H2MathsApplets

H2 Mathematics Applets
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Sequences & Series

Permutations & Combinations

Complex Numbers

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Introduction
Remainder & Factor Theorems Quadratic Equations	Trigonometric Identities	Partial Fraction
Polynomial Division		Binomial Expansion Binomial Expansion (worked solution) Range of Validity

Graphs
Ellipses & Hyperbolas	Rational Functions Graph of y² = f(x)	Transformation of Graphs Combination of Transformations Summary of Transformations
Test Point Method Solving Inequalities Inequalities with Modulus Signs	Inequalities by Graphical Method

Calculus
Differentiation Derivative from First Principle	Stationary Points Graph of Derivative	Tangents & Normals	Parametric Equations
Maclaurin's Series (Graph) Maclaurin's Series (for any function)	Integration by Standard Form Integration by Parts	Area of Rectangles under a Curve	Volume

Sequences
Arithmetic Progression (worked solution) Arithmetic Progression Geometric Progression	Series Sigma Notation Simplifying Expressions involving Summation	Method of Difference Mathematical Induction

Functions
Domain & Range of a Function	Composite Function Animation Composite Function	Graph of Composite & Inverse Functions

Permutations & Combinations
Problems involving Choosing: Choose People (Pictorial) Choose People	Choose Boys & Girls	Choose a few Groups
Problems involving Arranging: Arrange People	Arrange Boys & Girls	Arrange Letters

Vectors
Ratio Theorem Dot Product Cross Product	Vector Equation of a Line Equation of a Line in Cartesian form	Vector Problems involving Points & Lines Vector Problems involving Points & Planes Vector Problems involving Lines & Planes

Complex Numbers
Complex Number Nth Root of a Complex Number	Locus of Complex Numbers	Maximum & Minimum Distances

Statistics
Here are some Microsoft Excel Statistical Simulations: (Click each link and then press F9 on your keyboard)
1 Die	to simulate the tossing of 1 die
2 Dice	to simulate the tossing of 2 dice
Balls	to simulate the drawing of balls
Coins	to simulate the tossing of coins
Suits	to simulate the drawing of cards according to suits
Card	to simulate the drawing of cards according to suits & values
Binomial to Poisson	to show that the Binomial Distribution approaches the Poisson Distribution
Binomial to Normal	to show that the Binomial Distribution approaches the Normal Distribution
Poisson to Normal	to show that the Poisson Distribution approaches the Normal Distribution
Central Limit: 1, 3	to demonstrate the Central Limit Theorem for a symmetrical Distribution
Central Limit: 1, 1, 1, 3	to demonstrate the Central Limit Theorem for a skewed Distribution

Probability (Card) Probability (Dice)	Tree Diagram	Binomial, Poisson & Normal Distributions Approximations to the Binomial & Poisson Distributions Sums of Random Variables
Sampling Unbiased Estimates	Z Test T Test	Linear Regression

"An Applet A Day Brings 'A' Grades Your Way"

Dear Mathematics teachers and students,

These applets can be used for

lectures (please adjust screen resolution to 800 by 600 pixels for best effect),
classroom teaching (for classrooms with projectors installed),
self-discovery learning by students (in school or at home),
consultation after lessons (to consolidate concepts),
revision before tests and examinations.

Feel free to tell me of any

benefits which you have derived from these applets,
incompatibilities with your computer,
errors whether theoretical or computational,
ideas for improving these applets or developing new ones.

Yee Weng Hong
Hwa Chong Institution
Singapore

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