IB Mathematics AA SL
Analysis & Approaches - 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: Analysis and Approaches (AA) Standard Level (SL) is designed for students who want to develop a strong analytical foundation in mathematics. The course focuses on theoretical mathematical concepts, algebraic analysis, functions, trigonometry, statistics, and an introduction to differential and integral calculus. It is highly suitable for students planning to study Economics, Business, Medicine, or Social Sciences at the university level.
Assessment Outline
The IB Mathematics AA SL course is assessed through two final written examinations (80%) and an independent mathematical exploration task (20%). A graphic display calculator (GDC) is required only for Paper 2:
| Assessment Component | Duration | Calculator Policy | Marks | Weighting |
|---|---|---|---|---|
| Paper 1 (Section A & B) | 90 minutes (1.5 hours) | Non-calculator (Non-GDC) | 80 marks | 40% |
| Paper 2 (Section A & B) | 90 minutes (1.5 hours) | Calculator allowed (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 and logarithms
1.6: Simple deductive proofs
1.7: Rational exponents
1.8: Infinite geometric series
1.9: Binomial theorem
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: Composite and inverse functions
2.6: Quadratic functions and their graphs
2.7: Quadratic equations and discriminant
2.8: Reciprocal functions and graphs
2.9: Exponential and logarithmic functions
2.10: Solving equations graphically and analytically
2.11: Transformations of graphs
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: Radian measure, arc length, sector area
3.5: Unit circle trig definitions
3.6: Pythagorean identity and double angle formulae
3.7: Trigonometric graphs
3.8: Solving trigonometric equations
4.1: Population, sampling, discrete and continuous data
4.2: Data presentation: frequency tables, histograms, box plots
4.3: Measures of central tendency and dispersion
4.4: Linear correlation of bivariate data
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: Regression line and predictions
4.11: Conditional probability
4.12: Standardized normal variables (z-scores)
5.1: Concept of 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: Derivative rules: product, quotient, and chain rules
5.7: Second derivative, concavity, points of inflection
5.8: Local maximum and minimum points
5.9: Kinematic applications
5.10: Indefinite integrals of standard functions
5.11: Definite integrals and area under a curve
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 Exponentials & Logs | Notes | Questions |
| 1.3 Sequences & Series | Notes | Questions |
| 1.4 Proof & Reasoning | Notes | Questions |
| 1.5 Binomial Theorem | Notes | Questions |
| 2. Functions | ||
| 2.1 Linear Functions & Graphs | Notes | Questions |
| 2.2 Quadratic Functions & Graphs | Notes | Questions |
| 2.3 Functions Toolkit | Notes | Questions |
| 2.4 Further Functions & Graphs | Notes | Questions |
| 2.5 Transformations of Graphs | 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 The Unit Circle & Exact Values | Notes | Questions |
| 3.5 Trigonometric Functions & Graphs | Notes | Questions |
| 3.6 Trigonometric Equations & Identities | 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 |
| 5. Calculus | ||
| 5.1 Differentiation | Notes | Questions |
| 5.2 Further Differentiation | Notes | Questions |
| 5.3 Integration | Notes | Questions |
| 5.4 Further Integration | Notes | Questions |
| 5.5 Optimisation | Notes | Questions |
| 5.6 Kinematics | Notes | Questions |
