Algebra | - Sets, relations, and Functions: Sets and their representations/ Finite and Infinite sets/ Empty set; Equal sets; Subsets; Power set; Universal set/ Venn Diagrams/ Complement of a set/ Operations on Sets/ Applications of sets: Ordered Pairs, Cartesian Product of Two sets/ Relations, reflexive, symmetric, transitive and equivalence relations/ Domain, Co-domain and Range/ Functions: into, onto, one - one into, one-one onto Functions; Constant Function; Identity Function; composition of Functions/ Invertible Functions/ Binary Operations
- Complex Numbers: Complex Numbers in the form a + i b/ Real and Imaginary Parts of a Complex Number/ Complex Conjugate/ Argand Diagram/ Representation of Complex Number as a point in the plane/ Modulus and Argument of a Complex Number/ Algebra of Complex Numbers/ Triangle Inequality/ Polar Representation of a Complex Number and the square root of a complex number/ Solution of a Quadratic Equation in the Complex Number System
- Sequence and Series: Sequence and Examples of Finite and Infinite Sequences/ Arithmetic Progression (A..P): First Term, Common Difference, nth Term and the sum of n terms of an A.P.; Arithmetic Mean (A.M); Insertion of Arithmetic Means between any Two given Numbers/ Geometric Progression (G.P): first Term, Common Ratio, and nth term, Sum to n Terms, infinite GP and its sum/ Geometric Mean (G.M); Insertion of Geometric Means, Relation between AM and GM. between any two given numbers/ Formula for finding the sum of first n natural numbers/ sum of the squares of first n natural numbers and the sum of the cubes of first n natural numbers
- Permutations, Combinations, Binomial Theorem, and Mathematical Induction: Fundamental Principle of Counting/ The Factorial Notation/ Permutation as an Arrangement/ Meaning of P(n, r); Combination: Meaning of C(n,r)/ Applications of Permutations and Combinations/ Statement of Binomial Theorem; Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method/ General and Middle Terms in Binomial Expansions/ Properties of Binomial Coefficients/ Binomial Theorem for any Index (without proof)/ Application of Binomial Theorem/ The Principle of Mathematical Induction, simple Applications
- Matrices & Determinants: Concept of a Matrix/ Types of Matrices/ Equality of Matrices/ Operations of Addition/ Scalar Multiplication and Multiplication of Matrices/ Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only/ Determinant of a Square Matrix/ Minors and Cofactors/ singular and non-singular Matrices/ Applications of Determinants in finding the Area of a Triangle/ Concept of elementary row and column operations/ Transpose/ Adjoint and Inverse of a Matrix/ Consistency and Inconsistency of a system of Linear Equations/ Solving System of Linear Equations in Two or Three variables using Inverse of a Matrix
- Linear Inequalities: Solutions of Linear Inequalities in one variable and its Graphical Representation/ solution of system of Linear Inequalities in one variable/ Graphical solutions of Linear Inequalities in two variables/ solution of system of Linear Inequalities in two variables
- Mathematical Reasoning: Mathematically acceptable statements and their Negation/ Connecting words /phrases consolidating the understanding of if and only if condition, implies, and/or, implied by, there exists/ Validating the statements involving the connecting words/ difference among contradiction, converse and contrapositive
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Trigonometry | - Trigonometric functions and Inverse Trigonometric Functions: Degree measures and Radian measure of positive and negative angles/relation between degree measure and radian measure/ definition of trigonometric functions with the help of a unit circle/ periodic functions/ concept of periodicity of trigonometric functions/ trigonometric functions of sum and difference of numbers/ Trigonometric functions of multiple and submultiples of numbers/Graph of the following trigonometric functions
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Geometry | - Lines & Family of Lines: A cartesian system of coordinates in a plane/ shifting of origin/ Distance formula/ Slope of line/ parallel and perpendicular lines/ Various forms of equations of a line parallel to axes/ slope intercept form/ The Slope point form/ Intercept form, Normal form, General form/ Intersection of lines/ Equation of bisectors of the angle between two lines/ Angles between two lines/condition for concurrency of three lines/ Distance of a point from a line/ Equations of family of lines through the intersection of two lines
- Conic Sections: Sections of a cone/ Circles, standard form of the equation of a circle/ its radius and centre/ Equations of conic sections [Parabola, Ellipse and Hyperbola] in standard form and simple properties
- Vectors: Vectors and scalars/ Magnitude and Direction of a vector/ Types of vectors (Equal vectors, unit vector, Zero vector)/ Position vector of a point/ Localized and free vectors/ parallel and collinear vectors/ Negative of a vector/ components of a vector/ Addition of vectors/ multiplication of a vector by a scalar/ position vector of point dividing a line segment in a given ratio/ application of vectors in geometry/ Scalar product of two vectors/ projection of a vector on a line/ vector product of two vectors
