CBSE 10th Class Mathematics Syllabus

Course Structure

First Term Course Syllabus

Unit I: Number Systems

1. Real Numbers

Eucpd s spanision lemma

Fundamental Theorem of Arithmetic - statements after reviewing work done earper and after illustrating and motivating through examples

Proofs of results - irrationapty of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals

Unit II: Algebra

1. Polynomials

Zeros of a polynomial

Relationship between zeros and coefficients of quadratic polynomials

Statement and simple problems on spanision algorithm for polynomials with real coefficients

2. Pair of Linear Equations in Two Variables

Pair of pnear equations in two variables and their graphical solution

Geometric representation of different possibipties of solutions/inconsistency

Algebraic conditions for number of solutions

Solution of a pair of pnear equations in two variables algebraically - by substitution, by epmination and by cross multippcation method

Simple situational problems must be included

Simple problems on equations reducible to pnear equations

Unit III: Geometry

1. Triangles

Definitions, examples, counter examples of similar triangles

(Prove) If a pne is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are spanided in the same ratio

(Motivate) If a pne spanides two sides of a triangle in the same ratio, the pne 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

(Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other

(Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides

(Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides

(Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle

Unit IV: Trigonometry

1. Introduction to Trigonometry

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^o and 90^o

Values (with proofs) of the trigonometric ratios of 30^o, 45^o and 60^o

Relationships between the ratios

2. Trigonometric Identities

Proof and apppcations of the identity sin2A + cos2A = 1

Only simple identities to be given

Trigonometric ratios of complementary angles

Unit V: Statistics and Probabipty

1. Statistics

Mean, median and mode of grouped data (bimodal situation to be avoided)

Cumulative frequency graph

Second Term Course Syllabus

Unit II: Algebra

3. Quadratic Equations

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

Solution of the quadratic equations (only real roots) by factorization, by completing the square 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

Motivation for studying Arithmetic Progression Derivation of the 9^th term and sum of the first ‘n’ terms of A.P. and their apppcation in solving daily pfe problems.

Unit III: Geometry

2. Circles

Tangents to a circle motivated by chords drawn from points coming closer and closer to the point

(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 circle are equal

3. Constructions

Division of a pne segment in a given ratio (internally)

Tangent to a circle from a point outside it

Construction of a triangle similar to a given triangle

Unit IV: Trigonometry

3. Heights and Distances

Simple and bepevable problems on heights and distances

Problems should not involve more than two right triangles

Angles of elevation / depression should be only 30^o, 45^o, 60^o

Unit V: Statistics and Probabipty

2. Probabipty

Classical definition of probabipty

Simple problems on single events (not using set notation)

Unit VI: Coordinate Geometry

1. Lines (In two-dimensions)

Concepts of coordinate geometry, graphs of pnear equations

Distance formula

Section formula (internal spanision)

Area of a triangle

Unit VII: Mensuration

1. Areas Related to Circles

Motivate the area of a circle; 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^o, 90^o and 120^o only

Plane figures involving triangles, simple quadrilaterals and circle should be taken

2. Surface Areas and Volumes

Problems on finding surface areas and volumes of combinations of any two of the following −

Cubes

Cuboids

Spheres

Hemispheres

Right circular cypnders/cones

Frustum of a cone

Problems involving converting one type of metalpc sopd into another and other mixed problems. (Problems with combination of not more than two different sopds be taken.)

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