Applied Mathematics Class 11 Syllabus

There are eight units - (i) Numbers, Quantification and Numerical Applications, (ii) Algebra, (iii) Mathematical Reasoning, (iv) Calculus, (v) Probability, (vi) Descriptive Statistics, (vii) Basics of Financial Mathematics, and (viii) Coordinate Geometry.

Course Structure

S.No. Unit Marks
I Numbers, Quantification and Numerical Applications 9
II Algebra 10
III Mathematical Reasoning 6
IV Calculus 10
V Probability 10
VI Descriptive Statistics 12
VII Basics of Financial Mathematics 18
VIII Coordinate Geometry 5
  Total 80

Unit I: Numbers, Quantification and Numerical Applications

  • Prime Numbers, Encryptions using Prime Numbers
  • Binary Numbers
  • Complex Numbers (Preliminary idea only)
  • Indices, Logarithm and Antilogarithm
  • Laws and properties of logarithms
  • Simple applications of logarithm and antilogarithm
  • Numerical problems on averages, calendar, clock, time, work and distance, mensuration, seating arrangement

Unit II: Algebra

  • Sets
  • Types of sets
  • Venn diagram
  • De Morgan's laws
  • Problem solving using Venn diagram
  • Relations and types of relations
  • Introduction of Sequences, Series
  • Arithmetic and Geometric progression
  • Relationship between AM and GM
  • Basic concepts of Permutations and Combinations
  • Permutations, Circular Permutations, Permutations with restrictions
  • Combinations with standard results

Unit III: Mathematical and Logical Reasoning

  • Mathematically acceptable statements
  • Connecting words/ phrases in Mathematical statement consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
  • Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism etc)

Unit IV: Calculus

  • Introducing functions
  • Domain and Range of a function
  • Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function)
  • Graphical representation of functions
  • Concept of limits and continuity of a function
  • Instantaneous rates of change
  • Differentiation as a process of finding derivative
  • Derivatives of algebraic functions using Chain rule
  • Tangent line and equations of tangents

Unit V: Probability

  • Random experiment, sample space, events, mutually exclusive events
  • Independent and Dependent Events
  • Law of Total Probability
  • Bayes’ Theorem

Unit VI: Descriptive Statistics

  • Types of data (raw data, univariate data, bivariate and multi-variate data)
  • Data on various scales (nominal, ordinal, interval and ratio scale)
  • Data representation and visualization
  • Data interpretation (central tendency, dispersion, deviation, variance, skewness and kurtosis)
  • Percentile rank and quartile rank
  • Correlation (Pearson and Spearman method of correlation)
  • Applications of descriptive statistics using real time data

Unit VII: Basics of Financial Mathematics

  • Interest and interest rate
  • Accumulation with simple and compound interest
  • Simple and compound interest rates with equivalency
  • Effective rate of interest
  • Present value, net present value and future value
  • Annuities, calculating value of regular annuity
  • Simple applications of regular annuities (up to 3 period)
  • Tax, calculation of tax and simple applications of tax calculation in Goods and service tax, Income Tax
  • Bills, tariff rates, fixed charge, surcharge, service charge
  • Calculation and interpretation of electricity bill, water supply bill and other supply bills

(Comparing interest rates on various types of savings; calculating income tax; electricity bills, water bill; service surcharge using realistic data)

Unit VIII: Coordinate Geometry

  • Straight Line
  • Circles
  • Parabola

(only standard forms and graphical representation on two-dimensional plane)