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# CBSE Class 10 Mathematics Syllabus 2022-23

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CBSE Class 10 Mathematics Syllabus 2022-23 includes Number Systems, Algebra, Coordinate Geometry, Trigonometry etc for the session 2022 – 2023. Here is the detailed syllabus. To download class 10 Mathematics CBSE latest sample question papers for the 2023 exams, please install the myCBSEguide App which is the best mobile app for CBSE students. The myCBSEguide app not only provides you the CBSE class 10 Mathematics model question papers but it also provides class 10 Mathematics chapter-wise test papers, class 10 Mathematics best revision notes and other study material for class 10 Mathematics students.

CBSE Class – 10
Mathematics
(Code No. 041)
Syllabus (2022-23)

 Units Unit Name Marks I NUMBER SYSTEMS 06 II ALGEBRA 20 III COORDINATE GEOMETRY 06 IV GEOMETRY 15 V TRIGONOMETRY 12 V MENSURATION 10 VI 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 {tex}\sqrt{2}, \sqrt{3} \sqrt{5}{/tex}

## 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.
Standard form of a quadratic equation ax2 + bx + c = 0, (a {tex}\ne{/tex} 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 nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

## UNIT III: COORDINATE GEOMETRY

1. 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° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°. 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°, 45° and 60°.

## 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°, 90° and 120° 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.

Times : 3 Hrs
Marks : 80

S.NoTypology of QuestionsTotal 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
4354
2.Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.1924
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
1822
4.Total80100
 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

Times : 3 Hrs
Marks : 80

S.NoTypology of QuestionsTotal 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
6075
2.Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.1215
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
810
Total80100
 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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