CBSE Class 10 Mathematics Syllabus for academic session 2026-27
This page contains the CBSE Class 10 Mathematics syllabus for the academic session 2026-27, as prescribed by CBSE curriculum.
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 understanding and logical reasoning. The revised syllabus places strong emphasis on developing core mathematical competencies, including problem-solving, visualisation, mathematical modelling, mathematical communication, computational thinking, and data analytics. The syllabus integrate Indian Knowledge System with contemporary mathematical knowledge, highlighting the rich contributions of Indian 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 mathematical concepts with everyday situations and inter-disciplinary contexts. Continuous and holistic assessment through projects, activities, and investigations forms an integral part of the learning process, moving beyond summative examinations.
At the secondary stage, the curriculum focuses on developing essential global 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.
Objectives The broad objectives of teaching Mathematics at the secondary stage are to help the learners to:
•
develop logical thinking, critical reasoning, and a structured approach to problem-solving;
•
build the ability to recognise, analyse, and solve diverse problems with 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;
•
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.
Marking Scheme
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
Syllabus
UNIT I: NUMBER SYSTEMS
1.
REAL NUMBERS
Content
1.
Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples
2.
Proofs of irrationality of \sqrt2, \sqrt3, \sqrt5
Competencies
•
Develops understanding of numbers, including the set of real numbers and its properties.
•
Extends the understanding of powers (radical powers) and exponents.
•
Applies Fundamental Theorem of Arithmetic to solve problems related to real life contexts.
Explanation
•
Describes Fundamental Theorem of Arithmetic with examples
•
Prove algebraically the Irrationality of numbers like \sqrt2, \sqrt3, \sqrt5, {3 + 2\sqrt5} etc.
UNIT II: ALGEBRA
1.
POLYNOMIALS
Content
1.
Zeros of a polynomial
2.
Relationship between zeros and coefficients of quadratic polynomials.
Competencies
•
develops a relationship between algebraic and graphical methods of finding the zeroes of a polynomial.
Explanation
•
Find the zeros of polynomial graphically and algebraically and verifying the relation between zeros and coefficients of quadratic polynomials.
2.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Content
1.
Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.
2.
Algebraic conditions for number of solutions.
3.
Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.
Competencies
•
Describes plotting a pair of linear equations and graphically finding the solution.
•
Models and solves contextualised problems using equations (e.g., simultaneous linear equations in two variables).
Explanation
•
Find the solution of pair of linear equations in two variables graphically and algebraically (substitution and elimination method)
3.
QUADRATIC EQUATIONS
Content
1.
Standard form of a quadratic equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, (𝑎 ≠ 0).
2.
Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.
3.
Situational problems based on quadratic equations related to day-to-day activities to be incorporated
Content
•
demonstrates strategies of finding roots and determining the nature of roots of a quadratic equation.
Explanation
•
Solves quadratic equations using factorization and quadratic formula
•
Determines the nature of roots using discriminant
•
Formulates and solves problems based on real life context
4.
ARITHMETIC PROGRESSIONS
content
1.
Motivation for studying Arithmetic Progression
2.
Derivation of the nth term and sum of the first n terms of AP and their application in solving daily life problems.
Competencies
•
Develops strategies to apply the concept of A.P. to daily life situations.
Explanation
•
Applies concepts of AP to find the nth term and sum of n terms.
•
Application of AP in real life problems
UNIT III: COORDINATE GEOMETRY
1.
Coordinate Geometry
Content:
1.
Review: Concepts of coordinate geometry. Distance formula. Section formula (internal division).
Competencies
•
Derives formulae to establish relations for geometrical shapes in the context of a coordinate plane, such as, finding the distance between two given points, to determine the coordinates of a point between any two given points.
Explanation
•
Solves problems using distance formula and section formula
UNIT IV: GEOMETRY
1.
TRIANGLES
Content
Definitions, examples, counter examples of similar triangles.
1.
(Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2.
State (without proof) If a line divides two sides of a 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.
