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Home›12th TN - English Medium›MATHEMATICS-VOLUME 1

MATHEMATICS-VOLUME 1 · 12th TN - English Medium

7 chapters · 200 topics

Chapter 1: Chapter

. Introduction
Learning Objectives
. Inverse of a Non-Singular Square Matrix
or det ( ) .Let a ij be the element sitting at the
. . Definition of inverse matrix of a square matrix
. . Application of matrices to Geometry
. . Application of matrices to Cryptography
. . Elementary row and column operations
. . Row-Echelon form
. . Rank of a Matrix
. . Gauss-Jordan Method
] . Then
. Applications of Matrices: Solving System of Linear Equations
. . Formation of a System of Linear Equations
. . System of Linear Equations in Matrix Form
. . Solution to a System of Linear equations
. . (i) Matrix Inversion Method
EXERCISE .
. . (ii) Cramer’s Rule
. . (iii) Gaussian Elimination Method
Linear Equations by Rank Method
. . Non-homogeneous Linear Equations
. . Homogeneous system of linear equations
SUMMARY
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Complex Numbers

Chapter 2: Chapter

. . Powers of imaginary unit i
. Complex Numbers
. . Rectangular form
. . Argand plane
. . Algebraic operations on complex numbers
EXERCISE .
. . Properties of complex numbers
. Conjugate of a Complex Number
. . Geometrical representation of conjugate of a complex number
, where n is an integer
A complex number z is purely imaginary if and only if z
. Modulus of a Complex Number
. . Properties of Modulus of a complex number
Section
. Geometry and Locus of Complex Numbers
. Polar and Euler form of a Complex Number
. . Polar form of a complex number
axis when z is interpreted as a radius vector. The angle θ has an infinitely
. . Euler’s Form of the complex number
. . De Moivre's Theorem
. . Finding n th roots of a complex number
. . The n th roots of unity
value of ω
SUMMARY
ICT CORNER
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Chapter 3: Chapter

. Introduction
Learning Objectives
. . Different types of Polynomial Equations
. . Quadratic Equations
. . Vieta’s formula for Quadratic Equations
. . Vieta’s formula for Polynomial Equations
= − ∑ α α α
EXERCISE .
. . Imaginary Roots
( ) = a z
. . Irrational Roots
. . Rational Roots
. Applications of Polynomial Equation in Geometry
. Roots of Higher Degree Polynomial Equations
. . Imaginary or Surds Roots
. . Polynomial equations with Even Powers Only
. . Zero Sum of all Coefficients
. . Equal Sums of Coefficients of Odd and Even Powers
. . Roots in Progressions
. . Rational Root Theorem
. . Reciprocal Equations
. . Non-polynomial Equations
. . Statement of Descartes Rule
. . Attainment of bounds
ICT CORNER
SUMMARY
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Chapter 4: Chapter

. Introduction
Inverse Trigonometric Functions
. Some Fundamental Concepts
. . Graphs of functions
. . Amplitude and Period of a graph
. . Inverse functions
. . Graphs of inverse functions
. Sine Function and Inverse Sine Function
] as y
. . Properties of the sine function
. . The i nverse sine function and its properties
EXERCISE .
. The Cosine Function and Inverse Cosine Function
. . Properties of the cosine function
. . The inverse cosine function and its
] is called the principal domain of cosine function and the values of
] as an output (an angle in radian
. The Tangent Function and the Inverse Tangent Function
. . The graph of tangent function
. . Properties of the tangent function
. . The inverse tangent function and its properties
. . Graph of the inverse tangent function
Thus, the principal value of tan − (
. The Cosecant Function and the Inverse Cosecant Function
. . Graph of the cosecant function
. . The inverse cosecant function
. . Graph of the inverse cosecant function
. The Secant Function and Inverse Secant Function
. . The graph of the secant function
. . Graph of the inverse secant function
. The Cotangent Function and the Inverse Cotangent Function
. . The graph of the cotangent function
. . Inverse cotangent function
. . Graph of the inverse cotangent function
. Properties of Inverse Trigonometric Functions
(i) sin cos −
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and ( , )

Chapter 5: Chapter

. Introduction
Learning Objectives
. Circle
. . Equation of a circle in standard form
. . Equations of tangent and normal at a point P on a given circle
and finding the point of contact
EXERCISE .
. . Conics
. . The general equation of a Conic
. . Parabola
. . Ellipse
. . Hyperbola
Find the equation of the parabola with focus − (
. Conic Sections
. . Geometric description of conic section
. . Degenerate Forms
. . Identifying the conics from the general equation of the conic
. . Parametric equations
) and
. . Equation of tangent and normal to the parabola y
(the proof of the following are left to the reader)
+ to be a tangent to the conic sections
. . Reflective property of parabola
. . Reflective Property of an Ellipse
. . Reflective Property of a Hyperbola
SUMMARY
Tangent and normal
Parametric forms
ICT CORNER
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Chapter 6: Chapter

. Introduction
Learning Objectives
. Geometric introduction to vectors
. Scalar Product and Vector Product
. . Geometrical interpretation
. . Application of dot and cross products in plane Trigonometry
. . Application of dot and cross products in Geometry
. . Application of dot and cross product in Physics
EXERCISE .
. Scalar triple product
. . Properties of the scalar triple product
. Vector triple product
. Jacobi’s Identity and Lagrange’s Identity
. Application of Vectors to -Dimensional Geometry
. . Different forms of equation of a straight line
are given
. . Straight Line passing through two given points
. . Angle between two straight lines
. . Point of intersection of two straight lines
. . Shortest distance between two straight lines
. Different forms of Equation of a plane
the plane from the origin are given
a given point
. . Intercept form of the equation of a plane
. . Equation of a plane passing through three given non-collinear points
. . Equation of a plane passing through a given point and parallel to
is parallel to a non-zero vector
and (
. . Condition for a line to lie in a plane
. . Equation of plane containing two non-parallel coplanar lines
. . Angle between two planes
. . Angle between a line and a plane
. . Distance of a point from a plane
. . Distance between two parallel planes
. . Equation of line of intersection of two planes
given planes
. Image of a Point in a Plane
. . The coordinates of the image of a point in a plane
. Meeting Point of a Line and a Plane
SUMMARY
ICT CORNER
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COMPLEX NUMBER
THEORY OF EQUATION
FUNCTIONS
BOOKS FOR REFERENCE
Text Book Development Team - Class

Chapter 7: Front Matter

Untouchability is Inhuman and a Crime
Higher Order Thinking
Learning Objectives
CONTENTS
EXAMS
Scholarship and Research Opportunities

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