# Mathematics ISC (Commerce) Class 11 CISCE Syllabus 2024-25

CISCE Syllabus 2024-25 Class 11: The CISCE Class 11 Mathematics Syllabus for the examination year 2024-25 has been released by the Council for the Indian School Certificate Examinations, CISCE. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2024-25 CISCE Class 11 Mathematics Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new CISCE syllabus to prepare for their annual exam properly.

The detailed CISCE Class 11 Mathematics Syllabus for 2024-25 is below.

## CISCE Class 11 Mathematics Revised Syllabus

CISCE Class 11 Mathematics and their Unit wise marks distribution

## Syllabus

### CISCE Class 11 Mathematics Syllabus for Chapter 100: Sets and Functions

101 Sets
• Sets and Their Representations
• Roster or Tabular method or List method
• Set-Builder or Rule Method
• Types of Sets
• Empty Set (Null or Void Set)
• Finite and Infinite Sets
• Equal Sets
• Subsets
• Subsets of set of real numbers
• Intervals as subsets of R
• Power Set
• Universal Set
• Venn Diagrams
• Operations on Sets
• Union of Sets
• Union of sets
• Some Properties of the Operation of Union
• Intersection of Sets
• Intersection of sets
• Some Properties of Operation of Intersection
• Difference of Sets
• Difference of sets
• Complement of a Set
• De Morgan's Law
• Some Properties of Complement Sets
• Properties of Complement of Sets
• Problems on Union and Intersection of Two and Three Sets.
102 Relations and Functions
• Sets
• Ordered Pairs
• Cartesian Product of Sets
• Number of Elements in the Cartesian Product of Two Finite Sets
• Cartesian Product of set of the Reals with Itself
• Concept of Relation
• Definition of Relation
• Domain
• Co-domain and Range of a Relation
• Pictorial Diagrams
• Concept of Functions
• Function, Domain, Co-domain, Range
• Types of function
1. One-one or One to one or Injective function
2. Onto or Surjective function
• Representation of Function
• Graph of a function
• Value of funcation
• Some Basic Functions - Constant Function, Identity function, Power Functions, Polynomial Function, Radical Function, Rational Function, Exponential Function, Logarithmic Function, Trigonometric function
• Real Valued Function of the Real Variable
• Exponential Function

Domain and range of this function

• Sum, Difference, Product, Quotient of Functions
• Function as a Type of Mapping
• Types of Functions
• Types of Function based on Elements:
1) One One Function (or injective)
2) Many One Function
3) Onto Function (or surjective)
4) One One and Onto Function (or bijective)
5) Into Function
6) Constant Function
• Types of Function based on Equation:
1) Identity Function
2) Linear Function
4) Cubic Function
5) Polynomial Functions
• Types of Function based on the Range:
1) Modulus Function
2) Rational Function
3) Signum Function
4) Even and Odd Functions
5) Periodic Functions
6) Greatest Integer Function
7) Inverse Function
8) Composite Functions
• Types of Function based on the Domain:
1) Algebraic Functions
2) Trigonometric Functions
3) Logarithmic Functions
• Explicit and Implicit Functions
• Value of a Function
• Equal Functions
• Many to One Function

Type of Function

• Introduction to Function

Type of Function

• Some Functions and Their Graphs
• Identity function - Domain and range of this function
• Constant function - Domain and range of this function
• Polynomial function -Domain and range of this function
• Rational functions - Domain and range of this function
• The Modulus function - Domain and range of this function
• Signum function - Domain and range of this function
• Greatest integer function
103 Trigonometry
• Magnitude of an Angle

Measure of Angle

Circular measure

• Concept of Angle
• Part of Angle - Initial Side,Terminal Side,Vertex
• Types of Angle - Positive and Negative Angles
• Measuring Angles in Degrees
• initial side, terminal side, vertex,positive angle, negative angle
• Degree measure
• Relation between radian and real numbers
• Relation between degree and radian
• Conversion from One Measure to Another
• Introduction of Trigonometric Functions
• Trigonometric Functions with the Help of Unit Circle
• Trigonometric Functions
• Truth of the Identity

sin2x+cos2x=1, for All X.

• Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications
• Signs of Trigonometric Functions
• Domain and Range of Trigonometric Functions
• Domain and Range of Trignometric Functions and Their Graphs
• Trigonometric Functions of Sum and Difference of Two Angles
• Identities Related to Sin 2x, Cos2x, Tan 2x, Sin3x, Cos3x and Tan3x.
• Deducing the Identities
• Deducing the identities like the following:-
tan(x+-y)=(tanx+-tany)/(1+-tanxtany)", "cot(x+-y)=(cotxcoty+-1)/(coty+-cotx)
sinalpha+-sinbeta=2"sin"1/2(alpha+-beta)"cos"1/2(alpha+-beta)
cosalpha+cosbeta=2"cos"1/2(alpha+beta)"cos"1/2(alpha-beta)
cosalpha-cosbeta=-2"sin"1/2(alpha+beta)"sin"1/2(alpha-beta)
• Trigonometric Equations
• Solution of Trigonometric Equations (Solution in the Specified Range)
• Graphs of Trigonometric Functions
1. The graph of sine function
2. The graph of cosine function
3. The graph of tangent function
• Trigonometric Functions of Compound Angles
• Trigonometric Functions of Multiple Angles

upto double and triple angles only

• Trigonometric Functions of Half Angles
• Convention of Sign of Angles
• The Relation S = rθ Where θ is in Radians
• Relationship Between Trigonometric Functions
• Periods of Trigonometric Functions
• Compound and Multiple Angles- Addition and Subtraction Formula

sin(A  B); cos(A B); tan(A  B); tan(A + B + C) etc., Double angle, triple angle, half angle and one third angle formula as special cases.

• Trigonometric Functions of All Angles
• Sum and Differences as Products

Sum and differences as products

sinC + sinD = 2sin((C+D)/2)cos((C-D)/2)", etc."

• Product to Sum Or Difference

i.e.

2sinAcosB = sin(A + B) + sin(A – B) etc.

• Trigonometric Equations
• Properties of Δ
• Sine formula: a/sinA=b/sinB=c/sinC
• Cosine formula:cosA=(b^2+c^2-a^2)/(2bc), etc
• Area of triangle:Δ = 1/2bc A etc
• Simple applications of the above

### CISCE Class 11 Mathematics Syllabus for Chapter 200: Algebra

201 Principle of Mathematical Induction
202 Complex Numbers
• Concept of Complex Numbers
• Imaginary number
• Complex Number
• Square Root of a Complex Number
• Algebraic Properties of Complex Numbers
• The Modulus and the Conjugate of a Complex Number
• Modulus of Complex Number
• Conjugate of Complex Number
• Properties of Conjugate, Modulus and Argument (or Amplitude) of Complex Numbers
• Argand Plane and Polar Representation
• Cube Root of Unity
• Properties of 1, w, w2
• Properties of Cube Roots of Unity
• Algebraic Operations of Complex Numbers
• Equality of two Complex Numbers
• Conjugate of a Complex Number
• Properties of barz
• Subtraction of complex numbers - Properties of Subtraction
• Multiplication of complex numbers - Properties of Multiplication
• Powers of i in the complex number
• Division of complex number - Properties of Division
• The square roots of a negative real number
• Identities
• Locus Questions on Complex Numbers.
• Triangle Inequality
• Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient
• Equations Reducible to Quadratic Form
• Nature of Roots
• Product and sum of roots.
• Roots are rational, irrational, equal, reciprocal, one square of the other.
• Complex roots.
• Framing quadratic equations with given roots

Given alpha,beta as roots then find the equation whose roots are of the form alpha^3, beta^3 , etc

Case I:a>0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Case II:a<0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Where ‘a’ is the coefficient of x2 in the equations of the form ax2 + bx + c = 0.

Understanding the fact that a quadratic expression (when plotted on a graph) is a parabola.

