CBSE Class 10 Mathematics — Notes, Solutions & Papers

COURSE STRUCTURE CLASS –X

Units Unit Name Marks

TOTAL 80

S. No. Content Competencies Explanation

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

√2, √3, √5

 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

√2, √3, √5, 3 + 2√5

etc.

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

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

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 va rious problems.

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 sin e 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

1. AREAS RELATED TO

CIRCLES

1. Area of sectors and segments of a circle. 2. Problems based on areas and perimeter /circumference of the above said plane figures. (In calculating area of segment of a circle, problems sh ould be restricted to central angle of 60°, 90° and 120° only.  Derives and uses formulae to calculate areas of plane figures.  Visualises and evaluates areas of sector and segment of a circle

2. SURFACE AREAS AND

VOLUMES

1. Surface areas and volumes of comb inations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.  Visualises and uses mathematical thinking to discover formulae to calculate surface areas and volumes of solid objects (cubes, cuboids, spheres, hemispheres, right circular cylinders/cones, and their combinations).  Evaluates the surface areas and volumes of combinations of solids by visualisation

1. STATISTICS

1. Mean, median and mode of grouped data (bimodal situation to be avoided).  calculates mean, median and mode for different sets of data related with real life contexts.  Computes the mean, of a grouped frequency distribution using direct, assumed mean and step deviation method.  Computes the median and mode of grouped frequency distribution by algebraic method

2. PROBABILITY

1. Classical definition of probability. 2. Simple problems on finding the probability of an event.  Applies concepts from probability to solve problems on the likelihood of everyday events.  Determines the probabilities in simple real-life problems MATHEMATICS- STANDARD (Code – 041)