CBSE Class 11th(Commerce) Mathematics Syllabus 2020-21

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)

Practical: Use of spread sheet

Calculating average, interest (simple and compound), creating pictographs, drawing pie chart, bar graphs, calculating central tendency; visualizing graphs (straight line, circles and parabola using real time data)

Suggested practical using spread sheet

1. Plot the graph of functions on excel; study the nature of function at various points, drawing lines of tangents;

2. Create budget of income and spending;

3. Create compare sheet of price, features to buy a product;

4. Prepare best option plan to buy a product by comparing cost, shipping charges, tax and other hidden cost;

5. Smart purchasing during sale season;

6. Prepare a report card using scores of last four exams and compare the performance;

7. Collect the data on weather, price, inflation, and pollution. Sketch different types of graphs.