CLASS 10 MATHEMATICS SYLLABUS 2023-2024

 UNITS

                             UNIT NAME

                    MARKS

     I

      NUMBER SYSTEMS

                        06

     II

      ALGEBRA

                        20

     III

      COORDINATE

                       06

    IV

     GEOMETRY

                       15

    V

     TRIGONOMETRY

                       12

   VI

     MENSURATION

                       10

   VII

    STATISTICS & PROBABILITY

                       11

                    Total

                        80

 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 ,  , ...

  1. POLYNOMIALS

                             (8) Periods

 Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

  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. Simple situational problems.

    3. QUADRATIC EQUATIONS

                          (15) Periods

 Standard form of a quadratic equation  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  term and sum of the first n terms of A.P. and their application in solving daily life problems.

     1. COORDINATE GEOMETRY

                              (15) Periods

 Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula.

 Section formula (internal division).

  1. TRINGLES

                              (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.

   2. CIRCLES

                                (10) 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.

 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 of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

   2. TRIGONOMETRY IDENTITIES

                                 (15) Periods

Proof and applications of the identity sin²A + cos²A = 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 30°, 45°, and 60°.

  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 60°, 90° and 120° 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.

 1. 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.

                   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

                                           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