CBSE Class 10 Syllabus 2027 Mathematics

FOR CBSE CLASS 10 SYLLABUS EXAM PREPARATION

CBSE Class 10 Syllabus
2027
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

CBSE Class 10 Syllabus 2027 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Mathematics
Subject Code – 041 & 241
Class – X (2026-27)

The Mathematics curriculum for the Secondary stage has been redesigned in
alignment with the National Education Policy 2020 and the National Curriculum
Framework for School Education (NCF – SE) 2023, prioritizing deep conceptual
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understanding and logical reasoning. The revised syllabus places strong emphasis
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on developing core
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visualisation, mathematical modelling, mathematical communication, computational s
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thinking, and g
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contemporary
mathematicians to foster a sense of pride and historical context. A deliberate shift
from rote learning to competency-based education ensures that students build deep
conceptual understanding and logical reasoning rather than mere procedural fluency.
Greater emphasis has been laid on the integration of real-life applications and
experiential learning, encouraging students to connect mathematical concepts with
everyday situations and cross-disciplinary contexts. Greater emphasis has been laid
on competency based learning outcomes encouraging students to connect

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mathematical concepts with everyday situations and inter-disciplinary contexts.

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Continuous and holistic assessment through projects, activities, and investigations
forms an integral part of the learning process, moving beyond summative
examinations. s e
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At the secondary stage, the curriculum
mathematical competencies, including mathematical representation through
quantities and relations, mathematical modelling and algorithm building, and effective
mathematical communication. The study of the number system, algebra, geometry,
mensuration, statistics and probability is designed to build a strong foundation for
higher education while enhancing functional life skills. The curriculum thus aims to
build rich mathematical learning frameworks not only for higher academic pursuits
but also for the practical demands of life in a rapidly changing, data-driven world.
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Objectives The broad objectives of teaching Mathematics at the secondary stage
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are to help the learners to:

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s e  develop logical thinking, critical reasoning, and a structured approach to
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confidence and adaptability;
 communicate mathematical ideas effectively using appropriate language,
symbols, and representations;
 appreciate the beauty, history, and real-life relevance of Mathematics as a
discipline;

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 connect mathematical concepts to fields such as Science, Technology,
Engineering, and Economics;
 engage in both collaborative and independent mathematical exploration and
learning;
 develop habits of precision, accuracy, and logical consistency in mathematical
work;
 build confidence to explore, experiment, and grow in mathematical
understanding without fear of failure.

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COURSE STRUCTURE CLASS –X

Units Unit Name Marks

I NUMBER SYSTEMS 06
II ALGEBRA 20
III COORDINATE GEOMETRY 06
IV GEOMETRY 15
V TRIGONOMETRY 12
VI MENSURATION 10
VII STATISTICS AND PROBABILITY 11
TOTAL 80

S. No. Content Competencies Explanation

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS  Develops understanding  Describes
of numbers, including Fundamental
1. Fundamental Theorem of the set of real numbers Theorem of Arithmetic
Arithmetic - statements and its properties. with examples
after reviewing work done  Extends the  Prove algebraically
earlier and after illustrating understanding of the Irrationality of
and motivating through powers (radical powers) numbers like
examples and exponents. √2, √3, √5, 3 + 2√5
2. Proofs of irrationality of  Applies Fundamental etc.
√2, √3, √5 Theorem of Arithmetic to
solve problems related
to real life contexts.

UNIT II: ALGEBRA

1. POLYNOMIALS  develops a relationship  Find the zeros of
between algebraic and polynomial graphically
1. Zeros of a polynomial graphical methods of and algebraically and
2. Relationship between finding the zeroes of a verifying the relation
zeros and coefficients of polynomial. between zeros and
quadratic polynomials. coefficients of
quadratic polynomials.

