How to excel at IB Maths

Due to the structure of the IB, Maths forms a crucial part of every student’s educational journey. Yet there are a number of different options for Maths IB, which depends on whether you are taking Standard or Higher Level, as well as which subject within IB Maths you are studying: Analysis and approaches, or Applications and interpretations.

What do I need to know for IB Analysis and approaches?

The IB Mathematics: Analysis and Approaches course focuses on developing a deep understanding of mathematical concepts, emphasizing theoretical understanding, mathematical proofs, and advanced problem-solving skills. The knowledge required is as follows:

Standard Level (SL):

1. Functions and Equations:

  • Focuses on functions, their properties, transformations, and inverse functions.

  • Equations and inequalities involving polynomial, exponential, logarithmic, and trigonometric functions.

2. Calculus:

  • Introduction to calculus, covering differentiation, integration, and their applications.

  • Fundamental theorem of calculus, optimization, and related rates.

3. Series and Sequences:

  • Study of arithmetic and geometric progressions, series convergence, and summation techniques.

  • Applications in finance, physics, and other mathematical models.

Higher Level (HL) - Additional Content:

1. Advanced Calculus:

  • Extensive study of calculus concepts, including limits, derivatives of trigonometric and exponential functions, and applications of differentiation.

  • Techniques of integration, including integration by parts, partial fractions, and improper integrals.

2. Linear Algebra:

  • Introduction to matrices, determinants, vector spaces, and systems of linear equations.

  • Applications in solving simultaneous equations, transformations, and cryptography.

3. Further Topics in Analysis:

  • Advanced study of functions, continuity, differentiability, and higher-order derivatives.

  • Rigorous exploration of mathematical proofs and theoretical analysis.

Key Differences between SL and HL:

The key differences between SL and HL in Analysis and approaches are threefold. The first is in terms of depth and complexity. HL involves more intricate and theoretical content, particularly in calculus, linear algebra, and proof-based mathematical concepts. The second is in mathematical rigor. HL emphasizes a higher level of mathematical rigor, requiring students to comprehend and construct mathematical proofs. Finally, there is a marked difference in assessment complexity. HL assessments typically feature more complex problems, involving higher-order thinking skills and a deeper understanding of mathematical theories.

What do I need to know for IB Applications and Interpretations?

The IB Applications and Interpretations course emphasises the application of mathematical concepts in real-world contexts, fostering critical thinking, problem-solving skills, and mathematical modeling. The substantive knowledge required is as follows:

Standard Level (SL):

1. Functions:

  • Focuses on the study of functions, including polynomial, exponential, logarithmic, and trigonometric functions.

  • Emphasizes understanding the properties of functions, transformations, and their applications in various contexts.

2. Algebra:

  • Involves the study of algebraic techniques, inequalities, sequences, and series.

  • Applications in financial mathematics, such as interest rates, compound interest, and annuities.

3. Descriptive Statistics:

  • Introduction to statistical analysis, including measures of central tendency, dispersion, and correlation.

  • Interpretation and representation of data through graphical techniques.

4. Probability:

  • Fundamentals of probability theory, including probability distributions, expected values, and binomial distribution.

  • Applications in decision-making, risk assessment, and experimental design.

Higher Level (HL) - Additional Content:

1. Calculus:

  • Extends the study of calculus, including differentiation, integration, and their applications in various fields.

  • Advanced techniques for solving differential equations and their interpretations.

2. Complex Numbers:

  • Introduces complex numbers, their properties, and operations.

  • Applications in engineering, physics, and other sciences involving harmonic motion and wave theory.

3. Statistics and Probability:

  • Deeper exploration of statistical inference, including hypothesis testing and confidence intervals.

  • Advanced probability distributions and their applications in modeling real-world scenarios.


Key Differences between SL and HL:

As with the Analysis and Approaches strand, there are a number of marked differences between SL and HL within Applications and Interpretations. The first regards depth of content. HL involves more advanced and extensive content compared to SL, especially in calculus, complex numbers, and statistics. The second is in problem-solving. HL requires students to solve more complex problems, analyse data with higher mathematical rigor, and apply advanced techniques to a broader range of scenarios.

