In this page, we have covered the detailed syllabus of **CBSE Class 11 Applied Mathematics Syllabus** for Session 2022-23. Students must refer to the syllabus to start their preparation to score well by analysing the topics and chapters for this year examination.

**2022-23 Reduced Syllabus**

We have also provided the syllabus for the 2021-22 session that was previously restored so that you can compare the deleted and added topics.

**2021-22 Reduced Syllabus**

*<red> Marked in red: <red>** Topics <red> removed <red>for 2021-22*

**<red> 1.1 Prime Numbers, Encryptions using Prime Numbers <red>**

- <red> Definition and meaning <red>
- <red> Introduction to encryption /decryption using prime numbers by RSA algorithm <red>

**1.2 Binary Numbers**

- Definition of number system (decimal and binary)
- Conversion from decimal to binary system and vice - versa

**<red> 1.3 Complex Numbers (Preliminary Idea Only) <red>**

- <red> Definition and representation of Complex Numbers <red>
- <red> Basic operations (addition, subtraction, multiplication and division) on two or more complex numbers <red>
- <red> Properties of Conjugate and Modulus of complex numbers <red>

**1.4 Indices, Logarithm and Antilogarithm**

- Applications of rules of indices
- Introduction of logarithm and antilogarithm
- Common and Natural logarithm

**1.5 Laws and properties of logarithms**

- Fundamental laws of logarithm

**1.6 Simple applications of logarithm and antilogarithm**

- Express the problem in the form of an equation and apply logarithm/ antilogarithm

**1.7 Averages**

- Definition and meaning
- Problems on average, weighted average

**1.8 Clock**

- Number of rotations of minute hand / hour hand of a clock in a day
- Number of times minute hand and hour hand coincides in a day

**1.9 Calendar**

- Definition of odd days
- Odd days in a year/ century
- Day corresponding to a given date

**1.10 Time, Work and Distance**

- Basic concept of time and work
- Problems on time taken / distance covered / work done

**1.11 Mensuration**

- Comparison between 2D and 3D shapes
- Combination of solids
- Transforming one solid shape to another

**1.12 Seating Arrangement**

- Linear and circular seating arrangement
- Position of a person in a seating arrangement

**2.1 Introduction to sets – definition**

- Definition of a Set
- Examples and Non-examples of Set

**2.2 Representation of sets**

- Write elements of a set in Set Builder form and Roster Form
- Convert a set given in Roster form into Set builder form and vice-versa

**2.3 Types of sets and their notations**

- Types of Sets: Finite Set, Infinite Set, Empty Set, Singleton Set

**2.4 Subsets**

- Subset of a given set
- Familiarity with terms like Superset, Improper subset, Universal set, Power set

**2.5 Intervals**

- Open interval, closed interval, semi open interval and semi closed interval

**2.6 Venn diagrams**

- Venn diagrams as the pictorial representation of relationship between sets
- Practical problems based on Venn Diagrams

**2.7 Operations on sets**

- Operations on sets include

i) Union of sets

ii) Intersection of sets

iii) Difference of sets

iv) Complement of a set

v) De Morgan’s Laws

**2.8 Ordered pairs – Cartesian product of two sets**

- Ordered pair, order of elements in an ordered pair and equality of ordered pairs
- Cartesian product of two non-empty sets

**2.9 Relations**

- Definition of Relation, examples pertaining to relations in the real number system

**2.10 Types of relations**

- Types of relations: Empty relation, universal relation, reflexive relation, symmetric relation, transitive relation, equivalence relation
- Introducing a function as a special type of relation
- Examples and nonexamples of functions

**2.11 Sequence and Series**

- Sequence: a1, a2, a3, ... , an
- Series: a1 + a2 + a3 + ⋯ + an

**2.12 Arithmetic Progression**

- General term of AP: tn = a + (n − 1)d
- Sum of n terms of AP : Sn = n/2 [2a + (n − 1)d]
- AM of a and b = (a+b)/2

**2.13 Geometric Progression**

- General term of GP:

- Sum of n terms of a GP:

- Sum of infinite term of GP = a/(1−r), where −1 < r < 1
- Geometric mean of a and b = √ab
- <red> For two positive numbers a and b, AM ≥GM i.e., (a+b)/2 ≥ √ab <red>

**2.14 Applications of AP and GP**

Applications based on

- Economy Stimulation
- The Virus spread etc.

