CBSE Class 10 Mathematics Syllabus 2024-25
COURSE STRUCTURE
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 |
Â |
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 âˆš2, âˆš3, âˆš5
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 VARIABLESÂ – (15) Periods
PairÂ Â Â ofÂ Â Â linearÂ Â Â equationsÂ Â Â Â inÂ Â Â twoÂ Â Â variablesÂ Â Â Â andÂ Â Â Â Â Â Â Â Â graphicalÂ Â Â Â Â 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.
3. QUADRATIC EQUATIONS – (15) Periods
Standard form of a quadratic equation ax^{2} + bx + c = 0, (a â‰ 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 n^{th} 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.
- (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.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- (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 –Â (10) 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 contact.
- (Prove) The lengths of tangents drawn from an external point to a circle are
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 0o and 90o. Values of the trigonometric ratios of 30^{0}, 45^{0} and 60^{0}. 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.
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 30Â°, 45Â°, and 60Â°.
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 60Â°, 90Â° and 120Â° 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.Â 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.
MATHEMATICS-Standard
QUESTION PAPER DESIGN
Time: 3 Hours
Max. Marks: 80
Â S. No. |
Â Typology of Questions |
Â Total Marks |
% Weightage (approx.) |
Â 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 |
Â 43 |
Â 54 |
2 |
Â Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. |
Â 19 |
Â 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 |
Â |
Total |
80 |
100 |
INTERNAL ASSESSMENT – 20 MARKS |
Pen Paper Test and Multiple Assessment (5+5)Â Â – 10 Marks |
PortfolioÂ Â Â – 05 Marks |
Lab Practical (Lab activities to be done from the prescribed books)Â Â – 05 Marks |
MATHEMATICS-Basic
QUESTION PAPER DESIGN
Time: 3 Hours
Max. Marks: 80
Â 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 |
Â |
Total |
80 |
100 |
Â
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 publication.
- Mathematics exemplar problems for class X, NCERT publication.
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