Mathematics — Class 10
Unit I: Number Systems
6 marksReal Numbers
Fundamental Theorem of Arithmetic — statements after reviewing work done earlier and after illustrating and motivating through examples. Proofs of irrationality of √2, √3, √5.
Unit II: Algebra
20 marksPolynomials
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 the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day-to-day activities.
Arithmetic Progressions
Motivation for studying Arithmetic Progression. Derivation of the nth term and sum of the first n terms of an A.P. and their application in solving daily life problems.
Unit III: Coordinate Geometry
6 marksCoordinate Geometry
Review: concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).
Unit IV: Geometry
15 marksTriangles
Definitions, examples, counter examples of similar triangles. 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. Converse and AA, SSS, SAS similarity criteria for triangles.
Circles
Tangent to a circle at point of contact. The tangent at any point of a circle is perpendicular to the radius through the point of contact. The lengths of tangents drawn from an external point to a circle are equal.
Unit V: Trigonometry
12 marksIntroduction to Trigonometry
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°. 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°.
Unit VI: Mensuration
10 marksAreas 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.
Unit VII: Statistics and Probability
11 marksStatistics
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.