Applied Mathematics Class 12 Syllabus

There are eight units - (i) Numbers, Quantification and Numerical Applications, (ii) Algebra, (iii) Inferential Statistics, (iv) Index Numbers and Time-based data, (v) Calculus, (vi) Financial Mathematics, (vii) Linear Programming, and (viii) Probability.

Course Structure

S.No. Unit Marks
I Numbers, Quantification and Numerical Applications 6
II Algebra 10
III Inferential Statistics 6
IV Index Numbers and Time-based data 10
V Calculus 15
VI Financial Mathematics 15
VII Linear Programming 8
VIII Probability 5
  Total 80

Unit I: Numbers, Quantification and 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

Unit II: Algebra

  • Solution of simultaneous linear equations using elimination method (up to 3 variables)
  • Matrices and types of matrices
  • Algebra of matrices
  • Determinants
  • Inverse of a matrix
  • Cramer’s rule and its application
  • Simple applications of matrices and determinants including Leontiff input output model for two variables

Unit III: 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 simple algebraic functions (primitive, by substitution, by parts)
  • Application of Integration (consumer surplus-producer surplus)
  • Differential equation (definition, order, degree)
  • Formulating and solving linear differential equation
  • Application of differential equation (Growth and Decay Model)

Unit IV: Probability

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

Unit V: Inferential Statistics

  • Population and sample
  • Parameter, statistic and statistical inferences
  • t-Test (one sample t-test and two independent groups t-test)

Unit VI: Index numbers and Time-based data

  • Index numbers, uses of index numbers
  • Construction of index numbers (simple and weighted)
  • Tests of adequacy of index numbers (unit test and time reversal test)
  • Time series, Time series analysis for univariant data sets
  • Trend analysis by moving average method
  • Trend analysis by fitting of linear trend line using least squares

Unit VII: Financial Mathematics

  • Perpetuity, Sinking funds
  • Valuation of Bonds (Present value approach and Relative price approach)
  • Calculation of EMI
  • Calculation of returns, nominal rate of return, effective rate of interest
  • Compound annual growth rate
  • Stock, shares and debentures
  • Linear method of depreciation

Unit VIII: Linear Programming

  • Introduction and related terminologies (constraints, objective function, optimization)
  • Mathematical formulation of linear programming problems
  • Different types of linear programming problems (Transportation and assignment problem)
  • Graphical method of solution for problems in two variables
  • Feasible and infeasible regions (bounded and unbounded)
  • Feasible and infeasible solutions, optimal feasible solutions (up to three nontrivial constraints)