ISC Class 11 Syllabus 2028 Mathematics

ISC
INDIAN SCHOOL CERTIFICATE
EXAMINATION

YEAR 2028

MATHEMATICS
(860)

Developed by:
Research, Development and Curriculum Division (RDCD)
CISCE

January 2026
____________________________________________________________________________________________

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MISSION STATEMENT

The Council for the Indian School Certificate
Examinations is committed to serving the nation's
children, through high quality educational
endeavours, empowering them to contribute towards
a humane, just and pluralistic society, promoting
introspective living, by creating exciting learning
opportunities, with a commitment to excellence.

ETHOS OF CISCE

Trust and fair play.
Minimum monitoring.
Allowing schools to evolve their own niche.
Catering to the needs of the children.
Giving freedom to experiment with new ideas
and practices.
Diversity and plurality - the basic strength for
evolution of ideas.
Schools to motivate pupils towards the
cultivation of:
Excellence - The Indian and Global
experience.
Values - Spiritual and cultural - to be the bedrock
of the educational experience.
Schools to have an 'Indian Ethos', strong roots in
the national psyche and be sensitive to national
aspirations.

MATHEMATICS (860)

This subject may not be taken with Applied Mathematics.
(Note: For candidates who wish to pursue a career in Mathematics/ Physics/ Chemistry/ Engineering/
Architecture/ and other related fields.)
Aims
1. To enable candidates to acquire knowledge and to develop an understanding of the terms, concepts,
symbols, definitions, principles, processes and formulae of Mathematics at the Senior Secondary stage.
2. To develop the ability to apply the knowledge and understanding of Mathematics to unfamiliar situations
or to new problems.
3. To enhance ability of analytical and rational thinking in young minds.
4. To develop mathematical thinking and ability to communicate mathematical ideas logically and precisely.
5. To develop skills of –
a. Computation.
b. Logical thinking.
c. Handling abstractions.
d. Generalizing patterns.
e. Mathematical modeling to solve real-time problems.
f. Analyzing data and solving problems using multiple mathematical methods.
g. Reading and interpreting tables, charts, graphs, etc.
6. To enhance the ability to apply mathematical skills in interdisciplinary subjects
7. To develop an appreciation of the role of Mathematics in day-to-day life.
8. To develop a scientific attitude through the study of Mathematics.

CLASS XI
There will be two papers in the subject:
Paper I : Theory (3 hours) ……80 marks
Paper II: Project Work ……….20 marks

PAPER I (THEORY) : 80 Marks

DISTRIBUTION OF MARKS FOR THE THEORY PAPER

S.No. UNIT TOTAL WEIGHTAGE
1. Sets and Functions 18 Marks
2. Algebra 26 Marks
3. Coordinate Geometry 20 Marks
4. Calculus 8 Marks
5. Statistics & Probability 8 Marks
TOTAL 80 Marks

1

1. Sets and Functions
(i) Sets
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a
set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams.
Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement of
Sets.
(ii) Relations & Functions
Ordered pairs. Cartesian product of sets. Number of elements in the cartesian product of two finite
sets. Cartesian product of the set of reals with itself (upto R × R× R). Definition of relation,
pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation.
Function as a type of mapping, domain, co-domain and range of a function. Real valued functions,
domain and range of these functions, constant, identity, polynomial, rational, modulus, signum,
exponential, logarithmic and greatest integer functions. Sum, difference, product and quotient of
functions.
• Sets: Self-explanatory.
• Basic concepts of Relations and Functions
- Ordered pairs, sets of ordered pairs.
- Cartesian Product (Cross) of two sets, cardinal number of a cross product.
Relations as:
- an association between two sets.
- a subset of a Cross Product.
- Domain, Range and Co-domain of a Relation.
Functions:
- As special relations, concept of writing “y is a function of x” as y = f(x).
- Domain and range of a function.
- Reading, sketching and understanding the graphs of all standard real valued functions.

(iii) Trigonometry
Positive and negative angles. Measuring angles in radians and in degrees and conversion from
one measure to another. Definition of trigonometric functions with the help of unit circle. Truth
of the identity sin2 𝑥𝑥 + cos2 𝑥𝑥 =1, for all 𝑥𝑥. Signs of trigonometric functions. Domain and range
of trigonometric functions and their graphs. Expressing sin (𝑥𝑥 ± 𝑦𝑦) and cos (𝑥𝑥 ± 𝑦𝑦) in terms of sin 𝑥𝑥,
sin 𝑦𝑦, cos 𝑥𝑥 & cos 𝑦𝑦 and their simple applications. Deducing the identities like the following:
tan (𝑥𝑥 ± 𝑦𝑦) =
𝑡𝑡𝑡𝑡𝑡𝑡 𝑥𝑥±𝑡𝑡𝑡𝑡𝑡𝑡 𝑦𝑦
,
1∓𝑡𝑡𝑡𝑡𝑡𝑡 𝑥𝑥 𝑡𝑡𝑡𝑡𝑡𝑡 𝑦𝑦

cot (𝑥𝑥 ± 𝑦𝑦) = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ±𝑐𝑐𝑐𝑐𝑐𝑐 𝑥𝑥
𝑐𝑐𝑐𝑐𝑐𝑐 𝑥𝑥 𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦 ∓ 1

1 1
sin α ± sin β = 2sin ( α ± β ) cos ( α  β )
2 2
1 1
cos α + cos β = 2cos ( α + β ) cos (α - β )
2 2
1 1
cos α - cos β = - 2sin ( α + β ) sin (α - β )
2 2
Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x.
• Angles and Arc lengths
- Angles: Convention of sign of angles.
- Magnitude of an angle: Measures of Angles; Circular measure.
- The relation S = rθ where θ is in radians. Relation between radians and degree.

2

- Definition of trigonometric functions with the help of unit circle.
- Truth of the identity sin2x + cos2x =1
NOTE: Questions on the area of a sector of a circle are required to be covered.
• Trigonometric Functions
- Relationship between trigonometric functions.
- Proving simple identities.
- Signs of trigonometric functions.
- Domain and range of the trigonometric functions.
- Trigonometric functions of all angles.
- Periods of trigonometric functions.
- Graphs of simple trigonometric functions (only sketches).
NOTE: Graphs of sin x, cos x, tan x, sec x, cosec x and cot x are to be included.
• 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.
𝐶𝐶+𝐷𝐷 𝐶𝐶−𝐷𝐷
- Sum and differences as products sin C + sin D= 2𝑠𝑠𝑠𝑠𝑠𝑠 � � 𝑐𝑐𝑐𝑐𝑐𝑐 � �, etc.
2 2

- Product to sum or difference i.e. 2sinAcosB = sin (A + B) + sin (A – B) etc.

2. Algebra
(i) Complex Numbers
Introduction of complex numbers and their representation, Algebraic properties of complex numbers.
Argand plane and polar representation of complex numbers. Square root of a complex number. Cube root
of unity.
- Conjugate, modulus and argument of complex numbers and their properties.
- Sum, difference, product, and quotient of two complex numbers. Additive and multiplicative
inverse of a complex number.
- Square root of a complex number.
- Cube roots of unity and their properties.
(ii) Quadratic Equations
Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real
coefficients).
− b ± b 2 − 4ac
• Use of the formula: x = in solving quadratic equations.
2a
• Equations reducible to quadratic form.
• Nature of roots
- Product and sum of roots.
- Roots as rational, irrational, equal, reciprocal, one square of the other.
- Complex roots.
- Framing quadratic equations with given roots.
NOTE: Questions on equations having common roots are to be covered.
• Quadratic Functions
Given α, β as roots then find the equation whose roots are of the form α 3 , β 3 , etc.
Real roots
Case I: a > 0 Complex roots
Equal roots

3

Real roots
Case II: a < 0 Complex roots,
Equal roots
Where ‘a’ is the coefficient of x2 in the equations of the form ax2 + bx + c = 0.
• Sign of quadratic
Sign when the roots are real and when they are complex.
• Graph of quadratic function. Maximum/minimum value of quadratic function and value of x for
which maximum/minimum occurs.
• Inequalities
- Linear Inequalities
Algebraic solutions of linear inequalities in one variable and their representation on the number
line. Self-explanatory.
- Quadratic Inequalities
Using method of intervals for solving problems of the type:
x2 + x − 6 ≥ 0
+ - +
-3 2
A perfect square e.g. x 2 − 6 x + 9 ≥ 0 .
f ( x)
- Inequalities involving rational expression of type ≤ a , etc. to be covered.
g ( x)
(iii) Permutations and Combinations
Fundamental principle of counting. Factorial n (n!) . Permutations and combinations, derivation of
formulae for n Pr and n Cr , their connections, and applications.
• Factorial notation n! , n! =n (n-1)!
• Fundamental principle of counting.
• Permutations
- nP r .
- Restricted permutation.
- Certain things always occur together.
- Certain things never occur.
- Formation of numbers with digits.
- Word building - repeated letters - No letters repeated.
- Permutation of alike things.
- Permutation of Repeated things.
- Circular permutation – clockwise counterclockwise – Distinguishable / not distinguishable.
• Combinations
n
- C r , nC n =1, nC 0 = 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.

