CBSE Class 11 Applied Mathematics — Notes, Solutions & Papers

I Numbers, Quantification and Numerical Applications

10

Total 80

Internal Assessment 20

CLASS- XI

Sl. No.

Unit and

Chapter

Details of content Learning Outcomes

Numbers & Quantification 1.1 Binary Numbers ● Introduction to Binary Number System ● Conversion of decimal numbers to binary system and vice -versa and its applications. Students will be able to ● Understand the relation between decimal and binary number system. ● Able to convert from one system to another. ● Understand the application of Binary number system in programming, coding, machine learning etc. 1.2 Indices, Logarithm and Antilogarithm ● Indices and its properties ● Common and Natural logarithm ● Laws of logarithms ● Logarithm and exponential as inverse operations ● Procedure of finding logarithm and antilogarithms of given number ● Applications of logarithms Students will be able to ● Apply rules of indices to simplify expressions and solve problems involving powers ● Define logarithms and antilogarithms as inverse operations ● Distinguish between common logarithms and natural logarithms ● Apply logarithmic and antilogarithmic techniques to simplify complex calculations, and solve practical problems 1.3 Introduction To Bhartiya System of Numeration ● Introduction To Bhartiya System of Numeration Students will be able to ● Gain acquaintance with traditional way of expressing numbers Numbers in day-to-day Life 1.4 Clocks ● Evaluate the angular value of a minute ● Measure of angle formed between two hands of clock at given time ● Calculation of the time for which hands of clock meet Students will be able to • Calculate the angular displacement of hour and minute hands • Find the exact time when clock hands coincide, are opposite, or form a specific angle • Understand the practical utility of calendar 1.5 Calendar ● Odd days in a month/ year/ century ● Decode the day for the given date Students will be able to ● Calculate odd days in any given month, year, or century ● Find the day of the week for any given date 1.6 Time and Work ● Relationship between work and time ● Comparison of the work done by the individual / group w.r.t. time Students will be able to ● Solve time-work problems ● Represent time-work relationship graphically 1.7 Speed, Distance and Time ● The time taken/ distance covered from the given data. Students will be able to ● Represent distance-time relationship graphically

1.8

Seating arrangement ● Creation of seating plan/ draft as per given conditions (Linear/circular). ● Locating the position of a person in a seating arrangement. Students will be able to ● Design and create seating plans in linear and circular arrangements ● Determine the exact position of any person in a seating arrangement by analy sing the given conditions and applying logical reasoning ● Apply seating arrangement concepts to real-life situations

Sets 2.1 Introduction to Sets – Sets and their representati on ● Set as well-defined collection of objects. ● Representation of a set in Roster form and Set builder form ● Different types of sets on the basis of number of elements in the set ● Differentiate between equal set and equivalent set Students will be able to • understand the systematic development of set theory. • represent sets accurately using both roster form and set -builder form • differentiate between the two methods of expressing the same set.

2.2

2.3

Subsets, Intervals as subsets ● Subsets ● Power set and its elements ● Universal Set ● Subset of real numbers as intervals Students will be able to ● list all possible subsets of a given set, calculate the total number of subsets ● justify why the empty set is a subset of every set through logical reasoning. ● define power sets, construct the power set of a given set by identifying all its subsets ● Get an idea about the special sets i.e., intervals which have vide utility in the study of analysis. Venn Diagrams and Operations on Sets • Concept of Venn diagram to understand the relationship between sets • Problems using Venn diagram Students will be able to • Use set operations to solve problems in various fields, such as probability, and data analysis. • Develop problem -solving skills using set theory and Venn diagrams. • Operations on sets • Perform operations on sets to solve practical problems Relations 2.4 Ordered pairs Cartesian product of two sets • Significance of specific arrangement of elements in a pair • Cartesian product of two sets Students will be able to • Understand the concept of ordered pairs • Find the Cartesian product of two finite sets • Calculate the number of elements in a Cartesian product 2.5 Relations • Expressing relation as a subset of Cartesian product • Domain and range of a relation Students will be able to • Identify and express relations as subsets of Cartesian products • Determine the domain and range of any relation • Create and analy se custom relations from everyday situations Mathematical Logic 2.6 Mathematical Logic ● Logical problems involving odd man out, syllogism, blood relation and coding-decoding Students will be able to ● Identify patterns and solve odd man out problems ● Draw valid conclusions using syllogism ● Decode blood relations and solve coding-decoding problems ● Apply logical reasoning skills to real- life decision-making situations Sequences and Series 2.7 Sequence and Series • Differentiate between sequence and series Students will be able to • Distinguish between sequences and series 2.8 Arithmetic Progression • Arithmetic mean (AM) of two positive numbers Students will be able to • Calculate and apply arithmetic mean (AM) of two positive numbers to find average values in real-life situations 2.9 Geometric Progression • Introduction of Geometric Progression