• Steps to Solve Quadratic Inequalities

Sign when the roots are real and when they are complex

Using method of intervals for solving problems of the type:

A perfect square e.g. x^2-6x+9>=0

Inequalities involving rational expression of type

f(x)/g(x)<=a  etc to be covered

• Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation
• Graphical Solution of Linear Inequalities in Two Variables

Linear Inequalities - Graphical Representation of Linear Inequalities in Two Variables

• Solution of System of Linear Inequalities in Two Variables
204 Permutations and Combinations
• Introduction of Permutations and Combinations
• Fundamental Principles of Counting
• Tree Diagram
• Multiplication principle
• Permutations
• Permutation
• Permutation of repeated things
• Permutations when all the objects are not distinct
• Number of Permutations Under Certain Restricted Conditions
• Circular Permutations
• Circular Permutations
• Permutations of distinct objects
• Properties of Permutations
• Objects always together (String method)
• No two things are together (Gap method)
• Derivation of Formulae and Their Connections

Derivation of formulae for nPand nCr and their connections

• Simple Applications of Permutations and Combinations
• Restricted Permutation
• Permutation - Certain Things Always Occur Together
• Permutation - Certain Things Never Occur
• Permutation - Formation of Numbers with Digits
• Permutation - Permutation of Alike Things
• Permutation - Permutation of Repeated Things
• Permutation - Word Building

Repeated Letters

No Letters Repeated

• Properties of Combination
• Combination
• nCr , nCn =1, nC0 = 1, nCr = nCn–r, nCx = nCy, then x + y = n or x = y, n+1Cr = nCr-1 + nCr
• When all things are different
• When all things are not different.
• Mixed problems on permutation and combinations.
205 Binomial Theorem
• Introduction of Binomial Theorem
• History of Binomial Theorem
• Binomial Theorem for Positive Integral Indices
• Statement and Proof of the Binomial Theorem for Positive Integral Indices
• Proof of Binomial Therom by Induction
• Special Case in Binomial Therom
• Pascal's Triangle
• Binomial theorem for any positive integer n
• Some special cases-(In the expansion of (a + b)n)
• General and Middle Terms
• Binomial Theorem
• Simple Applications of Binomial Theorem
206 Sequence and Series
• Sequence and Series
• Introduction of Sequence and Series
• Arithmetic Progression (A.P.)
• Three Terms in Arithematic Progression (A.P.)
• Three terms in A.P. :- a - d, a, a + d
• Four Terms in Arithematic Progression (A.P.)
• Four terms in A.P.:- a - 3d, a - d, a+ d, a + 3d
• Inserting Two Or More Arithmetic Means Between Any Two Numbers
• Geometric Progression (G. P.)
• Nth Term of Geometric Progression (G.P.)
• General Term of a Geometric Progression (G.P.)
• Sum of First N Terms of a Geometric Progression (G.P.)
• Sum of infinite terms of a G.P.
• Geometric Mean (G.M.)
• Three Terms in Geometric Progression (G.P.)
• Three terms are in G.P. ar, a, ar-1
• Four Terms Are in Geometric Progression (G.P.)
• Four terms are in GP ar3, ar, ar-1,ar-3
• Inserting Two or More Geometric Means Between Any Two Numbers
• Relationship Between A.M. and G.M.
• Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)
• Arithmetico Geometric Series
• nth term of A.G.P.
• Sum of n terms of A.G.P.
• Properties of Summation

### CISCE Class 11 Mathematics Syllabus for Chapter 300: Coordinate Geometry

301 Straight Lines
• Straight Lines
• Brief Recall of Two Dimensional Geometry from Earlier Classes
• Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
• Equations of Bisectors of Angle Between Two Lines
• Family of Lines
• Shifting of Origin
• Slope of a Line
• Slope of a Line Or Gradient of a Line.
• Parallelism of Line
• Perpendicularity of Line in Term of Slope
• Collinearity of Points
• Slope of a line when coordinates of any two points on the line are given
• Conditions for parallelism and perpendicularity of lines in terms of their slopes
• Angle between two lines
• Collinearity of three points
• Various Forms of the Equation of a Line
• General Equation of a Line
• Different forms of Ax + By + C = 0 - Slope-intercept form, Intercept form, Normal form
• Distance of a Point from a Line
• Introduction of Distance of a Point from a Line
• Distance between two parallel lines
• Basic Concepts of Points and Their Coordinates
• Locus
• Definition and Equation of Locus
302 Circles
• Equations of a Circle in Standard Form
• Circle
• Equations of a Circle in Diameter Form
• Equations of a Circle in General Form
• Equations of a Circle in Parametric Form
• Conics
• Focus-directrix Property

focus-directrix property of parabola, ellipse, hyperbola, parabola

• Given the Equation of a Circle, to Find the Centre and the Radius
• Finding the Equation of a Circle

Finding the equation of a circle.

