6) H2 Mathematics (yearly access)

1) Basic Properties of Vectors
7 Topics
Basic Vectors
Vector Representation in 3D
Vector Calculations in 3D
Direction Cosines
Collinearity
Ratio Theorem
Coplanar Vectors
2) Scalar and Vector Products in Vectors
8 Topics
Scalar product of 2 vectors
Scalar product of 2 vectors and angles
Angle specified with 3 points
Perpendicular Vectors
Projection Vectors
Cross Product of 2 Vectors
Cross Product of Vectors For Perpendicular Distance
Geometric Interpretation
3) Equation of lines and planes
4 Topics
Vector Equation of Lines
Vector Equation of Planes
Parametric Equation of Planes
Standard Vector Equation of Planes
4) Three Dimensional Geometry
14 Topics
Foot of Perpendicular to a Line and Reflection
Distance From a Point to a Line
Foot of Perpendicular to a Plane and Reflection
Distance From a Point to a Plane
Angle between 2 Lines
Intersection of 2 Lines in 3D
Perpendicular Distance Between 2 Parallel Lines
Angle between a line and a plane
Intersection of a line and a plane
Line lies on a plane
Length of projection of line onto a plane
Angle between 2 planes
Intersection between 2 planes
Perpendicular Distance Between 2 Parallel Planes
5) Functions
7 Topics
Domain and Range
Vertical Line Test
Periodic Functions
Composite Functions
Inverse Functions
Solving Point of Intersection of Function and its Inverse
Self-Inverse Functions
6) Graphs and Transformations
7 Topics
Graph of Ellipses
Graph of Hyperbolas
Graph of Rational Functions
Graph of Quadratic over Linear
Axis of Symmetry
Asymptotes
Transformations
7) Equations and Inequalities
6 Topics
System of Linear Equations
Solving Equations
Properties of Inequalities
Modulus Function
Representing Intervals
Solving Inequalities
8) Sequence and Series
7 Topics
Sequence
Series
Method of Difference
Standard Series
Convergence and Sum to Infinity
Arithmetic Progression and Series
Geometric Progression and Series
9) Complex Number in Cartesian Form
7 Topics
Complex Numbers
Four Operations of Complex Numbers
Conjugate of a Complex Number
Equality of Complex Numbers
Complex Number Equations
Simultaneous Equations involving Complex Numbers
Conjugate roots of a Polynomial Equation with Real Coefficients
10) Complex Number in Polar Form
7 Topics
Argand Diagram
Polar Form
Argument of z
Euler’s Formula
Multiplication and Division of two complex numbers
Conjugate in Polar and Exponential Form
Properties of Modulus and Argument
11) Differentiation
8 Topics
Differentiation from First Principles
Rules of Differentiation
Derivatives of Common Functions
Interpretation of First Derivative
Interpretation of Second Derivative
Nature of Stationary Points
Graph of Gradient Function
Implicit Differentiation
12) Application of Differentiation
5 Topics
Parametric Equations
Parametric Differentiation
Tangents and Normals
Maxima and Minima
Connected Rates of Change
13) Maclaurin Series
9 Topics
Maclaurin Series
Standard Series Expansion 1
Standard Series Expansion 2
Standard Series Expansion 3
Standard Series Expansion 4
Standard Series Expansion 5
Approximation using Maclaurin Series
Small Angle Approximation
Maclaurin Series for other functions
14) Integration Techniques
8 Topics
Basic Rules of Integration
Why is there a Modulus for ln
Basic Form and General Form
Identities and Double Angle Formula
Factor Formula
Definite Integrals
Integration using Substitution
Integration by Parts
15) Application of Integration
3 Topics
Definite Integral as Limit of Summation
Definite Integral in Finding area under curve
Definite Integral in finding Volume of Revolution
16) Differential Equations
4 Topics
Differential Equations
Solving Differential Equations
Solving Differential Equations by Substitution
Formulation of Differential Equations
17) Permutations and Combinations
6 Topics
The Addition Principle
The Multiplication Principle
Combinations
Permutations
Circular Permutations
Practice Questions
18) Probability
9 Topics
Random Experiments
Properties of Sets
Probability
Probability Distribution
Mutually Exclusive Events
Conditional Probability
Independent Events
Probability Tree
Probability Examples
19) Discrete Random Variables
6 Topics
Random Variables
Discrete Random Variables
Expectation of Discrete Random Variables
Functions of Discrete Random Variables
Variance and Standard Deviation of Discrete Random Variable
Linear Combination of Independent Random Variables
20) Binomial Distribution
3 Topics
Binomial Experiment
Binomial Random Variable
Binomial Distribution
21) Normal Distribution
10 Topics
Continuous Random Variable
Normal Distribution
Normal Curve and its Properties
Normal Probabilities and GC Use
Inverse Normal and GC Use
Standard Normal Distribution
Properties of Expectation and Variance of Random Variables
Properties of Independent Normal Random Variables
Random Variable 2X vs X1 + X2
Normal Distribution Practice Questions
22) Sampling
10 Topics
Population and Sample
Random and non-random sampling
Population mean and population variance
Random sample of size n and sample statistics
Estimates of Population Parameters
Use of GC to find unbiased estimates
Sample Mean as a Random Variable
The Distribution of the Sample Mean
Sampling from a Normal Population
Central Limit Theorem
23) Hypothesis Testing
8 Topics
Null and Alternative Hypothesis
Level of Significance
Test Statistics
Critical Value and Critical Region
p value
z value
Hypothesis Tests on Population Mean
Hypothesis Testing Practice Questions
24) Correlation and Linear Regression
9 Topics
Relationship between variables
Scatter Diagram
Interpreting Scatter Diagram
Product Moment Correlation Coefficient
Product Moment Correlation Coefficient Properties
Correlation does not imply Causation
Linear Regression
Application and Interpretation
Linearization of Data
Next Lesson

1) Basic Properties of Vectors

6) H2 Mathematics (yearly access) 1) Basic Properties of Vectors

In this chapter, you will be learning

  • addition and subtraction of vectors, multiplication of a vector by a scalar, and their geometrical interpretations
  • use of various notations to represent vectors
  • position vectors, displacement vectors and direction vectors
  • magnitude of a vector
  • unit vectors
  • distance between two points
  • collinearity
  • use of the ratio theorem in geometrical applications
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