(GP)

● 𝑛𝑡ℎ term of a GP ● sum of n terms and sum of infinite terms of a GP ● Problems based on applications of GP ● Geometric mean (GM) of two positive numbers ● Relation between AM and GM and related problems ● Application problems based on AP and GP Students will be able to • Identify and construct geometric progressions • Calculate geometric mean (GM) of two positive numbers • Analyse and prove the AM -GM inequality relationship • Apply formulas of arithmetic an d geometric progressions strategically to solve real-world problems

Functions 3.1 Functions and their graphs • Dependent and independent variables ● Definition of function using dependent and independent variable ● Domain, range and co- domain of a given function • Types of functions ● Graphical representation of function Students will be able to ● Define dependent and independent variables ● Define and differentiate between domain, co-domain, and range of functions ● Classify and define various types of functions ● Determine domain, co-domain, and range of given functions ● Represent functions graphically on coordinate planes ● Apply function concepts to solve real-life problems involving mapping relationships like student enrolment systems, profit-loss calculations, and designing input-output models for business. Limits, Continuity and Derivatives 3.2 Limits and continuity of functions ● Limit of a function ● Continuity of a function Students will be able to ● Define and understand the concept of limit of a function by analy sing the behaviour of functions. ● Solve problems based on the algebra of limits. ● Define continuity of a function at a point and over an interval 3.3 Differentiation ● Instantaneous rate of change ● Finding the derivative of the functions Students will be able to ● Define the derivative of a function and relate it to the slope of the tangent to a curve. 3.4 Algebra of derivatives ● Differentiation of addition, subtraction, multiplication and division of two or more functions ● Differentiation of a function of a function Students will be able to • state and apply the fundamental rules of differentiation for sum, difference, product, and quotient of two or more functions ● understand the chain rule as the method for differentiating composite functions.

Combinatorics 4.1 Combinatorics ● Factorial of a number ● Fundamental Principle of Counting ● Concept of Permutation ● Simple problems based on permutations Students will be able to • Understand and calculate factorials of numbers • Appreciate how to count without counting • Define permutation and apply the ● Define combination ● Difference between permutation and combination ● Problems based on Combinations concept to solve problems • Define combination and differentiate it from permutation • Apply permutation and combination formulas strategically • Model complex counting situations using permutation and combination concepts Probability 4.2 Probability ● Random experiment and sample space with suitable examples ● Event and its Types ● Concept of Probability ● Problems based on calculating probabilities in real life situations ● Concept of conditional probability Students will be able to ● Define random experiment and sample space with suitable examples ● Recognize and differentiate different types of events and find their probabilities ● Appreciate the use of probability in daily life situations ● Apply reasoning skills to solve problems based on conditional probability

Measures of Dispersion and Percentiles 5.1 Measures of Dispersion ● Meaning of dispersion in a data set ● Range, mean deviation , standard deviation and variance Students will be able to ● Understand the meaning of dispersion in a data set ● Differentiate between range, mean deviation and standard deviation ● Calculate range, range standard deviation and variance, and standard deviation for ungrouped and grouped data set ● Choose appropriate measure of dispersion to calculate spread of data 5.2 Percentiles ● Concept of Percentile rank ● Calculate and interpret Percentile rank of scores in a given ungrouped data set. Students will be able to • Calculate, analyze and interpret Percentile rank of scores in a given ungrouped data set. Correlation 5.3 Correlation ● Concept of Correlation ● Karl Pearson’s coefficient of Correlation for ungrouped data ● Spearman’s Rank Correlation for ungrouped data Students will be able to • Analyze relationships between variables by calculating and interpreting Karl Pearson's coefficient of correlation and Spearman's rank correlation coefficient for ungrouped data. Regression 5.4 Regression ● Concept of Regression analysis ● Dependent and Students will be able to • Distinguish between correlation and regression analysis. Independent variables ● Regression Coefficients ● Regression Equations ● Properties of Regression Equations • Compute regression coefficients. • Solve real -world problems by selecting and applying appropriate correlation or regression techniques.

