ISC Class 11 Syllabus 2027 Mathematics

ISC YEAR 2027

INDIAN SCHOOL CERTIFICATE
EXAMINATION

MATHEMATICS
(860)

February 2025
____________________________________________________________________________________________

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Council for the Indian School Certificate Examinations (CISCE)

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.)

5. To develop skills of –
Aims a. Computation.
1. To enable candidates to acquire knowledge and b. Logical thinking.
to develop an understanding of the terms, c. Handling abstractions.
concepts, symbols, definitions, principles, d. Generalizing patterns.
processes and formulae of Mathematics at the e. Mathematical modeling to solve real-time
Senior Secondary stage. problems.
2. To develop the ability to apply the knowledge f. Analyzing data and solving problems using
and understanding of Mathematics to unfamiliar multiple mathematical methods.
situations or to new problems. g. Reading and interpreting tables, charts,
3. To enhance ability of analytical and rational graphs, etc.
thinking in young minds. 6. To enhance the ability to apply mathematical
4. To develop mathematical thinking and ability to skills in interdisciplinary subjects
communicate mathematical ideas logically and 7. To develop an appreciation of the role of
precisely. 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

ISC Examination Year 2027 1

1. Sets and Functions (iii) Trigonometry
(i) Sets Positive and negative angles. Measuring
angles in radians and in degrees and
Sets and their representations. Empty set.
conversion from one measure to another.
Finite and Infinite sets. Equal sets. Subsets.
Definition of trigonometric functions with
Subsets of a set of real numbers especially
the help of unit circle. Truth of the identity
intervals (with notations). Power set.
Universal set. Venn diagrams. Union and sin2x + cos2x=1, for all x. Signs of
Intersection of sets. Difference of sets. trigonometric functions. Domain and range
Complement of a set. Properties of of trignometric functions and their graphs.
Complement of Sets. Expressing sin (x±y) and cos (x±y) in terms
of sinx, siny, cosx & cosy and their simple
(ii) Relations & Functions applications. Deducing the identities like the
Ordered pairs, Cartesian product of sets. following:
Number of elements in the cartesian product
tan x ± tan y
of two finite sets. Cartesian product of the tan (x ± y) = ,
set of reals with itself (upto R x R x R). 1  tan x tan y
Definition of relation, pictorial diagrams,
domain, co-domain and range of a relation. cot x cot y  1
cot(x ± y)=
Function as a special type of relation. coty ± cotx
Function as a type of mapping, domain, co-
domain and range of a function. Real valued 1 1
sin α ± sin β =2sin ( α ± β )cos (α  β )
functions, domain and range of these 2 2
functions, constant, identity, polynomial,
1 1
rational, modulus, signum, exponential, cos α + cos β = 2 cos ( α + β ) cos (α - β )

logarithmic and greatest integer functions. 2 2
Sum, difference, product and quotient of 1 1
functions. cos α - cos β = - 2sin ( α + β ) sin (α - β )
2 2
• Sets: Self-explanatory.
Identities related to sin 2x, cos2x, tan 2x,
• Basic concepts of Relations and sin3x, cos3x and tan3x.
Functions
• Angles and Arc lengths
- Ordered pairs, sets of ordered - Angles: Convention of sign of
pairs. angles.
- Cartesian Product (Cross) of two - Magnitude of an angle: Measures of
sets, cardinal number of a cross
Angles; Circular measure.
product.
Relations as: - The relation S = rθ where θ is in
radians. Relation between radians
- an association between two sets. and degree.
- a subset of a Cross Product. - Definition of trigonometric
- Domain, Range and Co-domain of a functions with the help of unit
Relation. circle.
Functions: - Truth of the identity sin2x+cos2x=1
- As special relations, concept of NOTE: Questions on the area of a sector of
writing “y is a function of x” as y a circle are required to be covered.
= f(x). • Trigonometric Functions
- Domain and range of a function - Relationship between trigonometric
- Reading, sketching and functions.
understanding the graphs of all - Proving simple identities.
standard real valued functions. - Signs of trigonometric functions.
- Domain and range of the
trigonometric functions.

