All courses
Analysis & Approaches HL
Topic 1
Number & Algebra
Topic 1 All
All questions in Number & Algebra
Sequences & Series
Arithmetic & Geometric Progressions, Series, Sigma Notation, Infinite Sum...
Financial and Growth Models
Compound Interest & Depreciation, Exponential Growth & Decay, Real-World Financial Modelling...
Exponents & Logarithms
Exponent & Log Laws, Solving Exponential & Logarithmic Equations…
The Binomial Theorem
Pascal's Triangle, the Binomial Coefficient nCr, Binomial Expansions, Fractional & Negative Indices...
Counting Principles
Permutations & Combinations, Factorial Notation, Product Principle, Sum Principle…
Complex Numbers: Algebraic Operations
Sums & Products of Roots, Factorising, Solving Equations, Real Polynomials...
Complex Numbers: Geometric Representations
Different Forms, De Moivre’s Theorem, Argand Diagram, Geometric Applications…
Proof by Deduction, Contradiction, and Counterexample
Simple Deductive Proofs, LHS to RHS Proofs, Proof by Contradiction & Counterexample...
Proof by Induction: Series, Divisibility, and Inequalities
Proof by Induction including Propositions with Series, Divisibility and Inequalities...
Proof by Induction: Differentiation & Integration
Proof by Induction for Calculus Propositions, including Differentiation & Integration...
Systems of Linear Equations
Solving 3 x 3 Systems of Linear Equations, Row Operations, Unique/No/Infinite Solutions…
Topic 2
Functions
Topic 2 All
All questions in Functions
Composite & Inverse Functions
Composite Functions, One-to-One Functions, Domain & Range, Finding Inverses...
Linear and Quadratic Functions
Equations, Discriminant, Intercepts, Vertex Form, Roots, Modelling, Function Properties...
Rational Functions
Asymptotes, Intercepts, Sketching, Reciprocal Functions, GDC…
Exponential and Logarithmic Functions
Exponential & Logarithmic Functions & Graphs, Asymptotes, Intercepts…
Polynomials
Factor & Remainder Theorems, Sum & Product of Roots, Zeros, Roots, Factors…
Modulus Equations and Functions
Absolute-Value/Modulus Functions, Solving Equations & Inequalities…
Transformations
Translations, Reflections, Stretches, Graphs, Composite Transformations…
Function Sketching
Intercepts, Turning Points, Asymptotes, Symmetry, Transformations, End Behaviour...
Topic 3
Geometry & Trigonometry
Topic 3 All
All questions in Geometry & Trigonometry
Triangle Geometry
Sine & Cosine Rule, Area of a Triangle, Ambiguous Case, Right-Angled Trigonometry & 3D Applications...
Circle Geometry
Radians & Degrees, Arc Length & Area of Sector, Area of Segment, Problem-Solving & Applications...
Mixed Geometry
Sine & Cosine Rule, Arc Length & Sector Area, Triangles in Circles, Composite Areas & Applications...
Trigonometric Identities & Equations
Reciprocal Trig Functions, Compound & Double Angle Identities, Inverse Trig Functions, Symmetry Properties...
Trigonometric Functions & Graphs
Circular Functions, Amplitude, Period & Transformations, Domain, Range & Asymptotes, Modelling & Applications...
Vectors, Points & Lines
Vector Basics & Components, Scalar (Dot) Product & Angles, Vector Equation of a Line, Intersecting & Skew Lines...
Vectors & Planes
Vector (Cross) Product, Equations of a Plane, Line & Plane Intersections, Angles Between Lines & Planes...
Topic 4
Statistics & Probability
Topic 4 All
All questions in Statistics & Probability
Descriptive Statistics
Mean-Median-Mode, Variance, Standard Dev., IQR, Stem/Box Plot, Cumulative Freq…
Bivariate Statistics
Equation of Regression Line y=ax+b, Correlation Coefficient ‘r’, Strength, Applications…
Probability
Basics, Venn & Tree Diagrams, Combined Events, Independent, Mutually Exclusive, Conditional…
Discrete Random Variables
Probability Distributions, Expected Value, Variance, Applications...
Continuous Random Variables
Density Functions, Expected Value, Variance, Continuous Models...
The Binomial Distribution
Binomial Experiments, Parameters, Probabilities, Mean & Variance...
The Normal Distribution
Normal Models, Inverse Normal, Standardisation, z-Scores, Probabilities, Applications...
Topic 5
Calculus I
Calculus I All
All questions in Calculus I
Differentiation Fundamentals
Power Rule & Standard Derivatives, Chain, Product & Quotient Rules, Tangents & Normals, Second Derivative...
Trigonometric Differentiation
Derivatives of Sine, Cosine & Tangent, Reciprocal Trig Derivatives, Inverse Trig Derivatives, Chain Rule Applications...
Optimization
Setting Up & Solving Problems, First & Second Derivative Tests, Points of Inflexion, Real-World Applications...
L'Hopital's Rule
Indeterminate Forms, Evaluating Limits, L'Hôpital's Rule, Repeated Application & Maclaurin Series...
Implicit Differentiation
Differentiating Implicit Functions, Gradients of Implicit Curves, Tangents & Normals, Higher Order Derivatives...
Related Rates of Change
Chain Rule & Connected Rates, Rates of Change Over Time, Geometric & Physical Models, Problem-Solving Applications...
Kinematics I: Differentiation
Displacement, Velocity & Acceleration, Differentiating Position Functions, Speed & Direction, Analysing Motion...
Topic 5
Calculus II
Calculus II All
All questions in Calculus II
Integration Fundamentals and Areas
Antiderivatives, Definite Integrals, Area Under Curves, Fundamental Theorem of Calculus...
Volumes of Revolution
Volumes About the x- and y-axes, Definite Integrals, Geometric Applications...
Integration by Parts and by Substitution
Integration by Parts, Repeated Techniques, Applications, Trigonometric Substitutions...
Trigonometric Integration
Trig Identities, Powers of Trig Functions, Trigonometric Substitution...
Kinematics II: Integration and Mixed
Displacement, Velocity, Acceleration, Total Distance Traveled, Graphs, Applications using GDC…
Differential Equations
First Order DE’s, Euler’s Method, Variables Separable, Homogeneous, Integrating Factor, Applications…
Maclaurin Series
Common Expansions, Use of Substitution, Products, Integration, Differentiation, Differential Equations…