4

(iv) Binomial Theorem
History, statement and proof of the binomial theorem for positive integral indices. Pascal's
triangle, General and middle term(s) in binomial expansion, applications.
• Significance of Pascal’s triangle.
• Binomial theorem for positive integral powers,
i.e. (x + y )n = nC0 x n + nC1 x n-1 y + ...... + nCn y n .
• Binomial coefficients.
Questions based on the above.
(v) Sequence and Series
Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.). Geometric
Progression (G.P.), general term of a G.P., sum of first n terms of a G.P., infinite G.P. and its sum,
geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums
∑ n, ∑ n 2 , ∑ n 3 .
• Arithmetic Progression (A.P.)
- T n = a + (n - 1)d
𝑛𝑛
- S n = {2𝑎𝑎 + (𝑛𝑛 − 1)𝑑𝑑}
2

- Arithmetic mean: 2b = a + c
- Inserting two or more arithmetic means between any two numbers.
- Three terms in A.P. : a - d, a, a + d
- Four terms in A.P.: a - 3d, a - d, a + d, a + 3d
• Geometric Progression (G.P.)
- T n = arn-1,

a (r n − 1) 𝑎𝑎(1−𝑟𝑟 𝑛𝑛 )
- Sn = , |r|>1, 𝑆𝑆𝑛𝑛 = , |𝑟𝑟| < 1
r −1 1−𝑟𝑟

a
-=S∞ ; r <1
1− r

- Geometric Mean, b = ac
- Inserting two or more Geometric Means between any two numbers.
- Three terms are in G.P.: ar, a, ar-1
- Four terms are in G.P.: ar3, ar, ar-1, ar-3
• Special sums ∑ n, ∑ n 2 , ∑ n 3
Using these summations to sum up other related expression.
Finding nth term of a sequence using Method of difference.

3. Coordinate Geometry
(i) Straight Lines
Brief recall of two-dimensional geometry from earlier classes. Shifting of origin. Slope of a line and
angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form,
slope-intercept form, two-point form, intercept form and normal form. General equation of a line.
Equation of family of lines passing through the point of intersection of two lines. Distance of a point
from a line.

• Brief recall of basic concepts of Points and their coordinates.

5

- Section formula (internally/externally).
- Coordinates of incentre, Area of triangle when vertices are given.
- Condition for collinearity of three points.
• The straight line
- Slope or gradient of a line.
- Angle between two lines.
- Condition of perpendicularity and parallelism.
- Various forms of equation of lines.
- Slope intercept form.
- Two-point slope form.
- Intercept form.
- Perpendicular /normal form.
- General equation of a line.
- Distance of a point from a line.
- Distance between parallel lines.
- Equation of lines bisecting the angle between two lines.
- Equation of family of lines.
- Definition of a locus.
- Equation of a locus.
(ii) Circles
• Equations of a circle in:
- Standard form.
- Diameter form.
- General form.
- Parametric form.
• Given the equation of a circle, to find the centre and the radius.
• 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.
- When circles touching each other externally/internally.
• Intercepts made by the circle on the axes.
• Relative position of two circles.
(iii) Conic Section
Sections of a cone, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines
as a degenerated case of a conic section. Standard equations and simple properties of parabola,
ellipse and hyperbola.
• Conics as a section of a cone.
- Definition of Foci, Directrix, Latus Rectum.
- PS = ePL, where P is a point on the conics, S is the focus, PL is the perpendicular distance
of the point from the directrix.
(i) Parabola
- e =1, y2 = 4ax, x2 = 4ay, y2 = -4ax, x2 = -4ay.
- Rough sketch of the above.
- The latus rectum; quadrants they lie in; coordinates of focus and vertex; and equations of directrix
and the axis.
- Finding equation of Parabola when Foci and directrix are given, etc.
- Application questions based on the above.

6

(ii) Ellipse
- x2 y2
+ = 1 , e <1, b 2 = a 2 (1 − e 2 )
a2 b2
- Cases when a > b and a < b.
- Rough sketch of the above.
- Major axis, minor axis; latus rectum; coordinates of vertices, focus and centre; and equations of
directrices and the axes.
- Finding equation of ellipse when focus and directrix are given.
- Simple and direct questions based on the above.
- Focal property i.e. SP + SP′ = 2a.
(iii) Hyperbola