**3.1 Mathematical Reasoning**

- Meaning of mathematical statements
- Negation
- Compound statements
- Quantifiers
- Converse and Contrapositive of the statement
- Implications
- Validating statements

**3.2 Logical Reasoning**

- Odd man out
- Syllogism
- Blood relations
- Coding Decoding

**4.1 Functions**

- Dependent variable and independent variable
- Function as a rule or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)

**4.2 Domain and Range of a function**

- Domain as a set of all values of independent variable
- Co-domain as a set of all values of dependent variable
- Range of a function as set of all possible resulting values of dependent variable

**4.3 Types of functions**

- Types of functions with definitions and characteristics: Constant function, Identity function, Polynomial function, Rational function, <red> Composite function, <red> Logarithm function, Exponential function, Modulus function, Greatest integer function, Signum function, Algebraic function

**4.4 Graphical representation of functions**

- Graph of some Polynomial function, Logarithm function, Exponential Function, Modulus function, Greatest integer function, Signum function

**6.1 Types of data**

- Examples of raw data from different surveys, sports
- Multivariate data from not more than three variables
- Collection of data up to three variables from real life examples, such as, data of students (age, weight, height)

**6.2 Data on various scales**

- Examples and non-examples of data on different scales
- Benefit and limitations of collecting data on various scales

**6.3 Data representation and data visualization**

- Data organization in increasing/decreasing order, using frequency table and in class intervals of various length
- Graphical representation of data using pie-chart/ bar graphs/ histogram using class interval of equal and unequal length
- Visualization of data using Excel Spreadsheet or any other computer assisted tool

**6.4 Data Interpretation**

**<red> 6.4.1 Measure of Central Tendency <red>**

- <red> Mean using direct method, assumed mean method and step deviation method <red>
- <red> Median and Mode <red>
- <red> Examples of different kinds of data helping students to choose and compare different measures of central tendency <red>

**6.4.2 Measure of Dispersion**

- Mean deviation around mean and median
- Standard deviation and variance
- Examples of different kinds of data helping students to choose and compare different measures of dispersion

**6.4.3. Skewness and Kurtosis**

- Examples of symmetrical and asymmetrical data
- Visualization of graphical representation of data using Excel Spreadsheet or any other computer assisted tool

**6.5 Percentile rank and Quartile rank**

- Emphasis on visualizing, analysing and interpreting percentile and quartile rank scores

**6.6 Correlation**

- Emphasis on application, analysis and interpreting the results of coefficient of correlation using practical examples

**2.15 Factorial**

- Definition of factorial: n! = n(n-1)(n-2)...3.2.1
- Usage of factorial in counting principles

**2.16 Fundamental Principle of Counting**

- Fundamental Principle of Addition
- Fundamental Principle of Multiplication

**2.17 Permutations**

- Permutation as arrangement of objects in a definite order taken some or all at a time
- Theorems under different conditions resulting in nPr= n!/(n−r)! or n^r or n!/(n1!n2!...nk!) arrangements

**<red> 2.18 Circular permutation <red>**

- <red> (n-1)! as the number of permutations of n distinct objects in a circle <red>
- <red> Number of arrangements as (n−1)!/2, when clockwise and anticlockwise arrangement of objects are indistinguishable <red>

**<red> 2.19 Permutations <red>**

- <red> Permutations in which some objects come together or come at designated places. <red>
- <red> Permutations in which some objects are always included or excluded <red>

**2.20 Combinations**

- The number of combinations of n different objects taken r at a time is given by nCr = n!/ r!.(n−r)!
- Some results on combinations:

**<red> 2.21 Combination with repetition <red>**

- <red> Combination of n distinct objects taken r at a time if repetition is allowed <red>

**4.5 Concepts of limits and continuity of a function**

- Left hand limit, Right hand limit, Limit of a function, Continuity of a function

**4.6 Instantaneous rate of change**

- The ratio ∆y/∆x = (f(x+∆x)−f(x))/ ∆x, as instantaneous rate of change, where ∆y is change in y and ∆x is change in x at any instant

