Download CBSE Revision Notes for CBSE Class 10 Mathematics Real Numbers Euclid's division lemma, Fundamental Theorem ofArithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality. Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.
Download CBSE Revision Notes for CBSE Class 10 Mathematics 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.
Download CBSE Revision Notes for CBSE Class 10 Mathematics Quadratic Equations Standard form of a quadratic equation. Solutions of 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 incoporates.
Download CBSE Revision Notes for CBSE Class 10 Mathematics 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 on 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.
Download CBSE Revision Notes for CBSE Class 10 Mathematics 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 and 90 degree. Values (with proofs) of the trigonometric ratios of 30, 45 and 60 degree. Relationships between the ratios. Proof and applications of the identity. Only simple identities to be given. Trigonometric ratios of complementary angles.
Download CBSE Revision Notes for CBSE Class 10 Mathematics Some Applications of Trigonometry 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 degree.
Download CBSE Revision Notes for CBSE Class 10 Mathematics Circles Tangent to a circle at a 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.
Download CBSE Revision Notes for CBSE Class 10 Mathematics Area 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 degree only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
Download CBSE Revision Notes for CBSE Class 10 Mathematics 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.)