Chapter 1: LOGIC
Propositions
Compound Propositions.
Chapter 2: Sets
Representation of Sets
Types of Sets
Set Operation
Chapter 3: RELATIONS,FUNCTIONS AND OPERARTIONS
Cartesian Product
Relations
Equivalence Relations
Graph of Relation
Inverse of Relation
Functions
Kinds of Functions
Binary Operations
Composition of Functions
Chapter 4: NUMBER SYSTEM
Natural Numbers
Divisibility
The LCM and GCF
Integers
Word Problems
Modular Arithmetic
Rational numbers
Real Numbers
Decimal Forms of Real Numbers
Absolute Value
Exponents
Radical Expressions
Chapter 5: POLYNOMIALS
Operations on Polynomials
Factoring polynomials
The LCM and GCF of Polynomials
Polynomial Equations
The Remainder Theorem
Chapter 6: QUADRATIC EQUATIONS ,INEQUALITIES AND FUNCTIONS
Quadratic Equations
Character of the Roots
Relations between Roots and Coefficient
To Form a Quadratic Equation Whose Roots are Given
Equations That Lead To Quadratic Equations
Graphs of Quadratic Equations
UNIT 1: TRIGONOMETRY
Directed angles, the unit circle. Angle measure units, Principal
angle
Definition of trigonometric functions on unit circle
Definition of periodic function, The change in the graph of a.(b.sinx+c, Def. of
trig. rat. in a right tria., Trig. Ratios of two Complementary Angles
Trigonometric ratios of 30,45,60,90
Fundamental trigonometric identities
Trigonometric values of general angles (Reduction formulas),
Finding the remaining Trigonometric ratios if one of them is
known
Table of trigonometric functions, Graphs of trigonometric functions
Inverse
trigonometric functions and their graphs
Trigonometric laws and formulas, Compound and double
angles
Half angle formulas
Sum and difference formulas
Product formulas, Trigonometric equations
Trigonometric equations
UNIT 2: COMPLEX NUMBERS
Definition of
imaginary unit, complex num., equality of two comp. numbers
Geometric representation, conjugate, basic operations
Modulus of a complex number, Distance between two complex
numbers
Polar
coordinates, conversions between coordination systems
Basic operations in polar coordinates
Powers of
complex numbers, De Moivre's Theorem
Roots of complex numbers
UNIT 3: LOGARITHM
Exponential
function Graphs and the properties of exponential functions
Definition of logarithmic function and properties of logarithms
Properties of logarithms
Graphs of exponential and logarithmic functions
Common
and natural logarithms, Use of the logarithmic table
Exponential equations
Logarithmic equations
Logarithmic inequalities,
UNIT 4: PERMUTATION, COMBINATION, PROBABILITY
Factorial notation,
Permutation function
Number of permutations
Permutation of a set having like elements
Circular permutation,
Combination
Basic concepts of probability
Probability function, Calculation of probability
Equally, likely outcomes
Independent and dependent events
Conditional probability
UNIT 5: METHODS of PROOFS
Types of direct and
indirect
proofs
Mathematical Induction
Mathematical Induction
Properties of summation
notation
Properties of multiplication notation
UNIT 6: SEQUENCES
Sequences, finite sequences
Constant and equal sequences, Exercises
Operations on sequences, Monotonic
sequences
Sigma-neighborhood, almost every term
Convergency and limit, enlarged real numbers
Theorems on Convergent sequences
Arithmetic sequences
Series, limits of convergent series
Geometric sequences
Unit 1: SEQUENCES & SERIES
Definition of sequence
Finite, infinite and constant sequences
Equality of sequences
Basic operations in sequences
Monotone sequences
Almost every term
Convergence or limit of a sequence
Enlarged real numbers
Rules of limit
Arithmetic sequences
Geometric sequences
Series and limit of series
Unit 2: FUNCTIONS
Definition and inverse of a function
Increasing and decreasing functions
Even and odd functions
Parametric and implicit functions
Piecewise function
Absolute value function
Sign Function
Greatest integer function
Unit 3: LIMIT
Limit concept
Limit of a real valued function
One sided limits, existence of limit
Infinity as a limit
Infinite limits
Limit rules
The Indeterminate form 0/0
The
Indeterminate form 
The
Indeterminate form 
The
Indeterminate form 
Continuity at a point
Continuity of a function
Unit 4: DERIVATIVES
Definition of derivative
Left hand and right hand derivative
Rules of derivative
Geometric meaning of derivative
Derivative of composite functions
Chain rule
Derivative of trigonometric functions
Derivative of parametric functions
Derivative of implicit functions
Derivative of inverse functions
Derivative of inverse trigonometric functions
Derivative of logarithmic functions
Derivative of exponential functions
Higher order derivatives
L'Hopital's Rule
Extrema of a function
Rolle and Mean value theorems
First derivative test
Concavity and points of inflection
Second derivative test
Horizontal and vertical asymptotes
Drawing graphs of functions
Unit 5: INTEGRAL
Indefinite integral
Properties of indefinite integrals
Integrals of trigonometric functions
Substitution method for integral
Integral of rational functions
Integration by parts
Definite integral
Riemann integral
The fundamental theorem of calculus
Areas between two curves
Arc length
Volumes of revolutions