Class 10 :

**Mathematics Revised Syllabus**( 2020-21) |**CBSE Reduced Syllabus 2020-21**| Vyakhyaedu**UNIT I: NUMBER SYSTEMS**

**1. REAL NUMBER**

__REVISED TOPICS__

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2,√3,√5 Decimal representation of rational numbers interms of terminating/non-terminating recurring decimals.

__TOPICS REMOVED__- Euclid’s division lemma.

**UNIT II: ALGEBRA**

**1. POLYNOMIALS**

__REVISED TOPICS__Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials

__TOPICS REMOVED__- Statement and simple problems on division algorithm for polynomials with real coefficients

**2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES**

__REVISED TOPICS__

/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.Simple problems on equations reducible to linear equations.

__TOPICS REMOVED__- Cross multiplication method

**3. QUADRATIC EQUATIONS**

__REVISED TOPICS__

^{2}+ 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.

__TOPICS REMOVED__- Situational problems based on equations reducible to quadratic equations

**4. ARITHMETIC PROGRESSIONS**

__REVISED TOPICS__

__TOPICS REMOVED__- Application in solving daily life problems based on sum to n terms

**UNIT III: COORDINATE GEOMETRY**

**1. LINES (In two-dimensions)**

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

__TOPICS REMOVED__- Area of a triangle.

**UNIT IV: GEOMETRY**

**2. TRIANGLES**

__REVISED TOPICS__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.

6. (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.

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

__TOPICS REMOVED__- The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

**3. 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.

**4. CONSTRUCTIONS**

__REVISED TOPICS__

2. Tangents to a circle from a point outside it.

__TOPICS REMOVED__- Construction of a triangle similar to a given triangle.

**UNIT V: TRIGONOMETRY**

**1. INTRODUCTION TO TRIGONOMETRY**

__REVISED TOPICS__

**°**, 45

**°**and 60

**°**. Relationships between the ratios.

__TOPICS REMOVED__- motivate the ratios whichever are defined at 0
**°**and 90**°**

**2.TRIGONOMETRIC IDENTITIES**

__REVISED TOPICS__

^{2}A + cos

^{2}A = 1. Only simple identities to be given.

__TOPICS REMOVED__- Trigonometric ratios of complementary angles.

**3. 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°, 60°.

**UNIT VI: MENSURATION**

**1. AREAS RELATED TO CIRCLES**

__REVISED TOPICS__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°and 90° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

__TOPICS REMOVED__- Problems on central angle of 120°

**2. SURFACE AREAS AND VOLUMES**

__REVISED TOPICS__2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

__TOPICS REMOVED__- Frustum of a cone.

**UNIT VII: STATISTICS AND PROBABILITY**

**1.STATISTICS**

__REVISED TOPICS__

Mean, median and mode of grouped data (bimodal situation and step deviation method for finding the mean to be avoided).

__TOPICS REMOVED__- Step deviation Method for finding the mean
- Cumulative Frequency graph

**2. PROBABILITY**

Classical definition of probability. Simple problems on finding the probability of an
event.

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