Algebra
(i) Binomial Theorem: Binomial Theorem – of any index (without proof) - general term of the expansion (x ± y) n , (1 ± x) n : series infinite if n Î Q, but finite if n Î Z + - application to approximation using binomial theorem; mathematical induction - illustration of the method of proof - elementary applications only.
(ii) Determinants and Matrices: Determinants – of order 2 and 3 - minors and co-factors of a determinant - expansion of determinant - properties of determinant and their use in evaluation of a determinant - solution of a system of simultaneous equations in 2 or 3 variables using Cramer's rule - condition for consistency of 3 equations in two unknowns; matrices - rectangular arrays of order m x n, where m, n £ 3, including case m = n - addition/subtraction of matrices -multiplication by a scaler - multiplication of matrices - square matrix of order 2 x 2 and 3 x 3 - singular and non singular matrices of order 2 x 2 and 3 x 3 - adjoint and inverse of a square matrix of order 2 x 2 and 3 x 3 - use of matrices to solve simultaneous linear equations in 2 or 3 unknowns.
(iii) Permutations and Combinations: factorial notation; fundamental principle; concept of n P r - permutation of like things – restricted permutations - circular permutations; concept of n C r - restricted combinations – distribution of different things into groups - open selection of items from different things/from like things; mixed problems on permutation and combination.
Co-ordinate Geometry
(i) Conics: As sections of a cone; foci and directix; equation of a parabola, ellipse, hyperbola in standard form simple problems; general equation for a conic when focus, directrix and eccentricity are given.
Calculus - Differential
(i) Differential Calculus: Derivatives of exponential functions, logarithmic functions, inverse trigonometric functions reduceable to simple form by substitution; logarithmic differentiation; successive differentiation upto 2 nd order; condition of maxima and minima, application of maxima and minima to simple problems relating to positive integers, trigonometric functions; rectangles, semi circles, spheres, cylinders and cones.
(ii) Integral Calculus: Revision of formulae of integration from Class XI. Standard methods of integration - substitution or by change of independent variable, formulae for integrals of functions e x , tan x , cot x , sec x , cosec x ; integrals of the type: ∫ 2 2 x a dx±, ∫ 2 2 a - xdx,∫ 2 2 x adx±, ∫ 2 2 a - xdx, ∫ 2 ax bx cdx+ +,dxax bx cpx q ∫ 2 + ++, ∫ 2 ax bx cdx+ +, dxax bx cpx q ∫ 2 + ++, Integration of rational functional functions by partial fractions; Integration by parts, integrals of the type: ∫ -1 sin xdx , ∫ log xdx , _ a + b xdxcos,∫ a b sin xdx+.
Calculus - Integral
Definite integrals: evaluation of definite integrals, transformation of definite integrals bysubstitution, following properties of definite integrals:∫ ∫ baab ( x ) dx = - f ( x ) dx ,∫ ( ) ∫ ( ) ∫ ( ) , bacabcf x dx = f x dx + f x dx∫ ( ) ∫ ( ) ∫ (2 - ) , 2a0a0a0f x dx = f x dx + f ax dx∫ ( ) ∫ ( - ) , a0a0f x dx = f a x dx∫ ( ) 2 ∫ ( ) if (2 - ) ( ), 2a0a0 x dx = f x dx f a x = f x0 if (2 - ) - ( ) 0 = f a x = f x, Evaluation of some integrals using the above properties.
Application of definite integrals: area bounded by a curve between two ordinates and x-axis; area between two curves; volume of a solid of revolution about x or y-axis.
Differential Equations
(i) Meaning of differential equations, order and degree of a differential equation.
(ii) Solution of differential equations (1st order, 1st degree) of the type; variable separable; homogeneous equations; dy/dx+Py = Q where P & Q are functions of x.
(iii) Solution of differential equation of the type d 2 y/dx 2 = f(x) (general and particular solutions).
Measures of Dispersion
(i) Meaning of dispersion; quartile deviation; standard deviation; coefficient of variation.
(ii) Combined mean and standard deviation of two groups only.
(iii) Mean deviation from the mean or median.
Correlation and Regression
(i) Scatter diagrams and correlation: definition and meaning of correlation and regression coefficient; use of scatter diagram to interpret the values of correlation coefficient; calculation of coefficient of correlation by Karl Pearson's method for ungrouped data only; calculation of Spearman's rank correlation coefficient with correction for repeated data.
(ii) Regression: meaning of regression; calculation of regression; coefficient and the two lines of regression by the method of least squares; use of lines of regression for prediction.
Index Numbers and Moving Averages
(i) Index numbers: meaning and purpose of index numbers; methods of calculating index numbers - simple aggregate method - simple average of price relative method - weighted average of price relative method - weighted
aggregate method.
(ii) Moving averages: calculation of moving averages with the given periodicity and plotting on a graph.
Probability
(i) Events: sure events; impossible events; mutually exclusive events; equally likely events; independent and dependent events.
(ii) Definition of probability of an event.
(iii) Laws of probability; addition and multiplication laws, conditional probability; Baye's theorem.
(iv) Theoretical probability distribution; Probability density function; Binomial distribution - its mean, variance and S.D.
(v) Mathematical expectations: Calculating mean, variance and S.D. using expectations.
Discount
True discount; banker's discount; discounted value; present value; cash discount, bill of exchange.
Average due date
Zero date, equated periods; insurance policies, premiums.
Annuities
Meaning, formulae for present value and amount; deferred annuity, applied problems on loans, sinking funds, scholarships.
Application of derivatives in Commerce and Economics in the following:
Cost function or marginal cost, revenue function and break even point.
|
