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Units | Topics | Marks |
---|---|---|

I | Sets and Functions | 29 |

II | Algebra | 37 |

III | Co-ordinate Geometry | 13 |

IV | Calculus | 6 |

V | Mathematical Reasoning | 3 |

VI | Statistics and Probability | 12 |

Total |
100 |

**Chapter 1: Sets**

- Sets and their representations
- Empty set
- Finite and Infinite sets
- Equal sets. Subsets
- Subsets of a set of real numbers especially intervals (with notations)
- Power set
- Universal set
- Venn diagrams
- Union and Intersection of sets
- Difference of sets
- Complement of a set
- Properties of Complement Sets
- Practical Problems based on sets

**Chapter 2: Relations & Functions**

Ordered pairs

Cartesian product of sets

Number of elements in the cartesian product of two finite sets

Cartesian product of the sets of real (up to R × R)

Definition of −

Relation

Pictorial diagrams

Domain

Co-domain

Range of a relation

Function as a special kind of relation from one set to another

Pictorial representation of a function, domain, co-domain and range of a function

Real valued functions, domain and range of these functions −

Constant

Identity

Polynomial

Rational

Modulus

Signum

Exponential

Logarithmic

Greatest integer functions (with their graphs)

Sum, difference, product and quotients of functions.

**Chapter 3: Trigonometric Functions**

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

Truth of the sin

^{2}x + cos^{2}x = 1, for all xSigns 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 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.

**Chapter 1: Principle of Mathematical Induction**

Process of the proof by induction −

Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers

The principle of mathematical induction and simple applications

**Chapter 2: Complex Numbers and Quadratic Equations**

Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic 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

**Chapter 3: 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 solution of system of linear inequalities in two variables

**Chapter 4: Permutations and Combinations**

- Fundamental principle of counting
- Factorial n
- (n!) Permutations and combinations
- Derivation of formulae and their connections
- Simple applications.

**Chapter 5: Binomial Theorem**

- History
- Statement and proof of the binomial theorem for positive integral indices
- Pascal's triangle
- General and middle term in binomial expansion
- Simple applications

**Chapter 6: Sequence and Series**

- Sequence and Series
- Arithmetic Progression (A.P.)
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- General term of a G.P.
- Sum of n terms of a G.P.
- Arithmetic and Geometric series infinite G.P. and its sum
- Geometric mean (G.M.)
- Relation between A.M. and G.M.

**Chapter 1: Straight Lines**

Brief recall of two dimensional geometries from earlier classes

Shifting of origin

Slope of a line and angle between two lines

Various forms of equations of a line −

Parallel to axis

Point-slope form

Slope-intercept form

Two-point form

Intercept form

Normal form

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

**Chapter 2: Conic Sections**

Sections of a cone −

Circles

Ellipse

Parabola

Hyperbola − a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section.

Standard equations and simple properties of −

Parabola

Ellipse

Hyperbola

Standard equation of a circle

**Chapter 3. Introduction to Threeâ€“dimensional Geometry**

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

**Chapter 1: Limits and Derivatives**

Derivative introduced as rate of change both as that of distance function and geometrically

Intuitive idea of limit

Limits of −

Polynomials and rational functions

Trigonometric, 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

**Chapter 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

**Chapter 1: Statistics**

Measures of dispersion −

Range

Mean deviation

Variance

Standard deviation of ungrouped/grouped data

Analysis of frequency distributions with equal means but different variances.

**Chapter 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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