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Revision Notes

IB Maths AA HL

Expert revision notes for IB Mathematics Analysis & Approaches Higher Level — every syllabus topic with worked examples and exam tips for Paper 1, Paper 2 and Paper 3.

AA HL · Revision Notes

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Number & Algebra

10 Topics · 37 Revision Notes

10 Topics▾

Partial Fractions, Indices & Standard Form

3▾

Standard Form→ Laws of Indices→ Partial Fractions→

Exponentials & Logs

3▾

Introduction to Logarithms→ Laws of Logarithms→ Solving Exponential Equations→

Sequences & Series

6▾

Language of Sequences & Series→ Sigma Notation→ Arithmetic Sequences & Series→ Geometric Sequences & Series→ Applications of Sequences & Series→ Compound Interest & Depreciation→

Simple Proof & Reasoning

2▾

Proof by Deduction→ Disproof by Counter Example→

Proof by Induction & Contradiction

2▾

Proof by Induction→ Proof by Contradiction→

Binomial Theorem

3▾

Binomial Theorem→ Binomial Coefficients & Pascal’s Triangle→ Extension of The Binomial Theorem→

Permutations & Combinations

3▾

Counting Principles→ Permutations→ Combinations→

Complex Numbers

4▾

Introduction to Complex Numbers→ Operations with Complex Numbers→ Introduction to Argand Diagrams→ Modulus & Argument→

Further Complex Numbers

8▾

Geometry of Complex Numbers→ Modulus-Argument (Polar) Form→ Exponential (Euler’s) Form→ Conversion between Forms of Complex Numbers→ Complex Roots of Polynomials→ De Moivre’s Theorem→ Proof of De Moivre’s Theorem→ Roots of Complex Numbers→

Systems of Linear Equations

3▾

Systems of Linear Equations→ Solving Systems Using Row Reduction→ Number of Solutions to a System→

Functions

9 Topics · 37 Revision Notes

9 Topics▾

Linear Functions & Graphs

2▾

Equations of a Straight Line→ Parallel & Perpendicular Lines→

Quadratic Functions & Graphs

6▾

Quadratic Functions→ Factorising Quadratics→ Completing the Square→ Solving Quadratic Equations→ Quadratic Inequalities→ Discriminants→

Functions Toolkit

8▾

Language of Functions→ Composite Functions→ Inverse Functions→ Odd & Even Functions→ Periodic Functions→ Self-Inverse Functions→ Graphing Functions & Their Key Features→ Intersecting Graphs→

Other Functions & Graphs

4▾

Exponential & Logarithmic Functions→ Solving Equations Analytically→ Solving Equations Graphically→ Modelling with Functions→

Reciprocal & Rational Functions

2▾

Reciprocal & Rational Functions→ Rational Functions with Quadratics→

Transformations of Graphs

4▾

Translations of Graphs→ Reflections of Graphs→ Stretches of Graphs→ Composite Transformations of Graphs→

Polynomial Functions

4▾

Polynomial Division→ Factor & Remainder Theorem→ Graphs & Roots of Polynomial Functions→ Sum & Product of Roots of Polynomials→

Inequalities

2▾

Solving Inequalities Graphically→ Polynomial Inequalities→

Modulus Functions & Further Transformations

5▾

Modulus Functions→ Modulus Transformations→ Modulus Equations & Inequalities→ Reciprocal Transformations→ Square Transformations→

Geometry & Trigonometry

11 Topics · 51 Revision Notes

11 Topics▾

Geometry Toolkit

4▾

Coordinate Geometry→ Arcs & Sectors Using Degrees→ Radian Measure→ Arcs & Sectors Using Radians→

Geometry of 3D Shapes

2▾

3D Coordinate Geometry→ Volume & Surface Area→

Trigonometry

4▾

Pythagoras & Right-Angled Trigonometry→ Sine Rule, Cosine Rule & Area of a Triangle→ Angles of Elevation & Depression→ Bearings & Constructions→

The Unit Circle & Exact Values

2▾

The Unit Circle→ Exact Values→

Trigonometric Functions & Graphs

4▾

Graphs of Trigonometric Functions→ Solving Equations Using Trigonometric Graphs→ Transformations of Trigonometric Functions→ Modelling with Trigonometric Functions→

Trigonometric Equations & Identities

6▾

Simple Identities→ Compound Angle Formulae→ Double Angle Formulae→ Relationship Between Trigonometric Ratios→ Linear Trigonometric Equations→ Quadratic Trigonometric Equations→

