How DP Mathematics: Analysis and Approaches Is Assessed: Revision Notes

Condensed for quick recall of how the course is assessed. For the full subject overview, use the IB DP Mathematics: Analysis and Approaches subject overview.

Why the exploration deserves an early start

Because the mathematical exploration is worth 20% at both SL and HL – equivalent to half of Paper 1 or Paper 2 – and is completed over an extended period without exam-day time pressure, it is one of the most controllable components of the final grade if work begins early. A first draft written and checked against the criteria well before the deadline, then revised at least once, consistently outperforms one rushed in the final weeks, so treating exploration milestones with the same seriousness as an exam date protects a meaningful share of the overall grade.

SL vs HL

Component	SL	HL
Paper 1 (no calculator/technology)	40%, 1.5h	30%, 2h
Paper 2 (technology allowed)	40%, 1.5h	30%, 2h
Paper 3 (HL only, two extended-response problem-solving questions)	—	20%, 1h
Mathematical exploration (internal)	20%	20%

The defining feature vs. Applications and Interpretation

Paper 1 is sat without a calculator or any technology — it directly tests algebraic manipulation and proof by hand. This is the single biggest practical difference from Applications and Interpretation, where technology is permitted on every paper.

The mathematical exploration

• Internally assessed, worth 20% at both SL and HL.
• A written piece of independent mathematical investigation into a topic the student chooses.

Why Paper 1’s no-technology rule shapes revision

Because Paper 1 tests algebraic manipulation and proof entirely by hand, revision for it should deliberately avoid reaching for a calculator during practice, even for arithmetic that would normally be checked electronically – the point is to build genuine fluency in manual manipulation (expanding, factorising, solving equations, differentiating and integrating by hand) so that it holds up under the no-technology constraint on exam day. A student who has only ever checked their algebra with a calculator during revision often finds Paper 1 significantly harder than expected, not because the underlying mathematics is unfamiliar, but because the habit of manual verification was never built.

The mathematical exploration in more depth

Like the equivalent component in Applications and Interpretation, the exploration is graded against criteria covering presentation, mathematical communication, personal engagement, reflection, and use of mathematics – but in Analysis and Approaches, “use of mathematics” more often draws on algebraic, calculus-based or proof-oriented techniques rather than applied statistical modelling, reflecting the course’s own emphasis. A strong exploration in this course typically demonstrates some element of rigour – for example, a proof, a derivation, or a generalisation beyond the specific numerical case first investigated – since this is explicitly one of the criteria’s higher-scoring indicators.

How this compares to Applications and Interpretation

Both DP mathematics courses are assessed to the same demanding IB standard and carry equal recognition for university admission – neither is the “easier” option. The genuine difference is emphasis: this course develops algebraic manipulation, functions, calculus and proof primarily by hand, with technology permitted only from Paper 2 onward, while Applications and Interpretation is built around real-world modelling, statistics and technology-assisted problem-solving on every paper. Students intending to study a physical science, engineering or mathematics-heavy discipline at university more often choose this course, since its content and skill set map more directly onto those fields’ first-year requirements, though this is a general pattern rather than a strict rule.

Command terms across the papers

As with every DP mathematics course, command terms signal the depth of response expected: calculate, find, solve and write down point to a direct computational or algebraic answer; hence or hence or otherwise require building on a previous part of the same question, often reusing a result just derived; show that requires a fully justified derivation reaching a given result, with every algebraic step shown, rather than simply stating the answer is correct; prove requires a rigorous, logically complete argument, most often tested at HL. Losing marks on a “show that” question by skipping intermediate algebraic steps, even when the final answer matches, is one of the most common and avoidable errors in this course.

Exam traps

• Practising exclusively on a calculator/technology, then being caught out by Paper 1’s no-technology rule.
• Underweighting proof and algebraic manipulation skill, which Paper 1 specifically targets.
• HL students not practising extended, multi-step problem-solving specifically for Paper 3’s style.

Self-test

1. Which paper has no calculator/technology allowed, and what does it directly test?
2. What is the mathematical exploration, and what percentage is it worth?
3. What’s unique about Paper 3, and who sits it?
4. What are Paper 1 and Paper 2 each worth at SL?
5. What distinguishes “show that” from “calculate” as a command term?
6. Which criterion of the mathematical exploration typically rewards a proof, derivation or generalisation in this course?

Answers: 1. Paper 1 — it directly tests algebraic manipulation and proof by hand. 2. An independent written mathematical investigation into a student-chosen topic, worth 20% at both SL and HL. 3. Two extended-response problem-solving questions, using technology, sat only by HL students, worth 20%. 4. 40% each. 5. “Show that” requires a fully justified derivation with every step shown, reaching a given result; “calculate” points to a direct computational answer without that same justification requirement. 6. Use of mathematics.

Official syllabus

International Baccalaureate Organization, Diploma Programme Subject Brief – Mathematics: Analysis and Approaches, first assessment 2021, published 2019 – the same source cited by the full syllabus guide and the subject overview.