CBSE Board New Syllabus For Class 10th 2021-22 PDF Download, सीबीएसई बोर्ड ने 10th क्लास और 12th क्लास के एग्जाम में बदलाव करके नए नियम लागू किए हैं। सीबीएसई बोर्ड ने बताया है कि अब 10th क्लास और 12th क्लास के एग्जाम दो टर्म में लिए जाएंगे।

उन्होंने यह भी बताया है की फर्स्ट टर्म के एग्जाम नवंबर से दिसंबर के बीच में लिए जाएंगे और सेकंड टर्म के एग्जाम मार्च और अप्रैल के बीच में लिए जाएंगे नवंबर से दिसंबर के बीच में होने वाले एग्जाम में बच्चों के पास समय कम होने के कारण बोर्ड ने यह निर्णय लिया है कि उनके सिलेबस को भी कम किया जाएगा और फर्स्ट टर्म MCQ के होंगे जो कि 90 अंक परीक्षा की होगी।

### CBSE Class 10th Syllabus 2021-22 Maths

UNIT Ist: NUMBER SYSTEMS

REAL NUMBER :- Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of Decimal representation of rational numbers interms of terminating/non-terminating recurring decimals.

UNIT IInd: ALGEBRA

POLYNOMIALS :- Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

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 and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

QUADRATIC EQUATIONS :- Standard form of a quadratic equation . Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between ziscriminant 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.

UNIT IIIrd: COORDINATE GEOMETRY

LINES (In two-dimensions) :- Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

UNIT IVth: GEOMETRY

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. (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) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (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 angle.

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.
3. (Motivate) Alternative Segment theorem: If a chord is drawn through the point of contact of a tangent to a circle, then the angles made by the chord with the tangent are respectively equal to the angles subtended by the chord in the alternate segments.

CONSTRUCTIONS :-

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

UNIT Vth: TRIGONOMETRY

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 30 degree, 45 degree and 60 degree . Relationships between the ratios.

TRIGONOMETRIC IDENTITIES :-

Proof and applications of the identity. Only simple identities to be given. Trigonometric ratios of complementary angles.

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°.

UNIT VIth: MENSURATION

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°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

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. Frustum of a cone.

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).

UNIT VIIth: STATISTICS AND PROBABILITY

STATISTICS :- Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

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

यह भी पढ़े –