ISC Examination Year 2027 2

- Trigonometric functions of all - Product and sum of roots.
angles. - Roots are rational, irrational,
- Periods of trigonometric functions. equal, reciprocal, one square of
- Graphs of simple trigonometric the other.
functions (only sketches). - Complex roots.
NOTE: Graphs of sin x, cos x, tan x, sec x, - Framing quadratic equations with
cosec x and cot x are to be included. given roots.
• Compound and multiple angles NOTE: Questions on equations having
- Addition and subtraction formula: common roots are to be covered.
sin(A ± B); cos(A ± B); tan(A ± B);
• Quadratic Functions.
tan(A + B + C) etc., Double angle,
triple angle, half angle and one Given α, β as roots then find the
third angle formula as special equation whose roots are of the form
cases. α 3 , β 3 , etc.
- Sum and differences as products
sin C + sin D= Real roots
C+D C−D Case I: a > 0 Complex roots
2sin   cos   , etc.
 2   2  Equal roots
- Product to sum or difference Case II: a < 0 Real roots
i.e. 2sinAcosB = sin (A + B) + sin
Complex roots,
(A – B) etc.
Equal roots
2. Algebra Where ‘a’ is the coefficient of x2 in the
(i) Complex Numbers equations of the form ax2 + bx + c = 0.
Introduction of complex numbers and their • Sign of quadratic
representation, Algebraic properties of Sign when the roots are real and when
complex numbers. Argand plane and polar they are complex.
representation of complex numbers. Square • Graph of quadratic function.
root of a complex number. Cube root of Maximum/minimum value of quadratic
unity. function and value of x for which
- Conjugate, modulus and argument of maximum/minimum occurs.
complex numbers and their properties. • Inequalities
- Sum, difference, product and quotient of - Linear Inequalities
two complex numbers additive and
Algebraic solutions of linear
multiplicative inverse of a complex
inequalities in one variable and their
number.
representation on the number line.
- Square root of a complex number.
- Cube roots of unity and their properties. Self-explanatory.
- Quadratic Inequalities
(ii) Quadratic Equations
Using method of intervals for
Statement of Fundamental Theorem of solving problems of the type:
Algebra, solution of quadratic equations
(with real coefficients). x2 + x − 6 ≥ 0
• Use of the formula: + - +

− b ± b 2 − 4ac -3 2
x=
2a A perfect square e.g. x 2 − 6 x + 9 ≥ 0 .
In solving quadratic equations. - Inequalities involving rational
expression of type
• Equations reducible to quadratic form.
f ( x)
• Nature of roots ≤ a . etc. to be covered.
g ( x)

ISC Examination Year 2027 3

geometric mean (G.M.), relation between
(iii) Permutations and Combinations A.M. and G.M. Formulae for the following
Fundamental principle of counting. special sums ∑ n, ∑ n 2 , ∑ n 3 .
Factorial n. (n!) Permutations and
combinations, derivation of formulae for • Arithmetic Progression (A.P.)
nP
r
and n Cr and their connections, - T n = a + (n - 1)d
application.
• Factorial notation n! , n! =n (n-1)!
n
- Sn = {2a + (n − 1)d }
• Fundamental principle of counting. 2
• Permutations
- Arithmetic mean: 2b = a + c
n
- Pr .
- Inserting two or more arithmetic
- Restricted permutation. means between any two numbers.
- Certain things always occur
- Three terms in A.P. : a - d, a, a + d
together.
- Four terms in A.P.: a - 3d, a - d, a
- Certain things never occur.
+ d, a + 3d
- Formation of numbers with digits.
- Word building - repeated letters - • Geometric Progression (G.P.)
No letters repeated. - T n = arn-1,
- Permutation of alike things.
a (r n − 1)
- Permutation of Repeated things. - Sn = , |r|>1,
- Circular permutation – clockwise r −1
counterclockwise – Distinguishable 𝒂𝒂(𝟏𝟏−𝒓𝒓𝒏𝒏 )
𝑺𝑺𝒏𝒏 =
𝟏𝟏−𝒓𝒓
, |𝒓𝒓| < 𝟏𝟏
/ not distinguishable.
• Combinations a
-=S∞ ; r <1
- nC r , nC n =1, nC 0 = 1, nC r = nC n–r , 1− r
n
C x = nC y , then x + y = n or x = y,
n+1
C r = nC r-1 + nC r . - Geometric Mean, b = ac
- When all things are different. - Inserting two or more Geometric
- When all things are not different. Means between any two numbers.
- Mixed problems on permutation - Three terms are in G.P. ar, a, ar-1
and combinations. - Four terms are in GP ar3, ar, ar-1,
ar-3
(iv) Binomial Theorem
• Special sums ∑ n, ∑ n 2 , ∑ n 3
History, statement and proof of the
binomial theorem for positive integral Using these summations to sum up other
indices. Pascal's triangle, General and related expression.
middle term(s) in binomial expansion, Finding nth. term of a sequence using
applications. Method of difference.

