CBSE Class 11 Applied Mathematics Syllabus for 2022-23

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

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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

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

Units Unit Name Marks
Term I Term II
I Numbers, Quantification and Numerical Applications 09 -
II Algebra 10 06
III Mathematical Reasoning 06 -
IV Calculus 04 06
V Probability - 08
VI Descriptive Statistics 12 -
VII Basics of Financial Mathematics - 15
VIII Coordinate Geometry - 05
INTERNAL ASSESSMENT
Project Work (05) +
Term-end Presentation & Viva (05)
10 10
TOTAL 100

TERM I

Unit I: Numbers, Quantification and Numerical Applications

<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

Unit II: Algebra

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.

Unit III: Mathematical Reasoning

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

Unit IV: Calculus

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

Unit VI: Descriptive Statistics

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

TERM II

Unit II: Algebra

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>

Unit IV: Calculus

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>

Unit V: Probability

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)

Unit VII: Financial Mathematics

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

Unit VIII: Coordinate Geometry

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>

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