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Revision Notes

IB Maths

Expert revision notes for IB Mathematics — Analysis & Approaches and Applications & Interpretation, covering every topic from Number & Algebra to Calculus.

IB Maths · Revision Notes

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Number & Algebra

Indices, logarithms, sequences, proof, and binomial theorem.

14 notes▾

Number Toolkit

2▾

Standard Form→ Laws of Indices→

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→

Proof & Reasoning

1▾

Proof→

Binomial Theorem

2▾

Binomial Coefficients & Pascal’s Triangle→ Binomial Theorem→

Functions

Linear, quadratic, exponential, and transformations of graphs.

22 notes▾

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

5▾

Language of Functions→ Composite Functions→ Inverse Functions→ Graphing Functions & Key Features→ Intersecting Graphs→

Further Functions & Graphs

5▾

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

Transformations of Graphs

4▾

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

Geometry & Trigonometry

Coordinate geometry, 3D shapes, the unit circle and identities.

23 notes▾

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→ 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 Trig Graphs→ Transformations of Trig Functions→ Modelling with Trig Functions→

Trigonometric Equations & Identities

5▾

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

Statistics & Probability

Data, correlation, probability and probability distributions.

26 notes▾

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 PMCC→ Linear Regression→

Probability

5▾

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

Probability Distributions

2▾

Discrete Probability Distributions→ Expected Values→

Binomial Distribution

2▾

The Binomial Distribution→ Calculating Binomial Probabilities→

Normal Distribution

4▾

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

Calculus

Differentiation, integration, optimisation, and kinematics.

26 notes▾

Differentiation

4▾

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

Further Differentiation

8▾

Differentiating Special Functions→ Chain Rule→ Product Rule→ Quotient Rule→ Second 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→

Further Integration

7▾

Integrating Special 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→

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