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Revision Notes

IB Maths AI HL

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

AI HL · Revision Notes

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Number & Algebra

8 Topics · 33 Revision Notes

8 Topics▾

Number Toolkit

6▾

Standard Form→ Approximation→ Upper & Lower Bounds→ Percentage Error→ Accuracy & Estimation→ Solving Equations using a GDC→

Exponentials & Logs

3▾

Laws of Indices→ Introduction to Logarithms→ Laws of Logarithms→

Sequences & Series

5▾

Language of Sequences & Series→ Sigma Notation→ Arithmetic Sequences & Series→ Geometric Sequences & Series→ Applications of Sequences & Series→

Financial Applications

3▾

Compound Interest & Depreciation→ Amortisation→ Annuities→

Complex Numbers

5▾

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

Further Complex Numbers

5▾

Geometry of Complex Numbers→ Modulus-Argument (Polar) Form→ Exponential (Euler’s) Form→ Conversion between Forms of Complex Numbers→ Frequency & Phase of Trig Functions→

Matrices

4▾

Introduction to Matrices→ Operations with Matrices→ Determinants & Inverses→ Solving Systems of Linear Equations with Matrices→

Eigenvalues & Eigenvectors

2▾

The Characteristic Polynomial, Eigenvalues & Eigenvectors→ Diagonalisation & Powers of Matrices→

Functions

6 Topics · 25 Revision Notes

6 Topics▾

Linear Functions & Graphs

2▾

Equations of a Straight Line→ Parallel & Perpendicular Lines→

Further Functions & Graphs

7▾

Functions & Mappings→ Graphing Functions & Their Key Features→ Intersecting Graphs→ Quadratic Functions & Graphs→ Cubic Functions & Graphs→ Exponential Functions & Graphs→ Sinusoidal Functions & Graphs→

Modelling with Functions

7▾

Linear Models→ Quadratic Models→ Cubic Models→ Exponential Models→ Direct & Inverse Variation→ Sinusoidal Models→ Strategy for Modelling Functions→

Functions Toolkit

2▾

Composite Functions→ Inverse Functions→

Transformations of Graphs

4▾

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

Modelling with Logarithmic, Logistic & Piecewise Functions

3▾

Natural Logarithmic Models→ Logistic Models→ Piecewise Models→

Geometry & Trigonometry

10 Topics · 47 Revision Notes

10 Topics▾

Geometry Toolkit

5▾

Coordinate Geometry→ Perpendicular Bisectors→ 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→

Trigonometric Identities & Equations

4▾

The Unit Circle→ Simple Identities→ Graphs of Trigonometric Functions→ Solving Equations Using Trigonometric Graphs→

Voronoi Diagrams

3▾

Drawing Voronoi Diagrams→ Interpreting Voronoi Diagrams→ Toxic Waste Dump Problem→

Matrix Transformations

4▾

Matrix Transformations→ Matrices of Geometric Transformations→ Matrices of Composite Transformations→ Determinant of a Transformation Matrix→

Vector Properties

11▾

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→ Components of Vectors→ Geometric Proof with Vectors→

Vector Equations of Lines

5▾

Equation of a Line in Vector Form→ Equation of a Line in Parametric Form→ Angle Between Two Lines→ Shortest Distance Between a Point and a Line→ Shortest Distance Between Two Lines→

Modelling with Vectors

2▾

Kinematics with Vectors→ Constant & Variable Velocity→

Graph Theory

7▾

Introduction to Graph Theory→ Walks & Adjacency Matrices→ Minimum Spanning Trees (Kruskal’s Algorithm)→ Minimum Spanning Trees (Prim’s Algorithm)→ Chinese Postman Problem→ Travelling Salesman Problem→ Nearest Neighbour & Deleted Vertex Algorithms→

Statistics & Probability

13 Topics · 50 Revision Notes

13 Topics▾

Statistics Toolkit

11▾

Sampling→ Reliability & Validity of Data Collection Methods→ 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

5▾

Scatter Diagrams & Correlation→ Pearson’s Product-Moment Correlation Coefficient→ Spearman’s Rank Correlation Coefficient→ Comparison of Correlation Coefficients→ Linear Regression→

Non-linear Regression

3▾

Least Squares Regression Curves & Coefficient of Determination→ Logarithmic Scales→ Linearising using Logarithms→

Probability

5▾

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

Probability Distributions

2▾

Discrete Probability Distributions→ Expected Values→

Random Variables

2▾

Linear Combinations of Random Variables→ Unbiased Estimates→

Binomial Distribution

2▾

The Binomial Distribution→ Calculating Binomial Probabilities→

Normal Distribution

2▾

The Normal Distribution→ Calculations with Normal Distribution→

Combinations of Normal Distributions & Sample Mean Distributions

3▾

Sample Mean Distribution→ Central Limit Theorem→ Confidence Interval for the Mean→

Poisson Distribution

2▾

Poisson Distribution→ Calculating Poisson Probabilities→

Hypothesis Testing using the Chi-squared Distribution

3▾

Introduction to Hypothesis Testing→ Chi-squared Test for Independence→ Goodness of Fit Test→

Hypothesis Testing for Population Parameters

6▾

Hypothesis Testing for Mean (One Sample)→ Hypothesis Testing for Mean (Two Sample)→ Binomial Hypothesis Testing→ Poisson Hypothesis Testing→ Hypothesis Testing for Correlation→ Type I & Type II Errors→

Transition Matrices & Markov Chains

4▾

Markov Chains→ Transition Matrices→ Powers of Transition Matrices→ Steady State & Long-term Probabilities→

Calculus

7 Topics · 38 Revision Notes

7 Topics▾

Differentiation

6▾

Introduction to Derivatives→ Differentiating Powers of x→ Gradients, Tangents & Normals→ Increasing & Decreasing Functions→ Local Minimum & Maximum Points→ Modelling with Differentiation→

Further Differentiation

8▾

Differentiating Special Functions→ Chain Rule→ Product Rule→ Quotient Rule→ Related Rates of Change→ Second Order Derivatives→ Stationary Points→ Concavity & Points of Inflection→

Integration

5▾

Numerical Integration using the Trapezoidal Rule→ Introduction to Integration→ Integrating Powers of x→ Finding the Constant of Integration→ Finding Areas Using a GDC→

Further Integration

8▾

Integrating Special Functions→ Reverse Chain Rule→ Integration by Substitution→ Definite Integrals→ Negative Integrals→ Area Between Curve & y-axis→ Area Between a Curve and a Line→ Volumes of Revolution→

Kinematics

2▾

Displacement, Velocity & Acceleration→ Calculus for Kinematics→

Differential Equations

4▾

Separation of Variables→ Modelling with Differential Equations→ Slope Fields→ Approximate Solutions to Differential Equations using Euler’s Method→

Coupled & Second Order Differential Equations

5▾

Coupled Differential Equations→ Phase Portraits→ Equilibrium Points→ Sketching Solution Trajectories→ Second Order Differential Equations→

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