Competencies
•
works out ways to differentiate between congruent and similar figures.
•
establishes properties for similarity of two triangles logically using different geometric criteria established earlier such as, Basic Proportionality Theorem, etc.
Explanation
•
Prove Basic Proportionality theorem and applying the theorem and its converse in solving questions
•
Prove similarity of triangles using different similarity criteria
2.
CIRCLES
Content
Tangent to a circle at point of contact.
1.
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2.
(Prove) The lengths of tangents drawn from an external point to a circle are equal.
Competencies
•
derives proofs of theorems related to the tangents of circles.
Explanation
•
Prove the theorems based on the tangent to a circle.
•
Applies the concept of tangents of circle to solve various problems.
UNIT V: TRIGONOMETRY
1.
INTRODUCTION TO TRIGONOMETRY
Content:
1.
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined)
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.
Competencies:
•
Understands the definitions of the basic trigonometric functions (including the introduction of the sine and cosine functions).
Explanation:
•
Evaluates trigonometric ratios
•
Describes trigonometric ratios of standard angles and solving related expressions
2.
TRIGONOMETRIC IDENTITIES
Content:
1.
Proof and applications of the identity {\sin^2A + \cos^2A = 1}.
2.
Only simple identities to be given.
Competencies:
•
Uses Trigonometric identities to solve problems.
Explanation:
•
Proves trigonometric identities using {\sin^2A + \cos^2A = 1} and other identities
3.
HEIGHTS AND DISTANCES:
Topics:
Angle of elevation, Angle of Depression.
1.
Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.
Competencies:
•
Applies Trigonometric ratios in solving problems in daily life contexts like finding heights of different structures or distance from them.
Explanation:
•
Find heights and distances in real life word problems using trigonometric ratios
UNIT VI: MENSURATION
1.
AREAS RELATED TO CIRCLES
Topics:
1.
Area of sectors and segments of a circle.
2.
Problems based on areas and perimeter /circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.
Competencies:
•
Derives and uses formulae to calculate areas of plane figures.
Explanation:
•
Visualises and evaluates areas of sector and segment of a circle
2.
SURFACE AREAS AND VOLUMES
Topics:
1.
Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
Competencies:
•
Visualises and uses mathematical thinking to discover formulae to calculate surface areas and volumes of solid objects (cubes, cuboids, spheres, hemispheres, right circular cylinders/cones, and their combinations).
Explanation:
•
Evaluates the surface areas and volumes of combinations of solids by visualisation
UNIT VII: STATISTICS AND PROBABILITY
1.
STATISTICS
1.
Mean, median and mode of grouped data (bimodal situation to be avoided).
Competencies:
•
calculates mean, median and mode for different sets of data related with real life contexts.
Explanation:
•
Computes the mean, of a grouped frequency distribution using direct, assumed mean and step deviation method.
•
Computes the median and mode of grouped frequency distribution by algebraic method
2.
PROBABILITY
Topics:
1.
Classical definition of probability.
2.
Simple problems on finding the probability of an event.
Competencies:
•
Applies concepts from probability to solve problems on the likelihood of everyday events.
Explanation:
•
Determines the probabilities in simple real-life problems
QUESTION PAPER DESIGN
Time: 3 Hours
Max. Marks: 80
QUESTION PAPER DESIGN – MATHEMATICS STANDARD
S.
No.
No.
Typology of Questions
Total
Marks
Marks
%
Weightage(approx.)
Weightage(approx.)
1
Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.
Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas
43
54
2
Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.
19
24
3
Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations
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
18
22
Total
80
100
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
QUESTION PAPER DESIGN – MATHEMATICS BASIC
Time: 3Hours Max. Marks: 80
S.
No.
No.
Typology of Questions
Total
Marks
Marks
%
Weightage
(approx.)
Weightage
(approx.)
1
Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.
Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas
60
75
2
Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.
12
15
3
Analysing:
Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations
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
8
10
Total
80
100
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
PRESCRIBED BOOKS:
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.