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MATHS AIHL TOPICS
Topic 1
Number & Algebra
Number Skills
Approximation , Rounding, Significant Figures
Scientific Notation
Percentage errors
Sequences & Series
Arithematic & Geometric , Sigma Notation , Applications , Compound Interest .
Financial Mathematics
Compound Interest
Depreciation
Loans & Amortization , Annuities
Using Finance Solver in GDC
Complex Numbers
Forms of Complex Numbers
Roots
De Moivre's Theorem
Argand Diagram
Geometric Applications
Matrices
Operations ( Add/ Sub.)
determinants
Inverse
Solving Linear Equations Using Matrices, Eigen Vectors
Topic 2
Functions
Linear Equations & Graphs
Forms of Linear Equations , Gradient , Intercepts, Parallel & perpendicular Lines
Application of functions
Linear , Quadratic, Exponential , Log , Sinusodial , Logistic, Scaling and linearising using Logs
Properties of Functions
Domain & Range of a Function , Finding and interpreting a Composite function & Inverse Functions
Transformations
Translations , Reflections , Stretches , Dilations , Rotations of Functions and Composite functions
Topic 3
Geometry & Trigonometry
Geometry and Shapes
Surface Area Volumes , 3 D Shapes Including Spheres, Cnes & Prisms & Pyramids
Trignometry
Right & Non Right angle Triangles, SIN/COS/TAN ratios, SIN & COS RULES , Area , circles, Degrees and Radians
Voronoi Diagrams
Sites/ Edges/Cells /vertices,
Perpendicular Bisectors, Nearest neighbour Interpolation ..
Trignometric Functions
Circular Functions , Unit Circle ,
Trigonometric Ratios, Identities , Solving , Trigonometric Equations and Graphs
Geometric Transformations
Transformation of shapes and points using matrices, Reflection , Dilation , Translations Rotations
Vectors
Basics , Line Vectors , Planes ,
Angles, Intersections , Algebra of vectors including Sum and Product
Graph Theory
Basic s , Walks & Trails , Eulerian/Hamiltonian, Kruskal's.
Prim's Chinese postman, Travelling salesman
Topic 4
Statistics & Probability
Descriptive 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
Hypothesis Testing
Ho/H1 Sig testing, p-Values , chi squared test, t - test, Critical Value/ Reg ,Type 1/2 errors, Pop mean..
Estimation Confidence Intervals
Reliability, Validity of data, Collection , Unbiased Estimators, Central limit Theorem, Confidence Intervals
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