IB Mathematics AI SL
Applications & Interpretation - Standard Level
Welcome, students! This specialized section contains syllabus breakdowns, core study notes, targeted practice question banks, and actual exam past papers organized dynamically to optimize your learning and help you achieve a Grade 7.
1. Course Introduction
Mathematics: Applications and Interpretation (AI) Standard Level (SL) introduces students to the practical applications of mathematics in real-world contexts, modeling basic economic and physical systems, and foundational statistics and probability. It is designed for students interested in pursuing careers in Arts, Humanities, Social Sciences, Business, or Languages at the university level.
Assessment Outline
The IB Mathematics AI SL course is assessed through two final written examinations (80%) and an independent mathematical exploration task (20%). A graphic display calculator (GDC) is required for all written examinations:
| Assessment Component | Duration | Calculator Policy | Marks | Weighting |
|---|---|---|---|---|
| Paper 1 (Short Questions) | 90 minutes (1.5 hours) | Calculator required (GDC required) | 80 marks | 40% |
| Paper 2 (Long Questions) | 90 minutes (1.5 hours) | Calculator required (GDC required) | 80 marks | 40% |
| Internal Assessment (IA) - Exploration | Independent research (12-20 pages) | No restrictions | 20 marks | 20% |
Syllabus Structure
The syllabus is organized into five core topics at the standard level (Standard Level Core):
1.1: Operations in standard form
1.2: Arithmetic sequences and series
1.3: Geometric sequences and series
1.4: Financial applications
1.5: Laws of exponents with integer exponents
1.6: Approximation and significant figures
1.7: Amortization and annuities using technology
1.8: Systems of linear equations and polynomial solutions
2.1: Straight lines: equations, gradient, intercepts
2.2: Concept of a function: domain, range, notation
2.3: Graphs of functions
2.4: Key features of graphs
2.5: Financial and modeling applications
2.6: Mathematical modeling process
3.1: Distance and midpoint in 3D space
3.2: Right-angled trigonometry
3.3: Sine and cosine rules, area of a triangle
3.4: Circle geometry: arc length and sector area
3.5: Equations of perpendicular bisectors
3.6: Voronoi diagrams
4.1: Population, sampling, discrete and continuous data
4.2: Data presentation: frequency distributions
4.3: Measures of central tendency and dispersion
4.4: Bivariate data, correlation, and regression
4.5: Probability of events, Venn and tree diagrams
4.6: Independent and mutually exclusive events
4.7: Discrete random variables and expectation
4.8: Binomial distribution
4.9: Normal distribution
4.10: Spearman’s rank correlation coefficient
4.11: Chi-squared tests for independence and goodness of fit
5.1: Introduction to limits
5.2: Increasing and decreasing functions
5.3: Derivative of power functions and basic rules
5.4: Tangents and normals equations
5.5: Indefinite integration as anti-differentiation
5.6: Stationary points and local maximum/minimum
5.7: Optimization problems
5.8: Trapezoidal rule for approximating areas
Official Academic Resources
Download official IB resources and curriculum guides below (Google Drive links will be loaded from metadata):
2. Study Notes
Access curated study notes summarizing core formulas and key theorems across all topics:
| Topic | Notes | Questions |
|---|---|---|
| 1. Number & Algebra | ||
| 1.1 Number Toolkit | Notes | Questions |
| 1.2 Sequences & Series | Notes | Questions |
| 1.3 Financial Applications | Notes | Questions |
| 2. Functions | ||
| 2.1 Linear Functions & Graphs | Notes | Questions |
| 2.2 Further Functions & Graphs | Notes | Questions |
| 2.3 Modelling with Functions | Notes | Questions |
| 3. Geometry & Trigonometry | ||
| 3.1 Geometry Toolkit | Notes | Questions |
| 3.2 Geometry of 3D Shapes | Notes | Questions |
| 3.3 Trigonometry | Notes | Questions |