**4.7 Differentiation as a process of finding derivative**

- Derivatives of functions (non-trigonometric only)

**4.8 Derivatives of algebraic functions using Chain Rule**

● If y = f(u) where u = g(x), then differential coefficient of y w.r.t x is dy/dx = dy/du.du/dx

**<red> 4.9 Tangent line and Equation of tangent <red>**

- <red> The slope (gradient) of the tangent to the curve y = f(x) at the given point <red>
- <red> The equation of the tangent to the curve at the given point <red>

**5.1 Introduction**

- Probability as quantitative measure of uncertainty
- Use of probability in determining the insurance premium, weather forecasts etc.

**5.2 Random experiment and sample space**

- Sample space as set of all possible outcomes

**5.3 Event**

- Types of Event: Impossible and sure event, Independent and dependent event, mutually exclusive and exhaustive event

**5.4 Conditional Probability**

- Conditional Probability of event E given that F has occurred is: P(E|F) = P(E∩F)/P(F), P(F) ≠ 0

**5.5 Total Probability**

- Total Probability: Let E1,E2 , ...,En be a partition of the sample space S, then probability of an event A associated with S is: P(A) = ∑ P(Ej)P(A|Ej); j=1 to n

**5.6 Bayes’ Theorem**

- Bayes’ Theorem: If E1, E2, ... , En be n non empty events which constitute a partition of a sample space S and A be any event with non zero probability, then: P(Ei|A) = P(Ei)P(A|Ei)/∑ P(Ej)P(A|Ej)

**7.1 Interest and Interest Rates**

- Impact of high interest rates and low interest rates on the business

**7.2 Accumulation with simple and compound interest**

- Meaning and significance of simple and compound interest
- Compound interest rates applications on various financial products

**7.3 Simple and compound interest rates with equivalency**

- Concept of Equivalency
- Annual Equivalency Rate

**7.4 Effective rate of interest**

- Effective Annual Interest Rate = (1 + i/n)^n – 1, where i = Nominal Interest Rate, n = No. of Periods

**7.5 Present value, net present value and future value**

- Formula for Present Value: PV = CF/(1 + r)^n, where: CF = Cash Flow in Future Period, r = Periodic Rate of return or Interest (also called the discount rate or the required rate of return), n = no. of periods
- Use of PVAF, FVAF tables for practical purposes
- Solve problems based on application of net present value

**7.6 Annuities, Calculating value of Regular Annuity**

- Definition, Formulae and Examples

**7.7 Simple applications of regular annuities (upto 3 period)**

- Examples of regular annuity: Mortgage Payment, Car Loan Payments, Leases, Rent Payment, Insurance payouts etc.

**7.8 Tax, calculation of tax, simple applications of tax calculation in Goods and Service tax, Income Tax**

- Computation of income tax, Add Income from Salary, house property, business or profession, capital gain, other sources, etc. less deductions PF, PPF, LIC, Housing loan, FD, NSC etc.
- Assess the Individuals under Income Tax Act Formula for GST
- Different Tax heads under GST

**7.9 Bills, tariff rates, fixed charge, surcharge, service charge**

- Tariff rates: its basis of determination
- Concept of fixed charge service charge and their applications in various sectors of Indian economy

**7.10 Calculation and interpretation of electricity bill, water supply bill and other supply bills**

- Components of electricity bill/ water supply and other supply bills:

i) overcharging of electricity

ii) water supply bills

iii) units consumed in electricity bills

**8.1 Straight line**

- Gradient of a line
- Equation of line: Parallel to axes, point-slope form, two-points form, slope intercept form, intercept form
- Application of the straight line in demand curve related to economics problems

**8.2 Circle**

- Circle as a locus of a point in a plane
- Equation of a circle in standard form, central form, diameter form and general form

**8.3 Parabola**

- Parabola as a locus of a point in a plane.
- Equation of a parabola in standard form:
- Focus, Directrix, Axis, Latus rectum, Eccentricity
- <red> Application in parabolic reflector, beam supported by wires at the end of the support, girder of a railway bridge, etc. <red>