• Significance of Pascal’s triangle. 3. Coordinate Geometry
• Binomial theorem for positive integral (i) Straight Lines
powers,
Brief recall of two-dimensional geometry
i.e. (x + y )n = nC0 x n + nC1 x n-1 y + ...... + nCn y n . from earlier classes. Shifting of origin. Slope
• Binomial coefficients. of a line and angle between two lines.
Various forms of equations of a line:
Questions based on the above. parallel to axis, point-slope form, slope-
(v) Sequence and Series intercept form, two-point form, intercept
form and normal form. General equation of
Sequence and Series. Arithmetic a line. Equation of family of lines passing
Progression (A.P.). Arithmetic Mean through the point of intersection of two
(A.M.) Geometric Progression (G.P.), lines. Distance of a point from a line.
general term of a G.P., sum of first n terms
of a G.P., infinite G.P. and its sum,

ISC Examination Year 2027
4

• Brief recall of basic concepts of Points of a conic section. Standard equations and
and their coordinates. simple properties of parabola, ellipse and
hyperbola.
- Section formula
(internally/externally) • Conics as a section of a cone.
- Coordinates of incentre, Area of - Definition of Foci, Directrix, Latus
triangle when vertices are given Rectum.
- Condition for collinearity of three - PS = ePL where P is a point on the
points conics, S is the focus, PL is the
• The straight line perpendicular distance of the point
from the directrix.
- Slope or gradient of a line.
(i) Parabola
- Angle between two lines.
- e =1, y2 = ±4ax, x2 = 4ay,
- Condition of perpendicularity and y2 = -4ax,
parallelism.
x2 = -4ay.
- Various forms of equation of lines.
- Slope intercept form. - Rough sketch of the above.
- Two-point slope form. - The latus rectum;
- Intercept form. quadrants they lie in;
coordinates of focus and
- Perpendicular /normal form.
vertex; and equations of
- General equation of a line. directrix and the axis.
- Distance of a point from a line.
- Finding equation of
- Distance between parallel lines. Parabola when Foci and
- Equation of lines bisecting the directrix are given, etc.
angle between two lines. - Application questions
- Equation of family of lines based on the above.
- Definition of a locus.
(ii) Ellipse
- Equation of a locus.
- x2 y2
+ = 1 , e <1, b 2 = a 2 (1 − e 2 )
(ii) Circles a2 b2
• Equations of a circle in: - Cases when a > b and a <
- Standard form. b.
- Diameter form. - Rough sketch of the above.
- General form. - Major axis, minor axis;
- Parametric form. latus rectum; coordinates
• Given the equation of a circle, to find of vertices, focus and
the centre and the radius. centre; and equations of
directrices and the axes.
• Finding the equation of a circle.
- Finding equation of ellipse
- Given three non collinear points. when focus and directrix
- Given other sufficient data for are given.
example centre is (h, k) and it lies
on a line and two points on the - Simple and direct questions
circle are given, etc. based on the above.
- When circles touching each other - Focal property i.e. SP +
externally/internally. SP′ = 2a.
• Intercepts made by the circle on the (iii) Hyperbola
axes.
• Relative position of two circles. - x2 y2
− = 1 , e > 1, b2 = a 2 ( e 2 − 1)
a 2 b2
(iii) Conic Section
- Cases when coefficient y2 is
Sections of a cone, ellipse, parabola,
hyperbola, a point, a straight line and a pair negative and coefficient of
of intersecting lines as a degenerated case x2 is negative.

