IB Maths AI SL Resources
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Topic-wise IB questions with full solutions and explanations.
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IGCSE
Mathematics: Applications & Interpretation (AI)
Where Mathematics Meets the Real World
IB Mathematics: Applications & Interpretation (AI) is designed for students who enjoy using mathematics to understand, analyse, and solve real-life problems. From statistics and financial modelling to technology-driven investigations and data interpretation, this course shows how mathematics is applied in everyday life and modern industries.
Part of the International Baccalaureate Diploma Programme (IBDP), AI Mathematics develops strong analytical thinking, logical reasoning, and practical problem-solving skills while encouraging the effective use of technology and mathematical tools.
What Makes AI Mathematics Unique?
✔ Focus on real-world applications of mathematics
✔ Strong emphasis on statistics, modelling, and interpretation
✔ Encourages practical and technology-based learning
✔ Ideal for students interested in business, economics, social sciences, psychology, data science, and technology-related fields
✔ Develops confidence in interpreting mathematical results in context
Course Levels
Standard Level (SL)
- Approx. 150 teaching hours
- Balanced focus on applications, statistics, and modelling
- Suitable for students requiring practical mathematics for a wide range of university courses
Higher Level (HL)
- Approx. 240 teaching hours
- More advanced mathematical concepts and deeper analytical thinking
- Ideal for students aiming for mathematically demanding university programmes
Assessment Structure Overview
The IB Mathematics: Applications & Interpretation (AI) course is assessed through a combination of external examinations and an Internal Assessment (IA), designed to evaluate both conceptual understanding and practical application of mathematics.
| Assessment Component | Calculator-based Papers | SL | HL | Weighting |
|---|---|---|---|---|
| Paper 1 | Focused on mathematical reasoning, modelling, and problem-solving | 1 hour 30 minutes | 2 hours | SL: 40% HL: 30% |
| Paper 2 | Assessing real-world applications and interpretation of mathematical results | 1 hour 30 minutes | 2 hours | SL: 40% HL: 30% |
| Paper 3 | requiring deeper analytical and investigative skills (HL only) | — | 1 hour | HL: 20% |
| Mathematical Exploration (IA) | Internal Assessment involving an original mathematical investigation and exploration | 30 hours | 30 hours | 20% |
Key Highlights
✔ Strong emphasis on technology and real-world applications
✔ Balanced assessment of analytical, practical, and investigative skills
✔ Internal Assessment encourages creativity and independent mathematical exploration
✔ HL students undertake an additional advanced problem-solving paper
Assessment Philosophy
The AI course is designed not only to test mathematical knowledge, but also to develop students’ ability to:
- interpret mathematical information,
- apply mathematics in realistic contexts,
- communicate reasoning clearly,
- and use technology effectively to solve complex problems.
Topics
1 Number & Algebra
| SL Topics | HL Topics |
|---|---|
| 1.1 Standard Form | 1.9 Logarithmic Laws |
| 1.2 Sequences & Sigma Notation | 1.10 Fractional Exponents |
| 1.3 Geometric Sequences | 1.11 Infinite Geometric Series |
| 1.4 Compound Interest & Depreciation | 1.12 Introduction to Complex Numbers |
| 1.5 Exponents & Logarithms | 1.13 Advanced Complex Numbers |
| 1.6 Approximation & Estimation | 1.14 Matrices |
| 1.7 Loans & Amortization | 1.15 Eigenvalues & Eigenvectors |
| 1.8 Technology & Polynomial Equations |
2 Functions
| SL Topics | HL Topics |
|---|---|
| 2.1 Equations of a Line | 2.7 Composite & Inverse Functions |
| 2.2 Functions, Domain & Range | 2.8 Transformations of Graphs |
| 2.3 Graphing Functions | 2.9 HL Modelling Functions |
| 2.4 Features of Graphs | 2.10 Log-Log Graphs |
| 2.5 Mathematical Modelling | |
| 2.6 Modelling Skills |
3 Geometry & Trigonometry
| SL Topics | HL Topics |
|---|---|
| 3.1 3D Geometry & Midpoints | 3.7 Radians |
| 3.2 2D & 3D Trigonometry | 3.8 Unit Circle & Trig Equations |
| 3.3 Angles of Elevation & Depression | 3.9 Matrix Transformations |
| 3.4 Circle Geometry & Sectors | 3.10 Vector Basics |
| 3.5 Intersections & Perpendicular Bisectors | 3.11 Vector Equations of Lines |
| 3.6 Voronoi Diagrams | 3.12 Vectors in Kinematics |
| 3.13 Scalar & Vector Products | |
| 3.14 Graph Theory | |
| 3.15 Adjacency Matrices | |
| 3.16 Tree & Cycle Algorithms |
4 Statistics & Probability
| SL Topics | HL Topics |
|---|---|
| 4.1 Introduction to Statistics | 4.12 Data Collection & Reliability |
| 4.2 Data Presentation | 4.13 Non-Linear Regression |
| 4.3 Mean, Median & Mode | 4.14 Linear Transformations of RV |
| 4.4 Correlation | 4.15 Central Limit Theorem |
| 4.5 Trials & Outcomes | 4.16 Confidence Intervals |
| 4.6 Venn Diagrams | 4.17 Poisson Distribution |
| 4.7 Discrete Random Variables | 4.18 Hypothesis Testing (T & Z) |
| 4.8 Binomial Distribution | 4.19 Markov Chains |
| 4.9 Normal Distribution | |
| 4.10 Spearman’s Rank Correlation | |
| 4.11 Chi-Squared & T-Test |
5 Calculus
| SL Topics | HL Topics |
|---|---|
| 5.1 Introduction to Limits | 5.9 Derivative Rules |
| 5.2 Increasing & Decreasing Functions | 5.10 Second Derivatives |
| 5.3 Introduction to Derivatives | 5.11 Advanced Integration |
| 5.4 Tangents & Normals | 5.12 Areas & Volumes of Revolution |
| 5.5 Introduction to Integration | 5.13 Kinematics |
| 5.6 Stationary Points | 5.14 Differential Equations |
| 5.7 Optimisation | 5.15 Slope Fields |
| 5.8 Trapezoidal Rule | 5.16 Euler’s Method (1st Order) |
| 5.17 Phase Portraits | |
| 5.18 Euler’s Method (2nd Order) |
Why Choose IB Mathematics AI?
This course helps students:
- Think critically and logically
- Solve authentic real-world problems
- Analyse and interpret data effectively
- Use technology confidently in mathematics
- Build a strong foundation for university and future careers
AI SL vs AI HL
AI SL (Standard Level)
- Focuses on practical applications and core mathematical concepts
- Suitable for students who need mathematics as a supporting subject
AI HL (Higher Level)
- Includes deeper mathematical analysis and advanced applications
- Best for students pursuing mathematics-heavy or data-driven university courses
At Maths Republic Academy, we make IB Mathematics AI simple, engaging, and exam-focused — helping students build strong concepts, improve confidence, and achieve top scores.