# CBSE Maths Syllabus Class 10 | CBSE Syllabus for Class 10 Maths 2020-21 PDF

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## CBSE Maths Syllabus Class 10

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

Euclid’s division lemma, 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 (7) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic
polynomials. Statement and simple problems on division algorithm for polynomials with
real coefficients.

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 and by cross multiplication
method. 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.

Situational problems based on quadratic equations related to day to day activities to be
incorporated.

4. ARITHMETIC PROGRESSIONS (8) 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. LINES (In two-dimensions) (14) Periods

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

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.
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 other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares
of their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the
squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the
other two sides, the angles opposite to the first side is a right angle.

2. 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 contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

3. CONSTRUCTIONS (8) Periods

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

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
o o

of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES (15) Periods

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be
given.Trigonometric ratios of complementary angles.

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 (12) 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°, 90°
and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should
be taken.)

2. SURFACE AREAS AND VOLUMES (12) Periods

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids,
spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
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 (18) Periods

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative
frequency graph.

2. 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: 3 Hrs. 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:

• Mathematics – Textbook for Class X – NCERT Publication
• Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication
• Laboratory Manual – Mathematics, secondary stage – NCERT Publication
• Mathematics exemplar problems for class X, NCERT publication.
• CBSE Maths Syllabus Class 12