Interests and Annuities

6.1

Interest and Interest Rates ● Concept of Interest Rates ● Comparison between Nominal Interest Rate, Effective Rate and Real Interest Rate ● Practical applications of interest rate w.r.t simple and compound interest ● Concept of effective rate of interest Students will be able to • Understand the concept of interest rates • Differentiate between nominal interest rate, effective rate, and real interest rate • Calculate and compare simple and compound interest • Apply interest rate concepts to solve real-life financial problems • Define with examples the concept of effective rate of interest • Analyze and evaluate financial products and investment schemes

6.2

Annuities ● Meaning of Immediate Annuity, Annuity due and Deferred Annuity ● Future and present value of ordinary annuity, annuity due (up to 3 period) ● Concept of Annuity in real life situations Students will be able to • Understand and differentiate between immediate annuity, annuity due, and deferred annuity • Calculate the future and present value of regular annuity and annuity due • Apply annuity concepts to real -life financial situations Tax and Utility Bills 6.3 Taxes and Utility Bills • Concept of Income tax and GST w.r.t. tax new tax guidelines • Utility bills and its various types – Electricity, Water and PNG Bills Students will be able to • Understand the concept of income tax and GST • Calculate income tax and GST liabilities using applicable tax brackets • Analyse and calculate types of utility bills – Electricity and Water Bills • Apply taxation and utility billing concepts to real-life situations.

Straight Lines 7.1 Straight lines ● Concept of s lope of a line ● Various forms of equation of line Students will be able to ● Understand the gradient as the measure of steepness and calculate it using coordinates ● Derive and apply various algebraic forms to represent lines in a Cartesian plane. • Apply linear equations to model real - world scenarios like demand and supply curves in economics. Circles and Parabola 7.2 Circles and Parabola ● Determination of the equations of circle and parabola as a locus of a point in a plane under certain conditions ● Different form of equations of a circle ● Solve problems based on applications of circle Students will be able to ● Define circles and parabolas as sets of points satisfying specific geometric conditions in a plane. ● Formulate and solve equations of circles in standard, central, diameter, and general forms. ● Identify the properties of a parabola and express its standard form equation based on its focus and directrix. ● Utilize the properties of circles to solve practical and coordinate-based mathematical problems. Suggested Practicals using spreadsheet 1. Visualizing Functions and Their Properties : Plotting graphs of functions in GeoGebra to observe how coefficients change the graph’s shape and to find out their domain and range graphically. 2. Understanding Derivatives: Constructing a tangent line to a curve in GeoGebra and observing its slope as the point moves and demonstrating the derivative as the instantaneous rate of change. 3. Personal Budgeting : Designing a comprehensive monthly budget tracker in a spreadsheet to manage income and expenditures using summation and percentage formulas. 4. Comparative Cost-Benefit Analysis: Building a decision -making model to identify the most economical purchase for a high -value product by comparing cost, shipping charges, tax and other hidden costs. 5. Descriptive Measures of Data : Using spreadsheet functions (e.g., AVERAGE, STDEV.P etc.) to compute the mean, median, mode, variance, and standard deviation of a raw dataset. 6. Interest Growth Analysis: Developing a comparative sheet for Simple vs. Compound Interest to track the growth of an investment over time. 7. Environmental & Economic Data Model ling: Analysing real-world datasets regarding local weather, inflation or AQI by generating and interpreting scatter plots, histograms, bar graphs etc. to identify correlations and seasonal trends. Grade XII (2026-27)

Number of Paper: 1

Time: 3 Hours

Max Marks: 80 No. Units Marks I Numbers, Quantification and Numerical Applications

11

Total 80

Internal Assessment 20