| Syllabus Topic | Summary Guide |
|---|---|
| Topic 1: Number & Algebra | Download PDF |
| Topic 2: Functions | Download PDF |
| Topic 3: Geometry & Trigonometry | Download PDF |
| Topic 4: Statistics & Probability | Download PDF |
| Topic 5: Calculus | Download PDF |
3. Practice Questions
| Subtopic | Worksheet Title | Question Paper | Mark Scheme |
|---|---|---|---|
| Topic 1: Number & Algebra | |||
1.1-1.2
|
Numbers & Methods Of Proof | Questions | Solutions |
1.3-1.6
|
Sequences | Questions | Solutions |
1.7
|
Binomial Theorem | Questions | Solutions |
| Topic 2: Functions | |||
2.1-2.2
|
Lines & Quadratics | Questions | Solutions |
2.3-2.5
|
Functions & Composition & Inverse | Questions | Solutions |
2.6-2.7
|
Transformations & Asymptotes | Questions | Solutions |
2.8-2.10
|
Exponents & Logarithms | Questions | Solutions |
| Topic 3: Geometry & Trigonometry | |||
3.1-3.3
|
3D Geometry & Triangles | Questions | Solutions |
3.4
|
Arcs & Sectors | Questions | Solutions |
3.5-3.6
|
Trigonometric Identities & Equations | Questions | Solutions |
3.7
|
Trigonometric Functions | Questions | Solutions |
|
[math-aa 3.6] Trigonometric Equations | Questions | Solutions |
|
[math-aa 3.7] Trigonometric Functions | Questions | Solutions |
|
[math-aa 3.5] Sin, Cos, Tan On The Unit Circle & Identities | Questions | Solutions |
| Topic 4: Statistics & Probability | |||
4.1-4.3
|
Statistics & Basic Concepts | Questions | Solutions |
4.4
|
Linear Regression | Questions | Solutions |
4.5-4.8
|
Probability | Questions | Solutions |
4.9-4.10
|
Discrete Distributions & Binomial | Questions | Solutions |
4.11
|
Normal Distribution | Questions | Solutions |
| Topic 5: Calculus | |||
5.1-5.3
|
Derivatives & Tangent & Normal | Questions | Solutions |
5.4
|
Chain Rule | Questions | Solutions |
5.5-5.6
|
Monotony & Concavity & Graph Of F ’ | Questions | Solutions |
5.7
|
Problems Of Optimisation | Questions | Solutions |
5.8-5.9
|
Indefinite Integrals | Questions | Solutions |
5.10
|
Definite Integrals & Areas | Questions | Solutions |
5.11
|
Kinematics | Questions | Solutions |
| Topic Area | Paper 1 (Non-Calculator) | Paper 2 (Calculator Allowed) |
|---|---|---|
| Quadratics | Download Paper 1 | Download Paper 2 |
| Sequences & Series | Download Paper 1 | Download Paper 2 |
| Trigonometry | Download Paper 1 | Download Paper 2 |
| Vectors | Download Paper 1 | Download Paper 2 |
| Probability | Download Paper 1 | Download Paper 2 |
| Statistics | Download Paper 1 & 2 | |
| Calculus | Download Paper 1 | Download Paper 2 |
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 8 | Binomial Theorem | Part 1 | Part 1 |
| Ch 11 | Radians | Part 1 | Part 1 |
| Ch 12 | Trigonometry | Part 1 | Part 1 |
| Ch 14 | Lines & Planes | Part 1 | Part 1 |
| Ch 15 | Statistics | Part 1 | Part 1 |
| Ch 16 | Probability | Part 1 | Part 1 |
| Ch 17 | Differentiation | Part 1 | Part 1 |
| Ch 18 | Integration | Part 1 | Part 1 |
| Ch 20 | Kinematics | Part 1 | Part 1 |
| Ch 21 | Geometry | Part 1 | Part 1 |
| 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 8 | Binomial Theorem | Part 1 | Part 1 |
| Ch 11 | Radians | Part 1 | Part 1 |
| Ch 12 | Trigonometry | Part 1 | Part 1 |
| Ch 13 | Matrices | Part 1 | Part 1 |
| Ch 14 | Lines & Planes | Part 1 | Part 1 |
| Ch 15 | Statistics | Part 1 | Part 1 |
| Ch 16 | Probability | Part 1 | Part 1 |
| Ch 17 | Differentiation | Part 1 | Part 1 |
| Ch 18 | Integration | Part 1 | Part 1 |
| Ch 20 | Kinematics | 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 AA SL Past Papers
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