Master the IB Mathematics: Analysis and Approaches HL exam. All three papers — non-calculator Paper 1, GDC Paper 2, and the extended Paper 3 investigations — plus command terms, marking criteria (M/A/R), proof by induction, and exact-value technique.
240 teaching hours • 3 external papers • 1 internal assessment (Exploration)
Three external papers at HL — know exactly what each tests and how to maximise your marks.
What to expect:
Key Tips
Easy Marks
Watch Out
What to expect:
Key Tips
Easy Marks
Watch Out
What to expect:
Key Tips
Easy Marks
Watch Out
Command terms tell you exactly what the examiner expects. Filter by Assessment Objective (AO).
Match your answer depth to the marks available.
Example questions:
Show your method clearly — you can earn M marks even when the final answer is wrong.
Example questions:
In Paper 1 the accuracy mark usually needs an EXACT answer — decimals are not accepted.
Example questions:
Write a sentence of reasoning — R marks are lost when working stops at the number.
Example questions:
No marks if you assume or work backwards from the given answer — start from the beginning.
These concepts appear throughout Math AA HL exams. Master them to score higher.
Paper 1 is sat without a GDC — and at HL it runs two hours over the full syllabus. Drill exact trig values, surd, fraction and complex-number arithmetic, by-hand calculus, and algebra until they are automatic.
Paper 3 (HL only, 20%) is two extended investigations that build an unfamiliar result step by step. Practise generating data, conjecturing a pattern, then proving or justifying it — and writing your reasoning out in words.
HL proof goes beyond deduction. Learn the induction template (base case → assume n=k → prove n=k+1 → conclude) and contradiction, and set every line out as a justified logical step — never work backwards.
The IB rule (printed on all papers): unless told otherwise, give answers exactly — surds, fractions, multiples of π, exact complex forms — OR correct to three significant figures. Paper 1 wants exact form; round GDC results to 3 s.f. in Papers 2 and 3.
The HL extensions — complex numbers and De Moivre, 3D vectors and planes, l’Hôpital, implicit and related rates, differential equations, and Maclaurin series — recur across all three papers. Practise them until the methods are second nature.
Learn from others' mistakes. These cost students marks every exam session.
Giving decimals in Paper 1
Paper 1 expects exact answers. Leave results as surds, fractions, or multiples of π unless the question explicitly asks for a rounded value.
Skipping steps in "show that" / "prove" questions
The result is given — you must derive it. Show every line of working from the start; you earn nothing for restating the answer.
Wrong calculator angle mode in Paper 2
Check whether the question is in radians or degrees and set your GDC to match before any trig calculation.
A correct answer with no working
Full marks are not guaranteed for an unsupported answer — show your method, since method marks can rescue a wrong final answer. In the Paper 2 GDC paper, also sketch any graph you use to find a solution.
Rounding intermediate working
Keep full exact (Paper 1) or full GDC (Paper 2) precision until the final step. Early rounding causes accuracy errors in later parts.
Confusing "hence" and "hence or otherwise"
"Hence" means you must use the previous result; "hence or otherwise" allows any method. Ignoring "hence" can cost the method marks.
Forgetting the constant of integration
Every indefinite integral needs "+ C". For definite integrals, substitute the limits — do not leave the constant in.
20% of final grade • 12–20 pages
A written investigation in which students explore a mathematical topic of personal interest. The Exploration must demonstrate mathematical communication, personal engagement, reflection, and correct use of mathematical language and notation.
Marking Criteria
Tips for Top Marks
Apply these exam skills with our Math AA HL practice questions. Get instant AI feedback that shows exactly what scored marks and how to improve.