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Describes plotting a  m Find the solution of pair

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pair of linear equations
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and graphically finding two variables
1. Pair of linear equations in the solution. graphically and
two variables and graphical  Models and solves algebraically
method of their solution, contextualised (substitution and
consistency/inconsistency. problems using elimination method)
equations (e.g.,
2. Algebraic conditions for
simultaneous linear
number of solutions.
equations in two
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3. Solution of a pair of linear variables).
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equations in two variables
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situational

3. QUADRATIC EQUATIONS  demonstrates strategies  Solves quadratic
of finding roots and equations using
1. Standard form of a quadratic determining the nature factorization and
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equation + + = of roots of a quadratic quadratic formula
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0, ( ≠ 0). equation.  Determines the nature
of roots using
2. Solutions of quadratic
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equations (only real roots)
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Formulates and solves
by factorization, and by
using quadratic formula. ag 
problems based on
Relationship between real life context
discriminant and nature of
roots.

3. Situational problems based
on quadratic equations
related to day-to-day
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apply the conceptaofgA.P.
to  Applies concepts of

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to daily life situations. term and sum of n
terms.
Arithmetic Progression  Application of AP in
real life problems
2. Derivation of the nth term
and sum of the first n terms
of AP and their application in
solving daily life problems.
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UNIT III: COORDINATE GEOMETRY

1. Coordinate Geometry  Derives formulae to  Solves problems
establish relations for using distance
1. Review: Concepts of geometrical shapes in formula and section
coordinate geometry. the context of a formula
Distance formula. Section coordinate plane, such
formula (internal division). as, finding the distance
between two given
points, to determine the
coordinates of a point
between any two given
points.

UNIT IV: GEOMETRY

1. TRIANGLES  works out ways to  Prove Basic
differentiate between Proportionality
Definitions, examples, counter
congruent and similar theorem and applying
examples of similar triangles.
figures. the theorem and its
1. (Prove) If a line is drawn
 establishes properties converse in solving
parallel to one side of a
for similarity of two questions
triangle to intersect the other
triangles logically using  Prove similarity of
two sides in distinct points,
different geometric triangles using
the other two sides are
criteria established different similarity
divided in the same ratio.
earlier such as, Basic criteria
2. State (without proof) If a line
Proportionality
divides two sides of a
Theorem, etc.
triangle in the same ratio, the
line is parallel to the third
side.
3. State (without proof) If in two
triangles, the corresponding
angles are equal, their
corresponding sides are
proportional and the
triangles are similar.
4. State (without proof) If the
corresponding sides of two
triangles are proportional,
their corresponding angles
are equal and the two
triangles are similar.
5. State (without proof) If one
angle of a triangle is equal to
one angle of another triangle
and the sides including these
angles are proportional, the
two triangles are similar.

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2. CIRCLES  derives proofs of  Prove the theorems
theorems related to the based on the tangent
Tangent to a circle at point of tangents of circles. to a circle.
contact.  Applies the concept of
1. (Prove) The tangent at any tangents of circle to
point of a circle is solve various
perpendicular to the radius problems.
through the point of
contact.
2. (Prove) The lengths of
tangents drawn from an
external point to a circle are
equal.
UNIT V: TRIGONOMETRY

1. INTRODUCTION TO  Understands the  Evaluates
TRIGONOMETRY definitions of the basic trigonometric ratios
trigonometric functions  Describes
1. Trigonometric ratios of an (including the trigonometric ratios of
acute angle of a right-angled introduction of the sine standard angles and
triangle. Proof of their and cosine functions). solving related
existence (well defined) expressions
2. Motivate the ratios
whichever are defined at 0°
and 90°. Values of the
trigonometric ratios of 30° ,
45° and 60°.
3. Relationships between the
ratios.
2. TRIGONOMETRIC  Uses Trigonometric  Proves trigonometric
IDENTITIES identities to solve identities using
problems. 2 2
sin A + cos A = 1
1. Proof and applications of the and other identities
identity sin2 A + cos 2 A = 1.
2. Only simple identities to be
given.

