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

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.Simple problems on equations reducible to linear equations. 
TOPICS REMOVED
  •  Cross multiplication method

3. QUADRATIC EQUATIONS 

REVISED TOPICS

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. 
TOPICS REMOVED

  •  Situational problems based on equations reducible to quadratic equations


4. ARITHMETIC PROGRESSIONS 

REVISED TOPICS

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P.
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

Proof of the following theorems are deleted

  • 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

1. Division of a line segment in a given ratio (internally).
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

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.
TOPICS REMOVED
  • motivate the ratios whichever are defined at 0° and 90°
2.TRIGONOMETRIC IDENTITIES 


REVISED TOPICS

Proof and applications of the identity sin2 A + cos2 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
1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

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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