IB Mathematics Guide: Expert Exam Preparation & Revision Strategy

Subject Overview

Mathematics at IB level demands rigorous analytical thinking and sophisticated problem-solving abilities. Whether pursuing Mathematics: Analysis and Approaches (AA) or Applications and Interpretation (AI) at Standard or Higher Level, students face comprehensive assessments covering algebra, functions, calculus, statistics, and geometry. The subject develops essential quantitative reasoning skills valued by universities and employers worldwide.

The challenge lies not merely in computational accuracy but in demonstrating deep conceptual understanding, selecting appropriate methods, and communicating mathematical reasoning clearly. Success requires consistent practice, strategic revision, and mastery of both theoretical concepts and practical application techniques.

Students must develop strong time-management skills, as IB Mathematics examinations test knowledge across multiple domains simultaneously. The ability to connect different mathematical topics, recognise patterns, and apply techniques flexibly separates outstanding candidates from those who merely memorise procedures.

Exam Format

IB Mathematics courses follow a two-paper structure, with the addition of an Internal Assessment (exploration) contributing to the final grade:

• Paper 1: Non-calculator, testing pure mathematical techniques and algebraic manipulation (40% of final grade, 90 minutes for SL/120 minutes for HL)
• Paper 2: Calculator permitted, focusing on applied problem-solving and data analysis (40% of final grade, 90 minutes for SL/120 minutes for HL)
• Internal Assessment: Mathematical exploration of 12-20 pages (20% of final grade)

Questions progress from straightforward calculations through multi-step problems to complex investigations requiring synthesis of multiple topics. Higher Level papers include additional content depth and more challenging applications. Both papers assess all syllabus areas, with marks allocated proportionally to topic weighting.

Topic Breakdown

The IB Mathematics syllabus divides into five core themes, each requiring thorough understanding:

Number and Algebra (Mathematics AA: 15% SL, 10% HL | Mathematics AI: 10% SL, 10% HL)

Foundation concepts including arithmetic sequences, geometric progressions, binomial theorem, and proof techniques. Whilst appearing straightforward, these topics underpin advanced work and frequently appear in multi-step problems.

Functions (Mathematics AA: 31% SL, 18% HL | Mathematics AI: 31% SL, 18% HL)

The most heavily weighted area, covering quadratic, exponential, logarithmic, and trigonometric functions, along with transformations and equation-solving. Students must master graphical analysis, inverse functions, and function composition. Common difficulties include interpreting transformations and solving complex equations.

Geometry and Trigonometry (Mathematics AA: 18% SL, 18% HL | Mathematics AI: 18% SL, 20% HL)

Three-dimensional coordinate geometry, vectors, trigonometric identities, and triangle solutions. Higher Level extends to complex numbers and vector calculus. Students often struggle with spatial visualisation and selecting appropriate trigonometric approaches.

Statistics and Probability (Mathematics AA: 18% SL, 18% HL | Mathematics AI: 23% SL, 30% HL)

Discrete and continuous distributions, hypothesis testing, correlation, and regression analysis. Mathematics AI emphasises statistical modelling and real-world applications. Common challenges include interpreting probability contexts and applying the correct statistical tests.

Calculus (Mathematics AA: 18% SL, 36% HL | Mathematics AI: 18% SL, 12% HL)

Differentiation and integration techniques, with Mathematics AA placing substantially greater emphasis at Higher Level. Applications include optimisation, kinematics, and area calculations. Students frequently encounter difficulties with implicit differentiation, integration by substitution, and differential equations.

Key Skills Required

Excellence in IB Mathematics demands development of interconnected competencies assessed throughout examination papers:

Procedural Fluency

Rapid, accurate execution of standard techniques—algebraic manipulation, differentiation rules, trigonometric identities—forms the foundation for complex problem-solving. Develop this through regular practice of varied question types, focusing on speed without sacrificing accuracy.

Conceptual Understanding

Examiners reward students who demonstrate why methods work, not merely how to apply them. Develop deeper understanding by exploring connections between topics, investigating alternative approaches, and questioning underlying principles.

Problem-Solving Strategy

Unfamiliar contexts require systematic approaches: identifying given information, determining required outcomes, selecting appropriate methods, and verifying results. Strengthen this skill through exposure to diverse problem types and analysing model solutions.

Mathematical Communication

Clear, logical presentation of working earns method marks even when final answers contain errors. Practise structuring solutions coherently, labelling diagrams appropriately, and justifying conclusions with mathematical reasoning.

