CBSE Class 10th Maths Syllabus 20212022 (Combined for Term I and II)
CBSE Class 10 Maths Syllabus 202122 is provided here to help students chalk out proper planning for their studies in the new academic session. Students must note that CBSE will conduct the class 10 board exam in two parts and each exam will be based on 50 percent syllabus. We will soon update here the rationalised syllabus for each term. Till then students can go through the combined syllabus to start early preparations for their Term I exam that will be held in NovemberDecember 2021.
Also Check: CBSE Class 10 Board Exam 20212022: Changes in Syllabus and Exam Pattern Explained for Term 1 & 2
Check Course Structure for CBSE Class 10th:
Also Check  CBSE Class 10 Maths Complete & Best Study Material for 20212022
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/nonterminating 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.
3. QUADRATIC EQUATIONS (15 Periods)
Standard form of a quadratic equation ax^{2} + 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 twodimensions) (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. (Motivate) Alternative Segment theorem: If a chord is drawn through the point of contact of a tangent to a circle, then the angles made by the chord with the tangent are respectively equal to the angles subtended by the chord in the alternate segments.
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 rightangled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300 , 450 and 600 . Relationships between the ratios.
2. TRIGONOMETRIC IDENTITIES (15 Periods)
Proof and applications of the identity sin^{2}A + cos^{2}A = 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°, and 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.
MATHEMATICSStandard
QUESTION PAPER DESIGN
CLASS – X (202122)
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 
MATHEMATICSBasic
QUESTION PAPER DESIGN
CLASS – X (202122)
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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