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
- 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
- POLYNOMIALS (4) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
- 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.
- QUADRATIC EQUATIONS (10) 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.
- ARITHMETIC PROGRESSIONS (4) Periods
Motivation for studying Arithmetic Progression Derivation of the n^{th} term and sum of the first n terms of A.P.
UNIT III: COORDINATE GEOMETRY
- LINES (In two-dimensions) (10) Periods
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).
UNIT IV: GEOMETRY
- TRIANGLES (10) Periods
Definitions, examples, counter examples of similar triangles.
- (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
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are
- (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
- (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
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two
- CIRCLES (8) Periods
Tangent to a circle at, point of contact
- (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of
- (Prove) The lengths of tangents drawn from an external point to a circle are
- CONSTRUCTIONS (4) Periods
- Division of a line segment in a given ratio (internally).
- Tangents to a circle from a point outside
UNIT V: TRIGONOMETRY
- 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 30^{0}, 45^{0} and 60^{0}. Relationships between the ratios.
- TRIGONOMETRIC IDENTITIES (10) Periods
Proof and applications of the identity sin^{2}A + cos^{2}A = 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
- 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.)
- SURFACE AREAS AND VOLUMES (8) Periods
- Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
- 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
- STATISTICS (10) Periods
Mean, median and mode of grouped data (bimodal situation and step deviation method for finding the mean to be avoided).
- 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:
- Mathematics – Textbook for class IX – NCERT Publication
- Mathematics – Textbook for class X – NCERT Publication
- Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication
- Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication
- Laboratory Manual – Mathematics, secondary stage – NCERT Publication
- Mathematics exemplar problems for class IX, NCERT
- Mathematics exemplar problems for class X, NCERT