Technology Competence

Effective use of graphic display calculators for Paper 2 accelerates problem-solving and enables verification of algebraic work. Master your calculator's functions for graphing, statistical analysis, equation-solving, and numerical integration well before examinations.

Revision Strategy

Timeline Recommendations

Begin structured revision 12-16 weeks before examinations, allowing time for comprehensive coverage and intensive practice. Allocate the first 8 weeks to systematic topic review, the following 4 weeks to past paper practice under timed conditions, and the final 2-4 weeks to targeted weakness remediation and examination technique refinement.

Create a detailed revision timetable balancing all five syllabus areas proportionally to their examination weighting and your confidence level. Schedule more challenging topics during peak concentration periods, leaving routine practice for less optimal times.

Study Techniques

Active learning strategies prove far more effective than passive re-reading of notes:

• Construct summary sheets for each topic, condensing essential formulae, key concepts, and common pitfalls onto single pages for quick reference
• Teach concepts to others, exposing gaps in your understanding whilst reinforcing secure knowledge
• Complete topic-specific question sets before attempting full papers, building confidence systematically
• Analyse mark schemes thoroughly, understanding how examiners award partial credit and what constitutes sufficient justification
• Create error logs documenting mistakes, their causes, and corrective strategies to prevent repetition

Resource Allocation

Prioritise official IB past examination papers and mark schemes as your primary revision materials. Supplement with reputable textbooks aligned to your specific course (AA or AI, SL or HL), online resources providing worked solutions, and practice question banks organised by topic.

Dedicate approximately 60% of revision time to practice questions, 25% to reviewing and consolidating concepts, and 15% to examination technique development. Adjust these proportions based on diagnostic assessment results and your learning preferences.

Practise Schedule

Complete at least 8-10 full past papers under strict timed conditions before examinations. Begin with papers from 2-3 years prior, progressing to more recent examinations as your competence develops. Immediately mark each paper, identifying patterns in errors and allocating additional practice to problematic areas.

Incorporate regular mixed-topic question sessions preventing compartmentalisation of knowledge. The ability to recognise which techniques apply to unfamiliar problems distinguishes excellent candidates and develops only through varied practice.

Practise & Resources

Past Papers

Access official IB past papers through your school or the IB Follett online store. Focus on papers from your specific Mathematics course (AA or AI) and level (SL or HL), as question styles and content coverage vary significantly. Papers from 2021 onwards reflect the current syllabus structure introduced with the 2019 curriculum revision.

Mark Schemes

Study mark schemes alongside your attempts, noting how examiners allocate method marks, penalise errors, and reward clear communication. Understanding marking principles enables strategic approach selection—for instance, recognising when calculator-based numerical methods suffice versus when algebraic manipulation is required.

Practise Questions

Beyond past papers, utilise topic-specific question banks such as:

• Revision Village—comprehensive online platform with video solutions and difficulty-graded questions
• IB Questionbank—official IB resource organising questions by topic and difficulty
• Textbook exercises—particularly chapter reviews and cumulative assessments
• Practise examination papers from reputable publishers aligned to IB specifications

Recommended Materials

Invest in authorised IB Mathematics textbooks for your specific course: Haese Mathematics for comprehensive coverage, Oxford IB Diploma Programme for clear explanations, or Pearson for extensive practice questions. Supplement with online resources including Khan Academy for concept reinforcement, Wolfram Alpha for verification of complex calculations, and Desmos for interactive graphing exploration.

Expert Support from Taylor Tuition

Achieving excellence in IB Mathematics requires more than independent revision. Taylor Tuition's specialist Mathematics tutors provide the personalised guidance necessary to maximise examination performance. Our tutors hold advanced qualifications in mathematics and extensive experience preparing students for IB examinations at both Standard and Higher Level.

We create bespoke revision plans tailored to your specific course, current performance level, and target grade. Through diagnostic assessment, we identify precise knowledge gaps and technique deficiencies, focusing tutorial time on areas yielding maximum improvement. Our approach combines conceptual deepening with strategic examination technique, ensuring you demonstrate your full mathematical capability under examination conditions.

Our tutors teach sophisticated problem-solving strategies applicable across topics, develop efficient calculator skills for Paper 2, and provide extensive practice with examiner-style questions. We offer detailed feedback on Internal Assessment explorations, guidance on selecting appropriate topics, and support throughout the mathematical investigation process.

Whether you require comprehensive topic coverage, targeted examination technique coaching, or confidence-building through intensive practice, Taylor Tuition delivers the expert support necessary for IB Mathematics success. Contact us today to discuss your Mathematics preparation requirements and discover how our specialist tutors can help you achieve your target grade.