| 3.4 Voronoi Diagrams | Notes | Questions |
| 4. Statistics & Probability | ||
| 4.1 Statistics Toolkit | Notes | Questions |
| 4.2 Correlation & Regression | Notes | Questions |
| 4.3 Probability | Notes | Questions |
| 4.4 Probability Distributions | Notes | Questions |
| 4.5 Binomial Distribution | Notes | Questions |
| 4.6 Normal Distribution | Notes | Questions |
| 4.7 Hypothesis Testing | Notes | Questions |
| 5. Calculus | ||
| 5.1 Differentiation | Notes | Questions |
| 5.2 Integration | Notes | Questions |
| Syllabus Topic | Summary Guide |
|---|---|
| Topic 1A: Basic algebra | Download PDF |
| Topic 2A: Theory of functions | Download PDF |
| Topic 2B: Modelling with functions | Download PDF |
| Topic 3A: Trigonometry | Download PDF |
| Topic 4A: Descriptive Statistics - Probability | Download PDF |
| Topic 4B: Inferential Statistics | Download PDF |
| Topic 5A: Differentiation | Download PDF |
| Topic 5B: Integration | Download PDF |
3. Practice Questions
| Subtopic | Worksheet Title | Question Paper | Mark Scheme |
|---|---|---|---|
| Topic 1: Number & Algebra | |||
1.1
|
Numbers & Rounding & Percentage Error | Questions | — |
1.2-1.3
|
Exponents & Systems Of Linear Equations | Questions | — |
1.4-1.5
|
Arithmetic Sequences | Questions | — |
1.6
|
Geometric Sequences | Questions | — |
| Topic 2: Functions | |||
2.1
|
Lines | Questions | — |
2.2
|
Quadratics | Questions | — |
2.3-2.4
|
Functions | Questions | — |
2.5-2.6
|
Exponents & Logarithms-i | Questions | — |
2.16
|
Exponential Model | Questions | — |
2.17
|
Financial Applications | Questions | — |
| Topic 3: Geometry & Trigonometry | |||
3.1-3.4
|
3D Geometry & Triangles | Questions | — |
3.5
|
Arcs & Sectors | Questions | — |
| Topic 4: Statistics & Probability | |||
4.1-4.3
|
Descriptive Statistics | Questions | — |
4.4
|
Linear Regression | Questions | — |
4.5-4.7
|
Probability I (venn Diagrams & Tables) | Questions | — |
4.8
|
Probability Ii (tree Diagrams) | Questions | — |
4.9
|
Discrete Distributions | Questions | — |
4.10
|
Binomial Distribution | Questions | — |
4.11
|
Normal Distribution | Questions | — |
| Topic 5: Calculus | |||
5.1
|
The Concept Of The Limit | Questions | Solutions |
5.2-5.3
|
Basic Derivatives & Tangent & Normal | Questions | Solutions |
5.4
|
Monotony & Max & Min | Questions | Solutions |
5.5
|
Optimization | Questions | Solutions |
5.10-5.13
|
Basic Integrals & Areas | Questions | Solutions |
4. Topical past paper questions
Questions taken from actual exam questions organized by the main syllabus topics:
| Chapter | Topic / Concept Area | Paper 1 | Paper 2 |
|---|---|---|---|
| Ch 1 | Algebra, Functions & Roots | Part 1 | Part 1 |
| Ch 2 | Quadratics | Part 1 | Part 1 |
| Ch 3 | Exponents & Logarithms | Part 1 | Part 1 |
| Ch 4 | Graphs | Part 1 | Part 1 |
| Ch 5 | Sequences & Series | Part 1 | Part 1 |
| Ch 11 | Radians | Part 1 | Part 1 |
| Ch 12 | Trigonometry | Part 1 | Part 1 |
| Ch 14 | Planes | Part 1 | Part 1 |
| Ch 15 | Statistics | Part 1 | Part 1 |
| Ch 16 | Probability | Part 1 | Part 1 |
| Ch 17 | Differential Calculus | Part 1 | Part 1 |
| Ch 18 | Integration | Part 1 | Part 1 |
| Ch 20 | Relative Velocity | Part 1 | Part 1 |
| Ch 21 | Geometry | Part 1 | Part 1 |
| Chapter | Topic / Concept Area | Paper 1 | Paper 2 |
|---|---|---|---|
| Ch 1 | Numbers & Algebra | Part 1 Part 2 Part 3 | Part 1 |
| Ch 2 | Descriptive Statistics | Part 1 Part 2 | Part 1 |
| Ch 3 | Sets & Probability | Part 1 Part 2 | Part 1 |
| Ch 4 | Statistical Applications | Part 1 | Part 1 |
| Ch 5 | Geometry & Trigonometry | Part 1 Part 2 | Part 1 Part 2 |
| Ch 6 | Mathematical Models | Part 1 Part 2 | Part 1 |
| Ch 7 | Differentiation | Part 1 | Part 1 |
5. Past Papers Bank
Search and filter actual past exam papers. Use the quick filter bar to locate papers by year, component, or document type:
IB Mathematics AI SL Past Papers
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