Syllabus

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1. Sets

• Sets definition, roaster form and set-builder form
• Types of sets, problems based on empty, equal, equivalent, finite and infinite sets
• Subsets, proper subset, power set and interval form of set
• Venn diagram, operation on sets (union, intersection, difference, complement, symmetric difference)
• laws (properties) of sets
• Cardinal numbers, word problems of two and three sets

2. Relations and Functions

• Cartesian product of two or more sets, Operation on cartesian product
• Domain and range and co-domain of a relation
• Functions Definition
• Composition of Functions
• Graph of a function, domain and range of function

3. Trigonometric Functions

• Measurement of angles, relation between degrees and radians
• Relation between radius, length of arc and angle at the centre (Theta = l/r)
• Signs of trigonometric ratios in different quadrant
• Trigonometric ratios of allied angles
• Graph of trigonometric functions
• Trigonometric ratios of compound angles
• Transformation formulae and its application
• Trigonometric ratios of angle 2A in terms of angle A
• Trigonometric ratios of angle 3A in terms of angle A
• Trigonometric ratios of half angle (A/2 in terms of A)

4. Complex Numbers

• Integral powers of iota, Problems based on iota
• Equality, addition, subtraction, multiplication and division of complex numbers 
• Multiplicative inverse of complex numbers, conjugate of a complex number
• Modulus and argument of a complex number
• Polar form of a complex number, Problems based on polar form
• To solve the quadratic equation with imaginary roots
• Square root of a complex number

5. Linear Inequalities

• Inequalities rules
• To solve the linear inequalities in one variable and representation on number line
• To solve the rational linear inequalities
• To solve the linear inequalities in two variables graphically
• Word problems on linear inequalities

6. Permutations and Combinations

• Factorial, Problems based on factorial
• Fundamental principles of multiplication and addition, problems on number formation
• Fundamental principles of multiplication and addition, problems on number formation
• nPr and nCr formulae and application
• Properties of combinations, word problems on combinations
• word problems on combinations
• Problems based on permutations and combinations both and circular permutations

7. Binomial Theorem

• Binomial expansion formula
• Problems based on binomial expansion
• To find the general and particular terms in a binomial expansion
• Problems on general and middle terms
• To find the coefficient for the exponent of the variable, to find the term independent of the variable

8. Sequences and Series

• Introduction of sequences and series, Problems based on sequences
• Introduction of arithmetic progressions, To find the nth term of an AP
• Sum of n terms of an AP 
• Arithmetic means
• nth term of a GP
• Sum of n terms of a GP and its application
• Sum of infinite terms of a GP
• Geometric means and problems based on AM and GM

9. Straight Lines

• Distance formula and section formula
• Slope of a line and its application
• Angle between two lines, condition for perpendicular and parallel lines
• Equation of straight line slope intercept form, slope point form, two point form 
• Equation of straight line intercept form, normal form
• Equation of a line reducible to intercept form and normal form
• Distance from a point to the straight line, distance between two parallel lines
• To find the point of intersection of two lines, foot of perpendicular and coordinates of the image

10. Conic Sections

• Introduction of circles, equation of circle
• To find the centre and radius of a circle
• Equation of parabola, focus, directrix, axis and latus rectum of a parabola
• Equation of ellipse, vertices, foci, length of major and minor axes, directrices and length of latus rectum
• Equation of hyperbola, vertices, foci, length of major and minor axes, directrices and length of latus rectum

11. Introduction to Three Dimensional Geometry

• Coordinate axes, coordinate planes, octant
• Distance formula and its application

12. Limits and Derivatives

• Evaluate limit of algebraic functions by factorization method
• Evaluate limit of algebraic functions by rationalization method
• Formulae for trigonometric functions, Evaluate limit of trigonometric functions tends to zero 
• Problems based on limit of trigonometric functions tends to non-zero 
• Evaluate limit tend to infinite and limit of logarithmic and exponential functions
• Evaluate limit of signum functions
• Derivative by first principle method (Formula and application)
• Basic differentiation, product rule and quotient rule in differentiation
• Chain rule of differentiation

13. Statistics

• Formulae to find mean, median and mode in ungrouped and grouped data
• Mean deviation about mean and about median in ungrouped data
• Mean deviation about mean and about median in grouped data
• Variance and standard deviation in ungrouped data
• Variance and standard deviation in grouped data
• Mean, variance and standard deviation by shortcut method
• Word problems on mean, variance and standard deviation

14. Probability

• To evaluate the sample space of the event
• Events, to write different events from sample space
• Types of events (mutually exclusive and exhaustive events)
• To find the probability of an event (problems based on permutations and combinations)

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