CBSE 10 Mathematics
Syllabus
Total Marks 80NUMBER 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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