- Three Dimneisonal Geometry: Coordinate axes and coordinate planes in three dimensional space/ coordinate of a point in space/ distance between two points/ section formula, direction cosines, and direction ratios of a line joining two points/ projection of the join of two points on a given line/ Angle between two lines whose direction ratios are given/ Cartesian and vector equation of a line through (i) a point and parallel to a given vector (ii) through two points, Collinearity of three points/ coplanar and skew lines/ Shortest distance between two lines/ Condition for the intersection of two lines/ Angle between (i) two lines (ii) two planes (iii) a line and a plane/ Cartesian and vector equation of a plane (i) When the normal vector and the distance of the plane from the origin is given (ii) passing through a point and perpendicular to a given vector (iii) Passing through a point and parallel to two given lines through the intersection of two other planes (iv) containing two lines (v) passing through three points/ Condition of coplanarity of two lines in vector and Cartesian form, length of perpendicular of a point from a plane by both vector and Cartesian methods
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Statistics | - Statistics & Probability: Mean deviation, variance, standard deviation for grouped an ungrouped data/ Random experiments and sample space, Events as subset of a sample space, occurrence of an event/ sure and impossible events, Exhaustive events, Algebra of events/ Analysis of frequency distributions with equal means but different variances/ Meaning of equality likely outcomes, mutually exclusive events/ Probability of an event/ Theorems on probability/ Addition rule, Multiplication rule/ Independent experiments and events/ Finding P (A or B), P (A and B)/ Bayes' theorem/ random variables/ Probability distribution of a random variable and its mean and variance/ Repeated independent (Bernoulli) trials and Binomial distribution
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Calculus | - Functions, Limits, and Continuity: Concept of a real function; its domain and range/ Modulus Function, Greatest integer function: Signum functions/ Trigonometric functions and inverse trigonometric functions and their graphs/ composite functions/ Inverse of a function/ Limit of a function/ meaning and related notations/ Left and right-hand limits/ Fundamental theorems on limits without proof/Continuity of a function at a point, over an open/ closed interval/ Continuity of a function at a point, over an open/ closed interval/ Continuity of special functions- Polynomial, Trigonometric, exponential, Logarithmic and Inverse trigonometric functions
- Differentiation: Derivative of a function/ its geometrical and physical significance/ Relationship between continuity and differentiability/ Derivatives of polynomial, basic trigonometric, exponential, logarithmic and inverse trigonometric functions from first principles/ derivatives of sum, difference, product and quotient of functions/ Logarithmic differentiation/ derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric and implicit functions/ derivatives of functions expressed in parametric form/ chain rule and differentiation by substitution/ Derivatives of Second order
- Application of Derivatives: Rate of change of quantities/ Tangents and Normals/ increasing and decreasing functions and sign of the derivatives/ maxima and minima/ Greatest and least values/ Rolle's theorem and Mean value theorem/ Approximation by differentials/ Simple problems
- Indefinite Integrals: Integration as inverse of differentiation/ properties of integrals/ Integrals involving algebraic, trigonometric, exponential and logarithmic functions/ Integration by substitution/ Integration by parts; Integrals of the type/ Integration of rational functions/ Partial fractions and their use in integration/
- Definite Integrals: Definite integral as limit of a sum/ Fundamental theorems of integral calculus without proof/ Evaluation of definite integrals by substitution and by using the following properties/ Application of definite integrals in finding areas bounded by a curve, circle, parabola and ellipse in standard form between two ordinates and x-axis/ Area between two curves, line and circle/ ; line and parabola: line and ellipse
- Differential Equations: Definition/ order and degree/ general and particular solutions of a differential equation/ formation of differential equations whose general solution is given/ solution of differential equations by the method of Separation of variables/ Homogeneous differential equations of the first order and their solutions/
- Linear Programming: Introduction/ related terminology such as constraints, 0bjective function, optimisation/ mathematical formulation of Linear Programming Problems/ different types of linear programming problems/ graphical method of solution for problems in two variables/ feasible and infeasible regions/ feasible and infeasible solutions/ optimal feasible solutions
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