HS MATHEMATICS

1. Chapter 1 - Sets
• Definition of set
• Natural numbers, integers, rational numbers etc.,
• Elements of a set
Chapter 1.1
• Roster or tabular form
• Set-builder form
Chapter 1.2
• Empty Set
• Finite Set
• Equal sets
Chapter 1.3
• Subsets
• Super sets
• Singleton Set
Chapter 1.4
• Intervals as subsets of R
• Closed intervals and Open intervals
• Power set
• Universal set
Chapter 1.5
• Venn diagrams
• Union of sets
Chapter 1.6
• Intersection of sets
• Disjoint sets
Chapter 1.7
• Difference of two sets
Chapter 1.8
• Complement of a set
• De Morgan's Law
Chapter 1.9
• Practical problems involving two sets
Chapter 1.10
• Some interesting relations between two sets
Chapter 1.11
• Some interesting relations between three sets
Chapter 1.12
• Practical problems involving three sets
2. Chapter 2 - Relations and Functions
• Definition of Cartesian product of sets
• Ordered pairs and Ordered triplets
• Number of elements in a Cartesian product
Chapter 2.1
• Relations
• Arrow diagram
• Domain, Codomain and Range
Chapter 2.2
• Functions
• Identity function
Chapter 2.3
• Constant function
• Polynomial function
Chapter 2.4
• Rational function
Chapter 2.5
• Modulus function
• Signum function
Chapter 2.6
• Greatest integer function
Chapter 2.7
• Algebra of real functions
Chapter 2.8
• Solved examples on functions
3. Chapter 3 - Trigonometric Functions
• Derivation of some simple trigonometric identities
• Solved examples
Chapter 3.1
• Definition of angle
• Measurement of angles using degrees
Chapter 3.2
• Measurement of angles using radians
Chapter 3.3
• Conversion from degree to radian and vice versa
Chapter 3.4
• Trigonometric ratios of acute angles using unit circle
Chapter 3.5
• Trigonometric ratios of obtuse angles using unit circle
Chapter 3.6
• Trigonometric ratios of negative angles using unit circle
Chapter 3.7
• Input values for trigonometric functions
• Values at which sine and cosine functions become zero
Chapter 3.8
• Signs of trigonometric functions in the four quadrants
• Domain and range of sine and cosecant functions
• Graphs of sine and cosecant functions
Chapter 3.9
• Domain and range of cosine and secant functions
• Graphs of cosine and secant functions
Chapter 3.10
• Domain and range of tangent and cotangent functions
• Graphs of tangent and cotangent functions
Chapter 3.11
• Sum and difference of two angles
• Derivation of Trigonometric identities
Chapter 3.12
• Derivation of more Trigonometric identities
Chapter 3.13
• Solved examples related to Trigonometric identities
Chapter 3.14
• Period of Trigonometric functions
Chapter 3.15
• Trigonometric equations
• Theorem 1
Chapter 3.16
• Trigonometric equations
• Theorems 2 and 3
Chapter 3.17
• Solved examples on Trigonometric equations
Chapter 3.18
• More Solved examples on Trigonometric equations
Chapter 3.19
• Miscellaneous examples
Chapter 3.20
• Details about sine formula
Chapter 3.21
• Details about cosine formula
Chapter 3.22
• Napier's Analogies
• Solved examples

More topics can be seen here.