Syllabus
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)
- Trigonometric equations (Principal solution and general solution)
- Properties of triangles (sine and cosine rules)
4. Principle of Mathematical Induction
- PMI introduction, sequence type problems I
- Divisible by and multiple of type problems I
- Inequalities type problems
5. 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
6. 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
7. 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
8. 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
9. 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
- Arithmetico geometric series and some special series
10. 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
- Locus of a point, Shift of origin
11. 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
12. Introduction to Three Dimensional Geometry
- Coordinate axes, coordinate planes, octant, distance formula
- Section formula and its application
13. 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
14. Mathematical Reasoning
- Statements, types of statements, negation, quantifiers
- Contrapositive, converse, method of contradiction
15. 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
- To find the coefficient of varation, consistency
- Word problems on mean, variance and standard deviation
16. 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)