Class 10 - Mathematics

S. No.

Content

Competencies

Explanation

UNIT I: NUMBER SYSTEMS

1.

REAL NUMBERS

1.     Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples

2.   

Proofs  of  irrationality  of

·       Develops understanding of numbers, including the set of real numbers and its properties.

·       Extends                                the understanding                                                                of powers (radical powers) and exponents.

·       Applies Fundamental Theorem of Arithmetic to solve problems related to real life contexts.

·       Describes Fundamental Theorem of Arithmetic with examples

·       Prove algebraically the Irrationality of numbers                            like

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√2, √3, √5, 3 + 2√5

etc.

√2, √3, √5

UNIT II: ALGEBRA

1.

POLYNOMIALS

1.    Zeros of a polynomial

2.     Relationship between zeros and coefficients of quadratic polynomials.

·       develops a relationship between algebraic and graphical methods of finding the zeroes of a polynomial.

·       Find the zeros of polynomial graphically and algebraically and verifying the relation between zeros and coefficients                             of quadratic polynomials.

2.

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1.     Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

2.     Algebraic conditions for number of solutions.

3.     Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple                               situational problems.

·       Describes plotting a pair of linear equations and graphically finding the solution.

·       Models       and      solves contextualised problems                                 using

equations                            (e.g., simultaneous linear equations in two variables).

·       Find the solution of pair of linear equations in two                         variables graphically                                                  and algebraically (substitution                               and elimination method)

3.

QUADRATIC EQUATIONS

1.     Standard form of a quadratic equation  𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0, (𝑎 ≠ 0).

2.     Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship                                   between discriminant and nature of roots.

3.     Situational problems based on quadratic equations related to day-to-day activities to be incorporated

·       demonstrates strategies of finding roots and determining the nature of roots of a quadratic equation.

·       Solves                        quadratic equations                using

factorization                              and quadratic formula

·       Determines the nature of roots using discriminant

·       Formulates and solves problems based on real life context

4.

ARITHMETIC PROGRESSIONS

1.     Motivation for studying Arithmetic Progression

2.     Derivation of the nth term and sum of the first n terms of AP and their application in solving daily life problems.

·       Develops strategies to apply the concept of A.P. to daily life situations.

·       Applies concepts of AP to find the nth term and sum of n terms.

·       Application of AP in real life problems

UNIT III: COORDINATE GEOMETRY

1.

Coordinate Geometry

1. Review: Concepts of coordinate                                 geometry. Distance formula. Section formula (internal division).

·       Derives formulae to establish relations for geometrical shapes in the context of a coordinate plane, such as, finding the distance between two given points, to determine the coordinates of a point between any two given points.

·       Solves    problems

using                       distance formula and section formula

UNIT IV: GEOMETRY

1.

TRIANGLES

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.     State (without proof) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

3.     State (without proof) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

4.     State (without proof) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

5. State (without proof) 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.

·       works out ways to differentiate between congruent and similar figures.

·       establishes properties for similarity of two triangles logically using different    geometric

criteria                       established earlier such as, Basic Proportionality Theorem, etc.

·       Prove                      Basic Proportionality theorem and applying the theorem and its converse       in                     solving questions

·       Prove       similarity  of triangles                  using

different                         similarity criteria

2.

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.

·       derives proofs of theorems related to the tangents of circles.

·       Prove the theorems based on the tangent to a circle.

·       Applies the concept of tangents of circle to solve                            various problems.

UNIT V: TRIGONOMETRY

1.

INTRODUCTION                                         TO TRIGONOMETRY

1.     Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined)

2.     Motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30° , 45° and 60°.

3.     Relationships between the ratios.

·       Understands                              the definitions of the basic trigonometric functions (including                              the introduction of the sine and cosine functions).

·       Evaluates trigonometric ratios

·       Describes trigonometric ratios of standard angles and solving                            related expressions

2.

TRIGONOMETRIC IDENTITIES

1.     Proof and applications of the identity sin²A + cos²A = 1.

2.     Only simple identities to be given.

·       Uses Trigonometric identities to solve problems.

·       Proves                  trigonometric identities                  using sin²A + cos²A = 1 and other identities

3.

HEIGHTS AND DISTANCES:

Angle of elevation, Angle of Depression.

1. 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°.

·       Applies Trigonometric ratios in solving problems in daily life contexts like finding heights of different structures or distance from them.

·       Find heights and distances in real life word problems using trigonometric ratios