- x2 y2
− = 1 , e > 1, b2 = a 2 ( e 2 − 1)
a 2 b2
- Cases when coefficient y2 is negative and coefficient of x2 is negative.
- Rough sketch of the above.
- Focal property i.e. SP - S’P = 2a.
- Transverse and Conjugate axes; Latus rectum; coordinates of vertices, foci and centre; and
equations of the directrices and the axes.
(iv) Introduction to three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance
between two points and section formula.
- As an extension of 2-D
- Distance formula.
- Section and midpoint form

4. Calculus
(i) Limits and Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically.
Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and
logarithmic functions. Definition of derivative, relate it to slope of tangent of the curve, Derivative
of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric
functions.
• Limits
- Notion and meaning of limits.
- Fundamental theorems on limits (statement only).
- Existence of lim f(x).
x→a
- Left hand limit , Right hand limit.
- Limits of algebraic, trigonometric exponential and logarithmic functions.
NOTE: Indeterminate forms are to be introduced while calculating limits.
• Differentiation
- Meaning and geometrical interpretation of derivative.
- Derivatives of simple algebraic and trigonometric functions and their formulae.
- Differentiation using first principles.
- Derivatives of sum/difference.
- Derivatives of product of functions.
- Derivatives of quotients of functions.

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5. Statistics and Probability
(i) Statistics
Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped
data.
• Mean deviation about mean.
• Standard deviation - by direct method, short cut method and step deviation method.
• Combined mean and standard deviation.
(ii) Probability
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events,
'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic)
probability, connections with other theories studied in earlier classes. Probability of an event,
probability of 'not', 'and' and 'or' events.
• Random experiments and their outcomes.
• Events: sure events, impossible events, mutually exclusive and exhaustive events.
- Definition of probability of an event
- Laws of probability addition theorem.

PAPER II (PROJECT WORK) : 20 Marks
Candidates will be expected to have completed two projects.
Mark allocation for each Project [10 marks]:
Overall format 1 mark
Content 4 marks
Findings 2 marks
Viva-voce based on the Project 3 marks
Total 10 marks

List of suggested assignments for Project Work:
1. Explore different methods to prove the result “If a set has ‘n’ number of elements, then the total number
of subsets is 2n ”.
2. Verify that for two sets A and B, n(A × B) = pq, where n(A) = p and n(B)= q, the total number of relations
from A to B is 2pq.
3. Using Venn diagram, verify the distributive law for three given non-empty sets A, B and C.
4. Identify distinction between a relation and a function with suitable examples and illustrate graphically.
5. Establish the relationship between the measure of an angle in degrees and in radians with suitable
examples by drawing a rough sketch.
6. Illustrate with the help of a model, the values of sine and cosine functions for different angles which are
multiples of π/2 and π.
7. Draw the graphs of sin 𝑥𝑥, sin 2𝑥𝑥, 2 sin 𝑥𝑥, and sin 𝑥𝑥/2 on the same graph using same coordinate axes and
interpret the same.
8. Draw the graph of cos 𝑥𝑥, cos 2𝑥𝑥, 2 cos 𝑥𝑥, and cos 𝑥𝑥/2 on the same graph using same coordinate axes and
interpret the same.
9. Using argand plane, interpret geometrically, the meaning of 𝑖𝑖 = √−1 and its integral powers.
10. Draw the graph of quadratic function 𝑓𝑓(𝑥𝑥) = 𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐. From the graph find maximum/minimum
value of the function. Also determine the sign of the expression.

8

11. Construct a Pascal’s triangle to write a binomial expansion for a given positive integral exponent.
12. Obtain a formula for the sum of the squares/sum of cubes of ’n’ natural numbers.
13. Obtain the equation of the straight line in the normal form, for 𝛼𝛼 (the angle between the perpendicular to
the line from the origin and the x-axis) for each of the following, on the same graph:
(i) α < 90°
(ii) 90° < α < 180°
(iii) 180° < α < 270°
(iv) 270° < α < 360°
14. Identify the variability and consistency of two sets of statistical data using the concept of coefficient of
variation.
15. Construct the tree structure of the outcomes of a random experiment, when elementary events are not
equally likely. Also construct a sample space by taking a suitable example.
16. Let S and S 1 be two (non-concentric) circles with centres A , B and radii r 1 , r 2 and d be the distance
between their centres. Establish relation between r 1 , r 2 and d with respect to relative position of two circles.
17. Construct different types of conics by PowerPoint Presentation, or by making a model, using the concept
of double cone and a plane.
18. Use focal property of ellipse to construct ellipse.
19. Use focal property of hyperbola to construct hyperbola.
20. Write geometrical significance of x coordinate, y coordinate, and z coordinate in space. Using the above,
find the distance of the point in space from x-axis/y-axis/z-axis. Explain the above using a three-
dimensional model or a power point presentation.

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