CBSE Class 10 Mathematics Syllabus 2024-25

Class 10 Mathematics Mobile App

CBSE Class – 10
Mathematics (Code No. 041)
Syllabus (2024-25)

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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 & PROBABILTY	11
	Total	80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER (15) Periods
   Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of 2,35

UNIT II: ALGEBRA

1. POLYNOMIALS (8) Periods
   Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods
   Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.
   Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.
3. QUADRATIC EQUATIONS (15) Periods
   Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.
   Situational problems based on quadratic equations related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS (10) Periods
   Motivation for studying Arithmetic Progression Derivation of the n^th term and sum of the first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY

• Coordinate Geometry (15) Periods
  Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

1. TRIANGLES (15) Periods
   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. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
   3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
   4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
   5. (Motivate) 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.
2. CIRCLES (10) Periods
   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.

UNIT V: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (10) Periods
   Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0^o and 90^o. Values of the trigonometric ratios of 30^o, 45^o and 60^o. Relationships between the ratios.
2. TRIGONOMETRIC IDENTITIES (15) Periods
   Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given.
3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10) Periods
   Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30^o, 45^o and 60^o.

UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES (12) Periods
   Area of sectors and segments of a circle. 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^o, 90^o and 120^o only.
2. SURFACE AREAS AND VOLUMES (12) Periods
   Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS (18) Periods
   Mean, median and mode of grouped data (bimodal situation to be avoided).
2. PROBABILITY (10) Periods
   Classical definition of probability. Simple problems on finding the probability of an event.

MATHEMATICS-Standard
QUESTION PAPER DESIGN
CLASS – X (2024-25)

Time: 3 Hours
Max. Marks: 80

S.No	Typology of Questions	Total Marks	% 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

MATHEMATICS-Basic
QUESTION PAPER DESIGN
CLASS – X (2024-25)

Time: 3 Hours
Max. Marks: 80

S.No	Typology of Questions	Total Marks	% 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.

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