3. HEIGHTS AND DISTANCES:  Applies Trigonometric  Find heights and
Angle of elevation, Angle of ratios in solving distances in real life
Depression. problems in daily life word problems using
contexts like finding trigonometric ratios
1. Simple problems on heights heights of different
and distances. Problems structures or distance
should not involve more than from them.
two right triangles. Angles of
elevation / depression
should be only 30°, 45°, and
60°.

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1. AREAS
CIRCLES
RELATED TO  Derives aand uses  Visualises and
formulae to calculate evaluates areas of
areas of plane figures. sector and segment of
1. Area of sectors and
a circle
segments of a circle.
2. Problems based on areas
and perimeter
/circumference of the above
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said plane figures. (In
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calculating area of segment
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of a circle, problems should
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be restricted to central angle

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of 60°, 90° and 120° only.

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SURFACE AREAS AND  Visualises and uses  Evaluates the surface
VOLUMES mathematical thinking to areas and volumes of
discover formulae to combinations of
1. Surface areas and volumes calculate surface areas solids by visualisation
of combinations of any two and volumes of solid
of the following: cubes, objects (cubes, cuboids,
cuboids, spheres, spheres, hemispheres,
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circular cylinders/cones. cylinders/cones, and

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UNIT VII: a
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STATISTICS AND PROBABILITY

1. STATISTICS  calculates mean,  Computes the mean,
median and mode for of a grouped
1. Mean, median and mode of different sets of data frequency distribution
grouped data (bimodal related with real life using direct,
situation to be avoided). contexts. assumed mean and

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2. PROBABILITY  Applies concepts from  Determines the
probability to solve probabilities in simple
1. Classical definition of problems on the real-life problems
probability. likelihood of everyday
2. Simple problems on finding events.
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the probability of an event. .
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MATHEMATICS- STANDARD (Code – 041)
QUESTION PAPER DESIGN
CLASS – X (2026-27)
Time: 3 Hours Max. Marks: 80

S. %
Total Weightage
No. Typology of Questions
Marks (approx.)
Remembering: Exhibit memory of previously learned material
by recalling facts, terms, basic concepts, and answers.
43 54
1
Understanding: Demonstrate understanding of facts and
ideas by organizing, comparing, translating, interpreting,
giving descriptions, and stating main ideas

Applying: Solve problems to new situations by applying 19 24
2
acquired knowledge, facts, techniques and rules in a
different way.

Analysing:
Examine and break information into parts by identifying
motives or causes. Make inferences and find evidence to
support generalizations

Evaluating: 18 22
3 Present and defend opinions by making judgments about
information, validity of ideas, or quality of work based on a
set of criteria.

Creating:
Compile information together in a different way by combining
elements in a new pattern or proposing alternative solutions

80 100
Total

INTERNAL ASSESSMENT 20 MARKS
Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

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MATHEMATICS-BASIC (Code – 241)
QUESTION PAPER DESIGN
CLASS – X (2026-27)
Time: 3Hours Max. Marks: 80

Total %
S. Typology of Questions Weightage
No. Marks
(approx.)
Remembering: Exhibit memory of previously learned material
by recalling facts, terms, basic concepts, and answers.
1 60 75
Understanding: Demonstrate understanding of facts and
ideas by organizing, comparing, translating, interpreting, giving
descriptions, and stating main ideas

Applying: Solve problems to new situations by applying
2 12 15
acquired knowledge, facts, techniques and rules in a different
way.
Analysing:

Examine and break information into parts by identifying
motives or causes. Make inferences and find evidence to
support generalizations 8 10
3
Evaluating:

Present and defend opinions by making judgments about
information, validity of ideas, or quality of work based on a set
of criteria.

Creating:

Compile information together in a different way by combining
elements in a new pattern or proposing alternative solutions

80 100
Total

INTERNAL ASSESSMENT 20 MARKS
Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

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PRESCRIBED BOOKS:
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1. Mathematics - Textbook for class X - NCERT Publication
2. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
3. Laboratory Manual - Mathematics, secondary stage - NCERT Publication
4. Mathematics exemplar problems for class X, NCERT publication.

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