## CBSE 10 Mathematics

### Syllabus

**Total Marks 80**

**NUMBER SYSTEMS 06**

**REAL NUMBER**

👉 Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples,

👉 Proofs of irrationality of √2, √3, √5

**ALGEBRA 20**

**POLYNOMIALS**

👉 Zeros of a polynomial.

👉 Relationship between zeros and coefficients of quadratic polynomials.

**PAIR OF LINEAR EQUATIONS IN TWO VARIABLES**

👉 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.

**QUADRATIC EQUATIONS**

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

**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.

**GEOMETRY 15**

**TRIANGLES**

👉 Definitions, examples, counter examples of similar triangles.

👉 (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.

👉 (Motivate) If a line divides two sides of a triangle in the same ratio, the line 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.

**CIRCLES**

👉 Tangent to a circle at, point of contact

👉 (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 a circle are equal.

### COORDINATE GEOMETRY 06

**Coordinate Geometry**

👉 Review: Concepts of coordinate geometry, graphs of linear equations.

👉 Distance formula. Section formula (internal division)

### TRIGONOMETRY 12

**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 0o and 90o.

👉 Values of the trigonometric ratios of 300 , 450 and 600. Relationships between the ratios.

**TRIGONOMETRIC IDENTITIES**

👉 Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

**HEIGHTS AND DISTANCES**

👉 Angle of elevation, Angle of Depression.

👉 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°.

### MENSURATION 10

**AREAS RELATED TO CIRCLES**

👉 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.

**SURFACE AREAS AND VOLUMES**

👉 Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

### STATISTICS AND PROBABILITY 11

**STATISTICS**

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

**PROBABILITY**

👉 Classical definition of probability.

👉 Simple problems on finding the probability of an event.

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CBSE 10 Math

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