback stage is the last chance to move it. If your teacher's comments point to presentation, notation or reflection, those are usually the cheapest marks available. The guide to the Maths IA criteria explains what each criterion rewards.

2. The last parts of long questions.

Section B questions on Papers 1 and 2 build towards a final part that often carries the hardest marks. Students heading for a 6 tend to stop early; students heading for a 7 attempt every part, using earlier results even if they could not prove them. A "show that" result is given to you precisely so that you can use it in the next part.

3. Algebra without a calculator.

Paper 1 is two of your five hours of exams and has no technology. Slips in simplifying, in exact values and in logarithms add up. The AA Paper 1 no-calculator technique guide shows how to protect those marks.

4. Calculus at the HL standard.

Integration by parts, substitution, implicit differentiation and differential equations appear across all three papers. The AA HL calculus guide maps what is examined, and the integration by substitution and parts worksheet gives exam-style practice with a markscheme.

5. Knowing the syllabus edges.

Some marks are lost on content students did not realise was examinable. The complete AA HL syllabus guide lists every topic; to find your weak ones quickly, try the timed IB topic tests.

Here is an original question in the style of a Paper 1 Section B question. It is the kind of question where a 6 and a 7 separate: parts (a) and (b) are routine, part (c) needs you to reuse earlier work.

Question

(no calculator) [11 marks]

(a) Use integration by parts to show that $\int x\ln x\,dx = \frac{x^2}{2}\ln x - \frac{x^2}{4} + C$. [3]

(b) The region $R$ is bounded by the curve $y = x\ln x$, the $x$-axis and the line $x = e$, for $x \ge 1$. Find the exact area of $R$. [3]

(c) Hence find the exact value of $\int_1^e x(\ln x)^2\,dx$. [5]

Markscheme

(a) Let $u = \ln x$ and $\frac{dv}{dx} = x$, so $\frac{du}{dx} = \frac{1}{x}$ and $v = \frac{x^2}{2}$. M1

$\int x\ln x\,dx = \frac{x^2}{2}\ln x - \int \frac{x^2}{2}\cdot\frac{1}{x}\,dx$ A1

$= \frac{x^2}{2}\ln x - \frac{x^2}{4} + C$ A1 AG

(b) The curve meets the $x$-axis at $x = 1$ and $x\ln x \ge 0$ for $1 \le x \le e$, so the area is $\int_1^e x\ln x\,dx$. R1

$\left[\frac{x^2}{2}\ln x - \frac{x^2}{4}\right]_1^e = \left(\frac{e^2}{2} - \frac{e^2}{4}\right) - \left(0 - \frac{1}{4}\right)$ M1

$= \frac{e^2 + 1}{4}$ A1

(c) Let $u = (\ln x)^2$ and $\frac{dv}{dx} = x$, so $\frac{du}{dx} = \frac{2\ln x}{x}$ and $v = \frac{x^2}{2}$. M1

$\int_1^e x(\ln x)^2\,dx = \left[\frac{x^2}{2}(\ln x)^2\right]_1^e - \int_1^e x\ln x\,dx$ A1

$\left[\frac{x^2}{2}(\ln x)^2\right]_1^e = \frac{e^2}{2}$ A1

Uses the result of part (b) for $\int_1^e x\ln x\,dx$. M1

$= \frac{e^2}{2} - \frac{e^2 + 1}{4} = \frac{e^2 - 1}{4}$ A1

Where the marks go.

The R1 in (b) is often dropped: you must say why the integral equals the area. In (c), restarting from scratch wastes time; "hence" tells you that part (b) is the shortcut. Those two habits alone can be worth several marks across a paper.

For parents, grade boundaries answer one practical question: how far is my child from the next grade, and where can the gap be closed?

Three points are worth keeping in mind. First, a boundary from a past session is a guide, not a promise: the 7 has moved by up to eight marks between recent sessions. Second, a percentage on a school mock is not directly comparable with an IB boundary, because schools often mark mocks with their own boundaries or with a single past paper.

Ask the teacher which boundaries were used. Third, the exploration is worth 20% and is finished months before the exams, so a strong IA takes pressure off every paper.

If your child is consistently a few marks below the 7 in mocks, the gap is usually in the habits described above rather than in missing knowledge. My guide on how to read IB mock results in Maths and Physics explains which numbers to look at and which questions to ask the school.