ISC Examination Year 2027
5

- Rough sketch of the above. - Derivatives of product of functions.
- Focal property i.e. SP - S’P = Derivatives of quotients of
2a. functions.
- Transverse and Conjugate
axes; Latus rectum; 5. Statistics and Probability
coordinates of vertices, foci and
centre; and equations of the (i) Statistics
directrices and the axes. Measures of dispersion: range, mean
deviation, variance and standard deviation
(iv)Introduction to three-dimensional Geometry of ungrouped/grouped data.
Coordinate axes and coordinate planes in • Mean deviation about mean.
three dimensions. Coordinates of a point.
• Standard deviation - by direct method,
Distance between two points and section
short cut method and step deviation
formula.
method.
- As an extension of 2-D • Combined mean and standard deviation
- Distance formula. (ii) Probability
- Section and midpoint form
Random experiments; outcomes, sample
4. Calculus spaces (set representation). Events;
occurrence of events, 'not', 'and' and 'or'
(i) Limits and Derivatives events, exhaustive events, mutually
Derivative introduced as rate of change both exclusive events, Axiomatic (set theoretic)
as that of distance function and probability, connections with other theories
geometrically. studied in earlier classes. Probability of an
Intuitive idea of limit. Limits of polynomials event, probability of 'not', 'and' and 'or'
and rational functions trigonometric, events.
exponential and logarithmic functions. • Random experiments and their
Definition of derivative relate it to scope of outcomes.
tangent of the curve, Derivative of sum, • Events: sure events, impossible events,
difference, product and quotient of mutually exclusive and exhaustive
functions. Derivatives of polynomial and events.
trigonometric functions. - Definition of probability of an event
• Limits - Laws of probability addition
- Notion and meaning of limits. theorem.
- Fundamental theorems on limits
(statement only).
PAPER II
- Existence of lim f(x) PROJECT WORK – 20 Marks
x→a Candidates will be expected to have completed two
- Left hand limit , Right hand limit projects.
- Limits of algebraic, trigonometric Mark allocation for each Project [10 marks]:
exponential and logarithmic
functions. Overall format 1 mark
NOTE: Indeterminate forms are to be
Content 4 marks
introduced while calculating limits.
• Differentiation Findings 2 marks
- Meaning and geometrical Viva-voce based on the Project 3 marks
interpretation of derivative.
- Derivatives of simple algebraic and Total 10 marks
trigonometric functions and their
formulae.
List of suggested assignments for Project Work:
- Differentiation using first
principles. 1. Explore different methods to prove the result “If
- Derivatives of sum/difference. a set has ‘n’ number of elements, then the total
number of subsets is 2n”.

ISC Examination Year 2027
6

2. Verify that for two sets A and B, n(A × B) = perpendicular to the line from the origin and the
pq, where n(A) = p and n(B)= q, the total number x-axis) for each of the following, on the same
of relations from A to B is 2pq. graph:
3. Using Venn diagram, verify the distributive law (i) α < 90°
for three given non-empty sets A, B and C. (ii) 90° < α < 180°
4. Identify distinction between a relation and a (iii) 180° < α < 270°
function with suitable examples and illustrate
(iv) 270° < α < 360°
graphically.
14. Identify the variability and consistency of two
5. Establish the relationship between the measure sets of statistical data using the concept of
of an angle in degrees and in radians with coefficient of variation.
suitable examples by drawing a rough sketch.
15. Construct the tree structure of the outcomes of a
6. Illustrate with the help of a model, the values of random experiment, when elementary events are
sine and cosine functions for different angles not equally likely. Also construct a sample space
which are multiples of π/2 and π. by taking a suitable example.
7. Draw the graphs of sin x, sin 2x, 2 sin x, and sin 16. Let S and S1 be two(non-concentric) circles with
x/2 on the same graph using same coordinate centres A , B and radii r1, r2 and d be the
axes and interpret the same. distance between their centres. Relation between
8. Draw the graph of cos x, cos 2x, 2 cos x, and cos r1, r2 and d with respect to relative position of
x/2 on the same graph using same coordinate two circles.
axes and interpret the same. 17. Construct different types of conics by
9. Using argand plane, interpret geometrically, the PowerPoint Presentation, or by making a model,
meaning of 𝑖𝑖 = √−1 and its integral powers. using the concept of double cone and a plane.
10. Draw the graph of quadratic function 𝑓𝑓(𝑥𝑥) = 18. Use focal property of ellipse to construct ellipse.
𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐. From the graph find 19. Use focal property of hyperbola to construct
maximum/minimum value of the function. Also hyperbola.
determine the sign of the expression. 20. Write geometrical significance of X coordinate,
11. Construct a Pascal’s triangle to write a binomial Y coordinate, and Z coordinate in space. Using
expansion for a given positive integral exponent. the above, find the distance of the point in space
12. Obtain a formula for the sum of the squares/sum from x-axis/y-axis/z-axis. Explain the above
of cubes of ’n’ natural numbers. using a three-dimensional model/ power point
presentation.
13. Obtain the equation of the straight line in the
normal form, for 𝛼𝛼 (the angle between the

ISC Examination Year 2027 7