# IIT JEE, UPSC Civil Services Group-1, TNPSC Group-1 Study Material Mathematics free – Algebra and Trigonometry.

CONTENTS:          ALGEBRA  AND  TRIGNOMETRY

CHAPTER    1        FUNDAMENTAL ALGEBRAIC LAWS AND OPERATIONS

CHAPTER    2        LEAST COMMON MULTIPLE

GREATEST COMMON DIVISOR

CHAPTER    3        SETS AND SUBSETS

CHAPTER    4        ABSOLUTE VALUES

CHAPTER    5        OPERATIONS WITH FRACTIONS

CHAPTER    6        BASE, EXPONENT, POWER

Simplification and Evaluation of Roots

Rationalizing the Denominator

CHAPTER    8        ALGEBRAIC ADDITION, SUBTRACTION, MULTIPLICATION,

DIVISION

CHAPTER    9        FUNCTIONS AND RELATIONS

CHAPTER    10       SOLVING LINEAR EQUATIONS

Unknown in Numerator

Unknown in Numerator and/or Denominator

CHAPTER    11       PROPERTIES OF STRAIGHT LINES

Slopes, Intercepts, and Points on given Lines

Finding Equations of Lines

Graphing Techniques

CHAPTER    12       LINEAR INEQUALITIES

Solving Inequalities and Graphing

Inequalities with Two Variables

Inequalities Combined with Absolute Values

CHAPTER    13       SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

Solving Equations in Two Variables and Graphing

Solving Equations in Three Variables

Solving Systems of Inequalities and Graphing

CHAPTER    14       DETERMINANTS AND MATRICES

Determinants of Second Order

Determinants and Matrices of Third and Higher Orders

Applications

CHAPTER    15       FACTORING EXPRESSIONS AND FUNCTIONS

Nonfractional

Fractional

CHAPTER    16       SOLVING QUADRATIC EQUATIONS BY FACTORING

Solving by Completing the Square

CHAPTER    17       SOLUTIONS BY QUADRATIC FORMULA

Coefficients with Integers, Fractions, Radicals, Variables  Imaginary Roots

Interrelationships of Roots: Sums; Products

Determining the Character of Roots

CHAPTER    19       GRAPHING QUADRATIC EQUATIONS/CONICS AND

INEQUALITIES

Parabolas

Circles, Ellipses, and Hyperbolas

Inequalities

CHAPTER    20       SYSTEMS OF QUADRATIC EQUATIONS

Multivariable Combinations

CHAPTER    21       EQUATIONS AND INEQUALITIES OF DEGREE GREATER

THAN 2

Degree 3

Degree 4

CHAPTER    22       PROGRESSIONS AND SEQUENCES

Arithmetic

Geometric

Harmonic

CHAPTER    23       MATHEMATICAL INDUCTION

CHAPTER    24       FACTORIAL NOTATION

CHAPTER    25       BINOMIAL THEOREM/EXPANSION

CHAPTER    26       LOGARITHMS AND EXPONENTIALS

Expressions

Interpolations

Functions and Equations

CHAPTER    27       TRIGONOMETRY

Angles and Trigonometric Functions

Trigonometric Interpolations

Trigonometric Identities

Solving Triangles

CHAPTER    28       INVERSE TRIGONOMETRIC FUNCTIONS

CHAPTER    29       TRIGONOMETRIC EQUATIONS

Finding Solutions to Equations

Proving Trigonometric Identities

CHAPTER    30       POLAR COORDINATES

CHAPTER    31       VECTORS AND COMPLEX NUMBERS

Vectors

Rectangular and Polar/Trigonometric Forms of Complex Numbers

Operations with Complex Numbers

CHAPTER    32       ANALYTIC GEOMETRY

Points on Line Segments

Distances between Points and in Geometrical Configurations

Circles, Arcs and Sectors

Space-Related Problems

CHAPTER    33       PERMUTATIONS

CHAPTER    34       COMBINATIONS

CHAPTER    35       PROBABILITY

CHAPTER    36       SERIES

CHAPTER    37       DECIMAL/FRACTIONAL CONVERSIONS SCIENTIFIC

NOTATION

CHAPTER    38       AREAS AND PERIMETERS

CHAPTER    39       ANGLES OF ELEVATION, DEPRESSION AND AZIMUTH

CHAPTER    40       MOTION

CHAPTER    41       MIXTURES/FLUID FLOW

CHAPTER    42       NUMBERS, DIGITS, COINS AND CONSECUTIVE INTEGERS

CHAPTER    43       AGE AND WORK

CHAPTER    44       RATIOS, PROPORTIONS AND VARIATIONS

Ratios and Proportions

Direct Variation

Inverse Variation

Joint and Combined Direct-Inverse Variations

CHAPTER    45       COSTS

CHAPTER    46       INTEREST AND INVESTMENTS

CHAPTER    47       PROBLEMS IN SPACE Yum