What are the findings from recent examiners’ reports?

Examiners’ reports are a crucial resource when planning your revision. By thinking proactively about common pitfalls, it is possible to ensure that you will avoid dropping crucial marks when it comes to the day of the exams. Here we provide a summary of the findings from recent examiners reports as they relate to both pathways within IB Mathematics.

IB Mathematics Analysis and Approaches (AA):

Key Findings:

  • Conceptual Understanding:

    • Strong foundation in basic concepts but struggles with advanced theoretical topics, particularly at Higher Level (HL).

    • Challenges in applying abstract mathematical theories to real-world problems.

  • Problem-Solving Skills:

    • Difficulty in approaching multi-step problems and constructing logical solutions, especially in proof-based questions.

    • Insufficient explanation of reasoning and steps in solutions.

  • Mathematical Rigor:

    • HL students face challenges in constructing rigorous proofs and demonstrating a deep understanding of abstract mathematical concepts.

    • Issues with precise mathematical language and notation in solutions.

Areas for Improvement:

  • Deepen Conceptual Understanding:

    • Strengthen foundational knowledge before progressing to more complex topics.

    • Practice applying abstract concepts to diverse scenarios to bridge theory with real-world applications.

  • Enhance Problem-Solving Techniques:

    • Engage in regular problem-solving exercises across varying difficulty levels.

    • Emphasize step-by-step reasoning and clarity in problem-solving approaches.

  • Develop Mathematical Rigor:

    • Practice constructing proofs and explanations, emphasizing logical reasoning and precise mathematical language.

    • Pay attention to clear and concise notation in solutions.

IB Mathematics Applications and Interpretations (AI):

Key Findings:

  • Application of Mathematics:

    • Solid understanding of applying mathematical models in real-world contexts.

    • Struggles with advanced statistical and probabilistic concepts, especially at Higher Level (HL).

  • Interpreting and Analysing Data:

    • Challenges in interpreting complex data sets and analysing data to make informed conclusions.

    • Difficulty in applying statistical techniques to real-life scenarios.

Areas for Improvement:

  • Strengthen Statistical Proficiency:

    • Focus on practicing advanced statistical and probabilistic techniques, especially at HL.

    • Engage in data analysis tasks and real-world applications to reinforce understanding.

  • Enhance Interpretation Skills:

    • Work on interpreting complex data sets and drawing meaningful conclusions from statistical analyses.

    • Apply statistical techniques to practical scenarios for a better grasp of their real-world applications.

Our Insights

The International Baccalaureate is a challenging educational pathway for those entering Sixth Form education and students can, understandably, feel overwhelmed by the enormity of the task ahead of them. At Chapkin Edwards, we have a number of key strategies developed by our expert tutors in the field which can help put your mind at ease, and enable you to embark upon revision with confidence and purpose.

Master Core Concepts. Your focus should always be on understanding foundational concepts thoroughly before delving into more complex topics. Focus on topics like calculus, functions, and algebra, ensuring a strong grasp of their principles.

Practice Real-World Applications. Apply mathematical concepts to real-life scenarios. For example, apply calculus to physics problems or statistics to business cases. Practice using mathematical models in various contexts to understand their practical implications.

Diversify Practice Material. Solve past papers, sample questions, and textbook exercises extensively. Explore questions from different sources to familiarize yourself with various problem formats and styles.

Focus on Higher Level Content, if applicable. For Higher Level (HL), allocate sufficient time to understand and practice advanced topics like complex numbers, proofs, and further calculus concepts. Practice constructing mathematical proofs and explanations.

Utilise Technology Wisely. Use every opportunity to leverage graphing calculators or software like GeoGebra for visualising functions, graphs, and geometric concepts. Practice using these tools to reinforce understanding and solve problems efficiently.

IB Maths Tutoring at Chapkin Edwards

Chapkin Edwards is a leading provider of expert tuition, homeschooling and school and university admissions support. If your child requires tutoring in Maths or any other subject at IB, please contact us here.

Josh Chapkin