MATHEMATICS-VOLUME 1 · 12th TN - English Medium
8 chapters · 290 topics
Chapter 2: Chapter 2
Chapter 3: Chapter
- . Introduction
- Learning Objectives
- . Inverse of a Non-Singular Square Matrix
- or det ( ) .Let a ij be the element sitting at the
- or det ( ) .Let a ij be the element sitting at the · Part
- or det ( ) .Let a ij be the element sitting at the · Part
- . . 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
- . . Row-Echelon form · Part
- . . Row-Echelon form · Part
- . . 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
- . . Solution to a System of Linear equations · Part
- . . (i) Matrix Inversion Method
- EXERCISE .
- . . (ii) Cramer’s Rule
- . . (ii) Cramer’s Rule · Part
- . . (ii) Cramer’s Rule · Part
- EXERCISE .
- . . (iii) Gaussian Elimination Method
- EXERCISE .
- Linear Equations by Rank Method
- . . Non-homogeneous Linear Equations
- EXERCISE .
- . . Homogeneous system of linear equations
- . . Homogeneous system of linear equations · Part
- . . Homogeneous system of linear equations · Part
- . . Homogeneous system of linear equations · Part
- EXERCISE .
- EXERCISE . · Part
- or Scan the QR Code
- Learning Objectives
Chapter 4: Chapter
- Complex Numbers
- . . Powers of imaginary unit i
- . Complex Numbers
- . . Rectangular form
- . . Argand plane
- . . Algebraic operations on complex numbers
- EXERCISE .
- . . Properties of complex numbers
- . . Properties of complex numbers · Part
- . 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
- A complex number z is purely imaginary if and only if z · Part
- EXERCISE .
- . Modulus of a Complex Number
- . . Properties of Modulus of a complex number
- . . Properties of Modulus of a complex number · Part
- . . Properties of Modulus of a complex number · Part
- EXERCISE .
- . Geometry and Locus of Complex Numbers
- EXERCISE .
- . 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
- . . The n th roots of unity · Part
- . . The n th roots of unity · Part
- value of ω
- value of ω · Part
- EXERCISE .
- SUMMARY
- , where n is an integer
- ICT CORNER
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Chapter 5: Chapter
- . Introduction
- . Introduction · Part
- Learning Objectives
- . . Different types of Polynomial Equations
- . . Different types of Polynomial Equations · Part
- . . Quadratic Equations
- . . Vieta’s formula for Quadratic Equations
- . . Vieta’s formula for Quadratic Equations · Part
- . . Vieta’s formula for Polynomial Equations
- . . Vieta’s formula for Polynomial Equations · Part
- EXERCISE .
- . . Imaginary Roots
- ( ) = a z
- . . Irrational Roots
- . . Irrational Roots · Part
- . . Irrational Roots · Part
- . . Rational Roots
- . Applications of Polynomial Equation in Geometry
- EXERCISE .
- . 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
- EXERCISE .
- . . Rational Root Theorem
- . . Rational Root Theorem · Part
- . . Reciprocal Equations
- . . Reciprocal Equations · Part
- . . Reciprocal Equations · Part
- . . Reciprocal Equations · Part
- . . Non-polynomial Equations
- . . Statement of Descartes Rule
- . . Attainment of bounds
- . . Attainment of bounds · Part
- . . Attainment of bounds · Part
- EXERCISE .
- ICT CORNER
- SUMMARY
- or Scan the QR Code
Chapter 6: Chapter
- . Introduction
- Inverse Trigonometric Functions
- . Some Fundamental Concepts
- . . Domain and Range of trigonometric functions
- . . 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
- . . Properties of the cosine function · Part
- ] 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
- . 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
- . 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 −
- Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
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- and ( , )
Chapter 7: 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
- and finding the point of contact · Part
- EXERCISE .
- . . Conics
- . . The general equation of a Conic
- . . Parabola
- . . Parabola · Part
- . . Ellipse
- . . Ellipse · Part
- . . Ellipse · Part
- . . Ellipse · Part
- . . Hyperbola
- Find the equation of the parabola with focus − (
- Find the equation of the parabola with focus − ( · Part
- Find the equation of the parabola with focus − ( · Part
- EXERCISE .
- . Conic Sections
- . . Geometric description of conic section
- . . Degenerate Forms
- . . Identifying the conics from the general equation of the conic
- . . Identifying the conics from the general equation of the conic · Part
- . . 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
- + to be a tangent to the conic sections · Part
- EXERCISE .
- . . Parabola
- . . Ellipse
- . . Hyperbola
- . . Hyperbola · Part
- . . Reflective property of parabola
- . . Reflective Property of an Ellipse
- . . Reflective Property of a Hyperbola
- . . Reflective Property of a Hyperbola · Part
- EXERCISE .
- EXERCISE . · Part
- EXERCISE . · Part
- EXERCISE . · Part
- EXERCISE . · Part
- SUMMARY
- Tangent and normal
- Parametric forms
- ICT CORNER
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Chapter 8: Chapter
- . Introduction
- Learning Objectives
- . Geometric introduction to vectors
- . Geometric introduction to vectors · Part
- . Scalar Product and Vector Product
- . . Geometrical interpretation
- . . Application of dot and cross products in plane Trigonometry
- . . Application of dot and cross products in plane Trigonometry · Part
- . . 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
- . . Properties of the scalar triple product · Part
- . . Properties of the scalar triple product · Part
- . . Properties of the scalar triple product · Part
- . . Properties of the scalar triple product · Part
- EXERCISE .
- . Vector triple product
- . Jacobi’s Identity and Lagrange’s Identity
- . Jacobi’s Identity and Lagrange’s Identity · Part
- . Jacobi’s Identity and Lagrange’s Identity · Part
- EXERCISE .
- . Application of Vectors to -Dimensional Geometry
- . . Different forms of equation of a straight line
- are given
- . . Straight Line passing through two given points
- . . Straight Line passing through two given points · Part
- . . Straight Line passing through two given points · Part
- . . Angle between two straight lines
- . . Angle between two straight lines · Part
- EXERCISE .
- . . Point of intersection of two straight lines
- . . Shortest distance between two straight lines
- . . Shortest distance between two straight lines · Part
- . . Shortest distance between two straight lines · Part
- . . Shortest distance between two straight lines · Part
- EXERCISE .
- . 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
- . . Intercept form of the equation of a plane · Part
- . . Intercept form of the equation of a plane · Part
- EXERCISE .
- . . 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
- EXERCISE .
- and (
- . . Condition for a line to lie in a plane
- . . Condition for coplanarity of two lines
- . . Equation of plane containing two non-parallel coplanar lines
- EXERCISE .
- . . 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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- Exercise .
- Exercise .
- Exercise .
- COMPLEX NUMBER
- THEORY OF EQUATION
- FUNCTIONS
- BOOKS FOR REFERENCE
- Text Book Development Team - Class