# MATHEMATICS-X

## TERM-WISE SYLLABUS

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with the growth of the subject and emerging needs of society. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real-life problems and other subject areas, greater emphasis has been laid on the applications of various concepts. The curriculum at the Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distance. Carrying out experiments with numbers and forms of geometry, framing hypotheses and verifying these with further observations form an inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of number systems, algebra, geometry, trigonometry, mensuration, statistics, and graphs and coordinate geometry, etc. The teaching of Mathematics should be imparted through activities that may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments.

OBJECTIVES

The broad objectives of teaching Mathematics at the secondary stage are to help the learners

To

• Consolidate The Mathematical Knowledge And Skills Acquired At The Upper Primary Stage;
• Acquire Knowledge And Understanding, Particularly By Way Of Motivation And Visualization, Of Basic Concepts, Terms, Principles And Symbols And Underlying Processes And Skills;
• Develop Mastery Of Basic Algebraic Skills;
• Develop Drawing Skills;
• Feel The Flow Of Reason While Proving A Result Or Solving A Problem;
• Apply The Knowledge And Skills Acquired To Solve Problems And Wherever Possible, By More Than One Method;
• To Develop Ability To Think, Analyze And Articulate Logically;
• To Develop Awareness Of The Need For National Integration, Protection Of Environment, Observance Of Small Family Norms, Removal Of Social Barriers, Elimination Of Gender Biases;
• To Develop Necessary Skills To Work With Modern Technological Devices And Mathematical Softwares
• To Develop Interest In Mathematics As A Problem-Solving Tool In Various Fields For Its Beautiful Structures And Patterns, Etc.
• To Develop Reverence And Respect Towards Great Mathematicians For Their Contributions To The Field Of Mathematics;
• To Develop Interest In The Subject By Participating In Related Competitions;
• To Acquaint Students With Different Aspects Of Mathematics Used In Daily Life;
• To Develop An Interest In Students To Study Mathematics As A Discipline.

COURSE STRUCTURE CLASS –X (2021-22)

### SECOND TERM

 NO. UNIT NAME MARKS I ALGEBRA(Cont.) 10 II GEOMETRY(Cont.) 9 III TRIGONOMETRY(Cont.) 7 IV MENSURATION(Cont.) 6 V STATISTICS & PROBABILITY(Cont.) 8 Total 40 INTERNAL ASSESSMENT 10 TOTAL 50

UNIT-ALGEBRA

1. QUADRATIC EQUATIONS (10) Periods

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities (problems on equations reducible to quadratic equations are excluded)

1. ARITHMETIC PROGRESSIONS

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.

(Applications based on the sum to n terms of an A.P. are excluded)

UNIT- GEOMETRY

1. CIRCLES

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
4. Division of a line segment in a given ratio (internally).
5. Tangents to a circle from a point outside it.

UNIT-TRIGONOMETRY

1. SOME APPLICATIONS OF TRIGONOMETRY

HEIGHTS AND DISTANCES-Angle of elevation, Angle of Depression.

Simple problems with heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, 60°.

UNIT-MENSURATION

1. SURFACE AREAS AND VOLUMES
2. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
3. 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-STATISTICS & PROBABILITY

1. STATISTICS

Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only.