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# (2021-2022)

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with the growth of the subject and emerging needs of society. The senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Biological science, Commerce or Computer Applications. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real-life situations and other subject areas, greater emphasis has been laid on the application of various concepts.

## OBJECTIVES:

The broad objectives of teaching Mathematics at the senior school stage intend to help the students:

• to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and
• to feel the flow of reasons while proving a result or solving a
• to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one
• to develop a positive attitude to think, analyze and articulate
• to develop an interest in the subject by participating in related
• to acquaint students with different aspects of Mathematics used in daily
• to develop an interest in students to study Mathematics as a
• to develop an awareness of the need for national integration, protection of the environment, observance of small family norms, removal of social barriers, elimination of gender
• to develop reverence and respect towards great Mathematicians for their contributions to the field of Maths.

# TERM – II

 No. Units Marks I. Sets and Functions (Cont.) 8 II. Algebra (Cont.) 11 III. Coordinate Geometry (Cont.) 9 IV. Calculus (Cont.) 6 V. Statistics and Probability (Cont.) 6 Internal Assessment 10 Total 50

### Unit-I: Sets and Functions

1. Trigonometric Functions

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following

### Unit-II: Algebra

1. Linear Inequalities

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.

2. Permutations and Combinations

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula for nPr and nCr, simple applications.

### Unit-III: Coordinate Geometry

1.Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

2.Introduction to Three-dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

### Unit-IV: Calculus

1. Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically. Definition of Derivative, relate it to the slope of the tangent of the curve, a derivative of the sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

### Unit-V: Statistics and Probability

1. Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.