| Chapter |
Topics |
| Algebra |
- Concept of set, operations on sets, Venn diagrams.
- De Morgan laws, Cartesian product, relation, equivalence relation
- Representation of real numbers on a line.
- Complex numbers—basic properties, modulus, argument, cube roots of unity.
- Binary system of numbers. Conversion of a number in a decimal system to a binary system and vice-versa.
- Arithmetic, Geometric and Harmonic progressions.
- Quadratic equations with real coefficients.
- Solution of linear inequalities of two variables by graphs.
- Permutation and Combination. Binomial theorem and its applications.
- Logarithms and their applications.
|
| Matrices and Determinants |
- Types of matrices, operations on matrices.
- Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix,
- Applications- Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
|
| Trigonometry |
- Angles and their measures in degrees and in radians.
- Trigonometrical ratios.
- Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.
- Inverse trigonometric functions.
- Applications-Height and distance, properties of triangles
|
| Analytical Geometry of Two and Three Dimensions |
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere |
| Differential Calculus |
- Concept of a real valued function–domain, range and graph of a function.
- Composite functions, one to one, onto and inverse functions.
- Notion of limit, Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions.
- Derivative of function at a point, geometrical and physical interpretation of a derivative—applications.
- Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function.
- Second order derivatives. Increasing and decreasing functions.
- Application of derivatives in problems of maxima and minima
|
| Integral Calculus and Differential Equations |
- Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.
- Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications.
- Definition of order and degree of a differential equation, formation of a differential equation by examples.
- General and particular solution of differential equations, solution of first order and first degree differential equations of various types—examples.
- Application in problems of growth and decay.
|
| Vector Algebra |
- Vectors in two and three dimensions, magnitude and direction of a vector.
- Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors.
- Vector product or cross product of two vectors.
- Applications—work done by a force and moment of a force and in geometrical problems.
|
| Statistics and Probability |
- Statistics : Classification of data, Frequency distribution, cumulative frequency distribution—examples.
- Graphical representation—Histogram, Pie Chart, frequency polygon— examples.
- Measures of Central tendency—Mean, median and mode.
- Variance and standard deviation—determination and comparison. Correlation and regression.
- Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.
- Union and Intersection of events. Complementary, elementary and composite events.
- Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems.
- Conditional probability, Bayes’ theorem—simple problems. Random variable as function on a sample space.
- Binomial distribution, examples of random experiments giving rise to Binominal distribution.
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