Inverse & Reciprocal Trigonometric Functions

2▾

Reciprocal Trigonometric Functions→ Inverse Trigonometric Functions→

Trigonometric Proof & Equation Strategies

2▾

Trigonometric Proof→ Strategy for Trigonometric Equations→

Vector Properties

10▾

Introduction to Vectors→ Parallel Vectors→ Adding & Subtracting Vectors→ Position & Displacement Vectors→ Magnitude of a Vector & Unit Vectors→ The Scalar Product→ Angle Between Two Vectors & Perpendicular Vectors→ The Vector Product→ Areas using the Vector Product→ Geometric Proof with Vectors→

Vector Equations of Lines

8▾

Equation of a Line in Vector Form→ Equation of a Line in Parametric Form→ Equation of a Line in Cartesian Form→ Applications to Kinematics→ Coincident, Parallel, Intersecting & Skew Lines→ Angle Between Two Lines→ Shortest Distance Between a Point and a Line→ Shortest Distance Between Two Lines→

Vector Planes

7▾

Equation of a Plane in Vector Form→ Equation of a Plane in Cartesian Form→ Intersections of a Line & a Plane→ Intersections of Two Planes→ Angles Between a Line & a Plane→ Angles Between Two Planes→ Shortest Distances with Planes→

Statistics & Probability

7 Topics · 31 Revision Notes

7 Topics▾

Statistics Toolkit

10▾

Sampling & Data Collection→ Measures of Central Tendency→ Measures of Dispersion→ Frequency Tables→ Linear Transformations of Data→ Outliers→ Box & Whisker Diagrams→ Cumulative Frequency Graphs→ Histograms→ Interpreting Data→

Correlation & Regression

3▾

Scatter Diagrams & Correlation→ Pearson’s Product-Moment Correlation Coefficient→ Linear Regression→

Probability

6▾

Probability & Types of Events→ Independent & Mutually Exclusive Events→ Conditional Probability→ Bayes’ Theorem→ Venn Diagrams→ Tree Diagrams→

Discrete Random Variables

3▾

Discrete Probability Distributions→ Mean & Variance→ Transformation of a Single Variable→

Binomial Distribution

2▾

The Binomial Distribution→ Calculating Binomial Probabilities→

Normal Distribution

4▾

The Normal Distribution→ Calculations with Normal Distribution→ Standardisation of Normal Variables & z-Values→ Finding Unknown Parameters→

Continuous Random Variables

3▾

Probability Density Function→ Median & Mode of a CRV→ Mean & Variance of a CRV→

Calculus

12 Topics · 57 Revision Notes

12 Topics▾

Differentiation

4▾

Introduction to Derivatives→ Differentiating Powers of x→ Gradients, Tangents & Normals→ Increasing & Decreasing Functions→

Techniques & Applications of Differentiation

8▾

Differentiating Trigonometric, Exponential & Logarithmic Functions→ Chain Rule→ Product Rule→ Quotient Rule→ Higher Order Derivatives→ Stationary Points→ Concavity & Points of Inflection→ Derivatives & Graphs→

Integration

4▾

Introduction to Integration→ Integrating Powers of x→ Finding the Constant of Integration→ Finding Areas Using a GDC→

Techniques & Applications of Integration

7▾

Integrating Trigonometric, Exponential & Reciprocal Functions→ Reverse Chain Rule→ Integration by Substitution→ Definite Integrals→ Negative Integrals→ Area Between a Curve and a Line→ Area Between 2 Curves→

Optimisation

1▾

Modelling with Differentiation→

Kinematics

2▾

Displacement, Velocity & Acceleration→ Calculus for Kinematics→

Basic Limits & Continuity

2▾

Introduction to Limits→ Continuity & Differentiability→

Further Differentiation

7▾

First Principles Differentiation→ Differentiating Inverse Functions→ Implicit Differentiation→ Related Rates of Change→ Differentiating Reciprocal Trigonometric Functions→ Differentiating Inverse Trigonometric Functions→ Differentiating Exponential & Logarithmic Functions→

Further Integration

9▾

Integrating with Reciprocal Trigonometric Functions→ Integrating with Inverse Trigonometric Functions→ Integrating with Exponential & Logarithmic Functions→ Integration by Substitution→ Integration by Parts→ Integrating with Partial Fractions→ Area Between Curve & y-axis→ Volumes of Revolution→ Modelling with Volumes of Revolution→

Differential Equations

7▾

Introduction to First Order Differential Equations→ Euler’s Method→ Separation of Variables→ Homogeneous Differential Equations→ Integrating Factor→ Modelling with Differential Equations→ The Logistic Equation→

Maclaurin Series

4▾

Maclaurin Series of Standard Functions→ Maclaurin Series of Composites & Products→ Differentiating & Integrating Maclaurin Series→ Maclaurin Series from Differential Equations→

Limits using l’Hôpital’s Rule & Maclaurin Series

2▾

l’Hôpital’s Rule→ Limits using Maclaurin Series→

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