Mathematics ISC (Commerce) Class 11 CISCE Syllabus 2025-26

• Roster or Tabular method or List method
• Set-Builder or Rule Method

• De Morgan's Law
• Some Properties of Complement Sets

• Number of Elements in the Cartesian Product of Two Finite Sets
• Cartesian Product of set of the Reals with Itself

• Definition of Relation
• Domain
• Co-domain and Range of a Relation

• 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

• 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
  3) Quadratic 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

Type of Function

Type of Function

• 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

Measure of Angle

Circular measure

• Definition
• Properties of angle

• Trigonometric Functions with the Help of Unit Circle

• Domain and Range of Trignometric Functions and Their Graphs

• 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)`

1. The graph of sine function
2. The graph of cosine function
3. The graph of tangent function

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.

Sum and differences as products

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

i.e.

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

• 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 = `1/2`bc A etc
• Simple applications of the above

• Motivating the Application of the Method by Looking at Natural Numbers as the Least Inductive Subset of Real Numbers

• Imaginary number
• Complex Number

• Modulus of Complex Number
• Conjugate of Complex Number

• Properties of 1, w, w²

• Equality of two Complex Numbers 
• Conjugate of a Complex Number 
• Properties of `barz`
• Addition of complex numbers - Properties of addition, Scalar Multiplication
• 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

• Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient

• 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.

• Quadratic Formula
• Quadratic Inequalities

• 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

Linear Inequalities - Graphical Representation of Linear Inequalities in Two Variables

• Tree Diagram 
• Addition Principle 
• Multiplication principle

• Permutation
• Permutation of repeated things
• Permutations when all the objects are not distinct
• Number of Permutations Under Certain Restricted Conditions
• Circular Permutations

Derivation of formulae for ⁿP_r and ⁿC_r and their connections

Repeated Letters

No Letters Repeated

• ⁿC_r , ⁿC_n =1, ⁿC₀ = 1, ⁿC_r = ⁿC_n–r, ⁿC_x = ⁿC_y, then x + y = n or x = y, ⁿ⁺¹C_r = ⁿC_r-1 + ⁿC_r
• When all things are different
• When all things are not different.
• Mixed problems on permutation and combinations.

• History of Binomial Theorem

• 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)

• Three terms in A.P. :- a - d, a, a + d

• Four terms in A.P.:- a - 3d, a - d, a+ d, a + 3d

• N^th 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 are in G.P. ar, a, a^r-1

• Four terms are in GP ar³, ar, ar^-1,ar^-3

• Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)

• n^th term of A.G.P.
• Sum of n terms of A.G.P.
• Properties of Summation

• 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

• Different forms of Ax + By + C = 0 - Slope-intercept form, Intercept form, Normal form

• Introduction of Distance of a Point from a Line
• Distance between two parallel lines

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.

Left hand Limits

Right Hand Limis

• Measures of Dispersion - Range

• Mean deviation for grouped data
• Mean deviation for ungrouped data

(cost of living index, consumer price index)