Topic outline

  • General

  • Trigonometric Functions

    Trigonometric Functions Syllabus

    Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application. Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

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  • Principle of Mathematical Induction

    Principle of Mathematical Induction

  • Complex Numbers

    2. Complex Numbers and Quadratic Equations

    Need for complex numbers, especially v1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Square root of a complex number.


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  • Co-ordinate Geometry

    Co-ordinate Geometry

    1. Straight Lines


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  • Calculus

    Calculus

    1. Limits and Derivatives 

    introduced as rate of change both as that of distance function and geometrically. Intutive idea of limit. Limits of polynomials and rational functions, trignometric, exponential and logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions. The derivative of polynomial and trigonometric functions.

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  • Mathematical Reasoning

    Mathematical Reasoning

    1. Mathematical Reasoning

    Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words difference between contradiction, converse and contrapositive.

  • Statistics and Probability

    Statistics and Probability

    1. Statistics

    Measures of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

    2. Probability

    Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.

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