# Revised CBSE Syllabus 2021 for Class 10 Mathematics

Revised CBSE Syllabus 2021 for Class 10 Mathematics

# 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 (8) Periods

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of   Decimal representation of rational numbers interms of terminating/non-terminating recurring decimals.

# UNIT II: ALGEBRA

1. POLYNOMIALS (4) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

1. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (11) 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. Simple problems on equations reducible to linear equations.

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.

1. ARITHMETIC PROGRESSIONS (4) Periods

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P.

# UNIT III: COORDINATE GEOMETRY

1. LINES (In two-dimensions) (10) Periods

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

# UNIT IV: GEOMETRY

1. TRIANGLES (10) 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
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are
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
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each
7. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two

1. CIRCLES (8) 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
2. (Prove) The lengths of tangents drawn from an external point to a circle are

1. CONSTRUCTIONS (4) Periods
1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside

# UNIT V: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (8) Periods

Trigonometric ratios of an acute angle of a right-angled triangle. Proof  of  their  existence (well defined). Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.

1. TRIGONOMETRIC IDENTITIES (10) 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. (8) 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°, 60°.

# UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES (10) Periods

Motivate the area of a circle; 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°and  90° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

1. SURFACE AREAS AND VOLUMES (8) Periods
1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

# UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS (10) Periods

Mean, median and mode of grouped  data  (bimodal  situation and step deviation method  for finding the mean to be avoided).

1. PROBABILITY (10) Periods

Classical definition of probability. Simple problems on finding the probability  of  an event.

# MATHEMATICS-Standard QUESTION PAPER DESIGN CLASS – X (2020-21)

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 (2020-21)

Time : 3Hours                                                                                                    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 IX – NCERT Publication
2. Mathematics – Textbook for class X – NCERT Publication
3. Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication
4. Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication
5. Laboratory Manual – Mathematics, secondary stage – NCERT Publication
6. Mathematics exemplar problems for class IX, NCERT
7. Mathematics exemplar problems for class X, NCERT