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MATHS AAHL TOPICS
Topic 1
Number & Algebra
Sequences & Series
Arithematic & Geometric , Sigma Notation , Applications , Compound Interest .
Laws of Exponents
Log Laws,
Exponents Equations
Log Equations
Binomial Theorem
Binomial Expansion ,
Binomial Theorem
Pascal's Triangle
The Binomial Coffecient.
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Counting Principles
Permutations
Combinations
Factorial Notation
Product Principle
Sum Principle
Complex Numbers
Forms of Complex Numbers
Roots
De Moivre's Theorem
Argand Diagram
Geometric Applications
Proofs
Mathematical Induction
Contradiction
Counterexample
Simple deduction
Systems of Equations
Solving 2x2 Linear Equations
Solving 3x3 Linear Equations
Row Operations
Unique / No / Infinite solutions
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Topic 2
Functions
Properties of Functions
Domain , Range
Composite and Inverse Functions
Max & min , Intersects , Intercepts , Sketching
Quadratics
Quadratic Functions and Equations , Completing Square ,
Discriminant,
Vertex .
Rational Functions
Asymtotes, Intercepts , Sketching, Reciprocal Functions
GDC
Exponents & Log Functions
Exponential & Logarithmic Functions , Graphs, Asymptotes,
Intercepts
Transformations
Translations , Reflections , Stretches , Dilations , Rotations of Functions and Composite functions
Polynomials
Remainder Theorem
Factor Theorem
Product and sum of the roots
Zeros/Roots of the polynimials
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Modulus ( Abs Val) & Ineqalities
Absolute Value of Functions
Solving Equations
Solving Inequalities
Topic 3
Geometry & Trigonometry
Geometry and Shapes
2D & 3D shapes , Circles ,
Sectors, Arcs, Traingle,
Sine and Cos Rules , Ture Bearings ...
Trignometric Functions
Circular Functions , Unit Circle ,
Trigonometric Ratios, Identities , Solving , Trigonometric Equations and Graphs
Vectors
Basics , Line Vectors , Planes ,
Angles, Intersections , Algebra of vectors including Sum and Product
Topic 4
Statistics & Probability
Statistics
Mean, median, Mode,
Variance
Standard Deviation
IQR, Box & Whiskers
Cumulative Frequency
Bi Variate Statistics
Regression Equation
Correlations Coefficient 'r'
Strength of correlation
Applications
Probability
Probability Basics, Venn & Tree Diagrams
Combined Events, Independent and Mutually Exclusive
Conditional Probability
Distributions
Probability Distributions
Binomial & Normal Distributions
Random Variables
Applications
Topic 5
Calculus
Differential Calculus
Rules of Differentiation , Curve Properties, Optimisations rules, L Hospitals Rule
Integral Calculus
Integration Rules and Techniques, Area Under the curve and between limits
Volume of Solids & applications
Kinematics
Using Calculus to determine Displacement, Velocity , acceleration , using graphs and GDC
Differential Equations
Odder of DF equations , Euler's Method, Variables, Homogenous, Integrating factor, Applications
Maclurin Series
Common Expansion , Use of Substitution , Products , Integration , Differentiation and DF Equations