Applied Mathematics – CBSE 12

CBSE Syllabus 2020

Applied Mathematics

Numerical Applications : Modulo Arithmetic. Congruence Modulo. Simple arithmetic functions. Allegation or Mixture. Numerical problems on boats and streams, partnership, pipes and cistern, races and games, scheduling. Numerical Inequalities

Algebra : Simultaneous linear equations. Matrices. Determinants. Inverse of a Matrix. Cramer’s Rule and its application 7. Applications of Matrices and Determinants. Leontiff  Input Output model

Calculus:  Application of Derivatives. Increasing/Decreasing functions. Maxima and Minima. Marginal Cost and marginal revenue using derivatives. Integration. Indefinite integral as family of curves. Definite integral as area under the curve. Integration of Algebraic functions. Application of Integration (consumer surplus-producer surplus). Differential Equation. Linear differential equation. Application of differential equation (Growth and Decay Model).

Probability : Probability Distribution. Mathematical Expectation. Variance. Binomial Distribution. Poisson distribution. Normal distribution. Basic applications and inferences

Inferential Statistics : Population and Sample. Parameter, statistic and statistical inferences. t-Test

Index Numbers and Time-based Data : Index numbers. Uses of index numbers. Construction of index numbers. Tests of adequacy of index numbers. Time series. Time series analysis for univariant data sets. Trend analysis by moving average method. Trend analysis of linear trend line using least squares.

Financial Mathematics : Perpetuity. Sinking funds. Valuation of Bonds. Calculation of EMI. Calculation of Returns, Rate of return, Effective Rate of Interest. Compound annual growth rate. Stock, shares and debentures. Linear method of Depreciation

Linear Programming : Constraints. Objective Function. Optimization. Mathematical formulation of linear programming. Transportation and Assignment problem. Graphical solution of Linear Programming. Feasible and infeasible regions. Feasible and infeasible solutions, optimal feasible solutions (up to three nontrivial constraints)