• Given three non collinear points
• Given other sufficient data for example centre is (h, k) and it lies on a line and two points on the circle are given, etc.
• Condition for Tangency
• Equation of a Tangent to a Circle

### CISCE Class 11 Mathematics Syllabus for Chapter 400: Calculus

401 Limits and Derivatives
• Concept of Limits
• Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
• Limits of Polynomials and Rational Functions
• Limits of Exponential Functions
• Limits of Logarithmic Functions
• Fundamental Theorem on Limits
• Introduction of Limits

Left hand Limits

Right Hand Limis

• Limits of Trigonometric Functions
• Limits of Algebraic Functions
• Introduction of Derivatives
• The Concept of Derivative
• Derivative of Slope of Tangent of the Curve
• Differentiation Or Derivative Using First Principles
• Algebra of Derivative of Functions
• Derivative of Polynomials and Trigonometric Functions
• Derivative of Algebraic Functions

### CISCE Class 11 Mathematics Syllabus for Chapter 500: Statistics and Probability

501 Statistics - 1
502 Probability
• Random Experiments
• Event
• Types of Events
1. Simple or elementary event
2. Occurrence and non-occurrence of event
3. Sure Event
4. Impossible Event
5. Complimentary Event
• Exhaustive Events
• Types of Event - Exhaustive Events
• Mutually Exclusive Events
• Types of Event - Mutually Exclusive Events
• Occurrence of an Event
• Probability
• Addition Theorem – for Any Two Events a and B, Result on Complementary Events
• Probability of 'Not', 'And' and 'Or' Events
• Axiomatic Approach to Probability

### CISCE Class 11 Mathematics Syllabus for Chapter 600: Conic Section

• Sections of a Cone
• Conics as a Section of a Cone
• Definition of Foci, Directrix, Latus Rectum
• Parabola
• Standard Equations of Parabola
• Latus Rectum
• Ellipse
• Standard Equations of an Ellipse
• Latus Rectum
• Latus Rectum in Ellipse
• Hyperbola
• Standard Equation of Hyperbola
• Transverse and Conjugate Axes
• Coordinates of Vertices
• Foci and Centre
• Equations of the Directrices and the Axes
• General Second Degree Equation in x and y
• The necessary conditions for a general second degree equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
1. abc + 2fgh - af2 - bg2 - ch2 = 0
2. h2 - ab ≥ 0
• General Equation of Tangents
• Point of Contact and Locus Problems

### CISCE Class 11 Mathematics Syllabus for Chapter 700: Introduction to Three-dimensional Geometry

• Three - Dimensional Geometry
• Coordinate Axes and Coordinate planes

Coordinate Axes and Coordinate Planes in Three Dimensions

• Coordinates of a Point in Space
• Distance Between Two Points
• Distance Between Two Points in 3-D Space
• Section Formula
• As an Extension of 2-D
• Distance Formula
• Midpoint Formula

### CISCE Class 11 Mathematics Syllabus for Chapter 900: Statistics - 2

• Combined Mean and Standard Deviation
• Central Tendency - Median
• Concept of Mode
• Deciles
• Percentiles

### CISCE Class 11 Mathematics Syllabus for Chapter 1000: Correlation Analysis

• Definition and Meaning of Covariance
• Statistics (Entrance Exam)
• Karl Pearson’s Coefficient of Correlation
• Rank Correlation by Spearman’s

Correction Included

### CISCE Class 11 Mathematics Syllabus for Chapter 1100: Index Numbers and Moving Averages

1101 Index Numbers
• Price Index Or Price Relative
• Construction of Index Numbers
• Simple Aggregate Method
• Weighted Aggregate Method
• Laspeyre's Price Index Number
• Paasche’s Price Index Number
• Dorbish-Bowley’s Price Index Number
• Fisher’s Ideal Price Index Number
• Marshall-Edgeworth’s Price Index Number
• Walsh’s Price Index Number
• Simple Average of Price Relatives
• Weighted Average of Price Relatives

(cost of living index, consumer price index)

1102 Moving Averages
• Meaning and Purpose of the Moving Averages
• Calculation of Moving Averages with the Given Periodicity and Plotting Them on a Graph
• If the Period is Even, Then the Centered Moving Average is to Be Found Out and Plotted