Topics
Sets and Functions
Sets
Relations and Functions
- Ordered Pairs
- Cartesian Product of Sets
- Relation
- Pictorial Diagrams
- Concept of Functions
- Function as a Type of Mapping
- Types of Functions
- Many to One Function
- Introduction to Function
- Real Valued Function of the Real Variable
- Some Functions and Their Graphs
- Exponential Function
- Sum, Difference, Product, Quotient of Functions
Trigonometry
- Magnitude of an Angle
- Concept of Angle
- Conversion from One Measure to Another
- Introduction of Trigonometric Functions
- Truth of the Identity
- Signs of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications
- Trigonometric Functions of Sum and Difference of Two Angles
- Trigonometric Equations
- Solution of Trigonometric Equations (Solution in the Specified Range)
- Graphs of Trigonometric Functions
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Half Angles
- Convention of Sign of Angles
- The Relation S = rθ Where θ is in Radians
- Relationship Between Trigonometric Functions
- Periods of Trigonometric Functions
- Compound and Multiple Angles- Addition and Subtraction Formula
- Trigonometric Functions of All Angles
- Sum and Differences as Products
- Product to Sum Or Difference
- Trigonometric Equations
Algebra
Principle of Mathematical Induction
Complex Numbers
- Concept of Complex Numbers
- The Modulus and the Conjugate of a Complex Number
- Properties of Conjugate, Modulus and Argument of Complex Numbers
- Argand Plane and Polar Representation
- Square Root of a Complex Number
- Cube Root of Unity
- Properties of Cube Roots of Unity
- Algebraic Properties of Complex Numbers
- Algebra of Complex Numbers
- Locus Questions on Complex Numbers.
- Triangle Inequality
Quadratic Equations
- Quadratic Equations
- Equations Reducible to Quadratic Form
- Nature of Roots
- Quadratic Functions
- Sign of Quadratic
- Quadratic Inequalities
- Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation
- Graphical Solution of Linear Inequalities in Two Variables
- Solution of System of Linear Inequalities in Two Variables
Permutations and Combinations
- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Permutations
- Derivation of Formulae and Their Connections
- Simple Applications of Permutations and Combinations
- Circular Permutations
- Restricted Permutation
- Permutation - Certain Things Always Occur Together
- Permutation - Certain Things Never Occur
- Permutation - Formation of Numbers with Digits
- Permutation - Permutation of Alike Things
- Permutation - Permutation of Repeated Things
- Permutation - Word Building
- Properties of Combination
- Combination
Binomial Theorem
Sequence and Series
- Introduction of Sequence and Series
- Arithmetic Progression (A.P.)
- Three Terms in Arithematic Progression (A.P.)
- Four Terms in Arithematic Progression (A.P.)
- Inserting Two Or More Arithmetic Means Between Any Two Numbers
- Geometric Progression (G. P.)
- Three Terms in Geometric Progression (G.P.)
- Four Terms Are in Geometric Progression (G.P.)
- Inserting Two Or More Geometric Means Between Any Two Numbers.
- Relationship Between A.M. and G.M.
- Arithmetico Geometric Series
Coordinate Geometry
Straight Lines
- Brief Recall of Two Dimensional Geometry from Earlier Classes
- Shifting of Origin
- Slope of a Line
- Various Forms of the Equation of a Line
- General Equation of a Line
- Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
- Distance of a Point from a Line
- Equations of Bisectors of Angle Between Two Lines
- Family of Lines
- Basic Concepts of Points and Their Coordinates
- Definition and Equation of Locus
Circles
- Equations of a Circle in Standard Form
- Equations of a Circle in Diameter Form
- Equations of a Circle in General Form
- Equations of a Circle in Parametric Form
- Focus-directrix Property
- Given the Equation of a Circle, to Find the Centre and the Radius
- Finding the Equation of a Circle
- Condition for Tangency
- Equation of a Tangent to a Circle
Calculus
Limits and Derivatives
- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
- Introduction of Limits
- Limits of Polynomials and Rational Functions
- Limits of Exponential Functions
- Limits of Logarithmic Functions
- Limits of Trigonometric Functions
- Limits of Algebraic Functions
- Fundamental Theorem on Limits
- Introduction of Derivatives
- Derivative of Slope of Tangent of the Curve
- Derivative of Algebraic Functions
- Differentiation Or Derivative Using First Principles
- Algebra of Derivative of Functions
- Derivative of Polynomials and Trigonometric Functions
Statistics and Probability
Statistics - 1
- Central Tendency - Mean
- Concept of Range
- Measures of Dispersion - Quartile Deviation
- Mean Deviation
- Standard Deviation
- Standard Deviation - by Direct Method
- Standard Deviation - by Step Deviation Method"
- Introduction of Variance and Standard Deviation
- Comparison of Two Frequency Distributions with Same Mean
Probability
Conic Section
- Sections of a Cone
- Conics as a Section of a Cone
- Definition of Foci, Directrix, Latus Rectum
- Standard Equations of Parabola
- Latus Rectum
- Standard Equations of an Ellipse
- Latus Rectum
- Standard Equation of Hyperbola
- Transverse and Conjugate Axes
- Coordinates of Vertices
- Foci and Centre
- Equations of the Directrices and the Axes
- General Second Degree Equation in x and y
- General Equation of Tangents
- Point of Contact and Locus Problems
Introduction to Three-dimensional Geometry
Mathematical Reasoning
Statistics - 2
Correlation Analysis
Index Numbers and Moving Averages
Index Numbers
Moving Averages
description
Given `alpha`,`beta` as roots then find the equation whose roots are of the form `alpha^3`, `beta^3` , etc
Case I:a>0 -> 1)Real roots, 2)Complex roots,3)Equal roots
Case II:a<0 -> 1)Real roots, 2)Complex roots,3)Equal roots
Where ‘a’ is the coefficient of x2 in the equations of the form ax2 + bx + c = 0.
Understanding the fact that a quadratic expression (when plotted on a graph) is a parabola.
- Quadratic Formula
- Quadratic Inequalities
- Steps to Solve Quadratic Inequalities
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