Mathematics (100 Marks)
- Sets and their representations
- Union
- Intersection and complement of sets and their algebraic properties
- Power set
- Relation
- Type of relations
- Equivalence relations
- Functions
- One - One, into and onto functions
- Composition of functions
2. Complex number and Quadratic Equations
- Complex numbers as ordered pairs or real
- Representation of complex numbers in the form a+ib and their representation in a plane
- Argand diagram
- Algebra of complex numbers
- Modulus and argument of a complex number
- Square root of a complex number
- Triangle inequality
- Quadratic equation in real and complex number system and their solutions
- Relation between roots and co-efficient
- Nature of roots
- Formation of quadratic equations with given roots
- Matrices
- Algebra of matrices
- Types of matrices
- Determinants and matrices of order two and three
- Properties of determinants
- Evaluation of determinants
- Area of triangles using determinants
- Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations. Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
4. Permutation And Combinations -
- Fundamental principle of counting
- Permutation as an arrangement and combination as selection
- Meaning of P (n, r) and C (n, r). Simple applications
5. Mathematical Induction -
- Principle of mathematical induction and its simple applications
6. Binomial theorem and its simple application-
- Binomial theorem for a positive integral index
- General term and middle term
- Properties of binomial coefficients and simple applications
7. Sequences And Series -
- Arithmetic and geometric progressions
- Insertion of arithmetic, geometric means between two given numbers
- Relation between A.M. and G.M., Sum up to n terms of special series Sn, Sn2, Sn3
- Arithmetic-Geometric progression
8. Limit, Continuity And Differentiability-
- Real functions
- Valued functions
- Algebra of functions
- Polynomial functions
- Rational functions
- Trigonometric functions
- Logarithmic and exponential functions
- Inverse functions
- Graphs of simple functions
- Limits, continuity and differentiability
- Differentiation or the sum, difference
- Product and quotient of two functions
- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions
- Derivatives of order up to two
- Rolle's and Lagrange's mean value theorems
- Applications of derivatives
- Rate of change of quantities
- Monotonic - increasing and decreasing functions
- Maxima and minima of functions of one variable
- Tangents and normals
9. Integral Calculus -
- Fundamental integrals involving algebraic, trigonometric , exponential and logarithmic functions
- Integration by substitution, by parts and by partial fractions
- Integration using trigonometric identities
- Integral as limit or a sum
- Fundamental theorem of calculus
- Properties of definite integrals
- Evaluation of definite integrals
- Determining areas of the regions bounded by simple curves in standard form
10. Differential Equations -
- Ordinary differential equations and their order and degree
- Formation of differential equations
- Solution of differential equations by the method of separations of variables
- Solution of differential equations by the method of separations of variables
- Solution of homogeneous and linear differential equations of the type : dy/dx+p(x)y=q(x)
11. Co-ordinate Geometry -
- Cartesian system of rectangular co-ordinates 10 in a plane
- Distance formula
- Section formula
- Locus and its equation
- Translation of axes
- Slope of a line
- Parallel and perpendicular lines
- Intercepts of a line on the coordinate axes
- Various forms of equations of a straight line
- Intersection of lines
- Angles between two lines
- Conditions for concurrence of three lines
- Distance of a point from a line
- Equations of internal and external bisectors of angles between two lines
- Coordinates of centroid
- Orthocenter and circumcenter of a triangle
- Equation of family of lines passing through the point of intersection of two lines
- Standard form of equation of a circle
- General form of the equation of a circle, its radius and center
- Equation of a circle when the end points of a diameter are given
- Points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle
- Equation of the tangent
- Sections of cones
- Equation of conic sections in standard forms
- Condition for y = mx + c to be a tangent and point (s) of tangency
12. Three Dimensional Geometry -
- Coordinates of a point in space
- Distance between two points
- Section formula
- Direction ratios and direction cosines
- Angle between two intersecting lines
- Skew lines and the shortest distance between them and its equation
- Equations of a line and a plane in different forms
- Intersection of a line and a plane
- Coplanar lines
13. Vector Algebra -
- Vectors and scalars
- Addition of vectors
- Components of a vector in two dimensions and three dimensional space
- Scalar and vector products
- Scalar and vector triple products
14. Statistic And Probability -
- Measures of dispersion
- Calculation of mean and median
- Mode of grouped and ungrouped data calculation of standard deviation
- Variance and mean deviation for grouped and ungrouped data
- Probability of an event
- Addition and multiplication theorems of probability
- Baye's theorem
- Probability distribution of a random variate
- Bernoulli trials and binomial distribution
15. Trigonometry. -
- Trigonometrical identities and equations, trigonometrical functions
- Inverse trigonometrical functions and their properties
- Heights and distances
16. Mathematical Reasoning -
- Statements
- Logical operations and, or, implies, implied by, if and only if
- Understanding of tautology
- Contradiction
- Converse and contrapositive
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