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Real Numbers
Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results -irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.


Polynomials
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to 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. Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.


Quadratic Equations
Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated.


Arithmetic Progressions
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.


Triangles
Definitions, examples, counter examples of similar triangles. Various theorems and their profs such as 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. 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 triangle.


Coordinate Geometry
LINES (In two-dimensions) Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.


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 & 90o. Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios.


Some Applications of Trigonometry
TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometricratios of complementary angles.

HEIGHTS AND DISTANCES

Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30o, 45o, 60o.


Circles
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Prove that the lengths of tangents drawn from an external point to circle are equal.


Constructions
Division of a line segment in a given ratio (internally). Tangent to a circle from a point outside it. Construction of a triangle similar to a given triangle.


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 60o, 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)


Surface Areas and Volumes
Problems on finding 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.)


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


Probability
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.


Algebra
This download covers CBSE class 10 test papers for Zeros of a polynomial. Relationship polynomials. Statement and simple problems on division algorithm for polynomials. Pair of linear equations in two variables. Algebraic conditions for number of solutions. Standard form of a quadratic equation and Solution. Motivation for studying AP. Derivation of standard results



Coordinate Geometry
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.

Geometry
TRIANGLES :Definitions, examples, counter examples of similar triangles. CIRCLES : Tangents to a circle motivated by chords drawn from points coming closer and closer and closer to the point. CONSTRUCTIONS : Division of a line segment in a given ratio (internally).

Mensuration
AREAS OF PLANE FIGURES : Motivate the area of a circle; area of sectors and segments of a circle. Plane figures involving triangles, simple quadrilaterals and circle should be taken. SURFACE AREAS AND VOLUMES : Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboid, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

Number System
This download covers cbse class 10 test papers for Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results - irrationality of Ö2, Ö3, Ö5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

Statistics and Probability
STATISTICS : Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph. PROBABILITY : Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.

Trigonometry
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios and Relationships between the ratios. Proof and applications of the identity . Only simple identities to be given. Trigonometric ratios of complementary angles. Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression.

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