CBSE Board Math Syllabus for Class 10

                                                              CLASS X Mathematics Syllabus-2013
UNITS

I.     NUMBER SYSTEMS
II.    ALGEBRA
III.   GEOMETRY
IV    TRIGONOMETRY
V     STATISTICS

UNIT I : NUMBER SYSTEMS
 
1. REAL NUMBERS
 
Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier
and after il ustrating 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.

UNIT II : ALGEBRA
 
1. 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 their graphical solution. Geometric representation of different
possibilities of solutions/inconsistency.
 
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraical y - by substitution, by elimination and by cross multiplication. Simple situational problems must be included.

UNIT III : GEOMETRY
 
1. 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 paral el 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 traingle.

UNIT IV : TRIGONOMETRY
 
1. INTRODUCTION TO TRIGONOMETRY
 
2. Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined);motivate the ratios, whichever are defined at zero degree & ninty degree. Values (with proofs) of the trigonometric ratios of thirty degree, fourtyfive degree & sixty degree. Relationships between the ratios.

TRIGONOMETRIC  IDENTITIES    
Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.
 
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS
 
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
 
UNITS

II.      ALGEBRA (Contd.)
III.     GEOMETRY (Contd.)
IV.     TRIGONOMETRY (Contd.)
V.       PROBABILITY
VI.     COORDINATE GEOMETRY
VII.     MENSU RATION

UNIT II : ALGEBRA (Contd.)
 
3. QUADRATIC  EQUATIONS
 
4. Standard form of a quadratic equation ax2 + bx + c = 0, (a = 0). Solution of the quadratic equations(only real roots) by factorization, by completing the square and by using quadratic formula. Relationship between discriminant and nature of roots.

ARITHMETIC  PROGRESSIONS    
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
 
UNIT III : GEOMETRY (Contd.)

2. CIRCLES
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
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 circle are equal.

3.     CONSTRUCTIONS
1.    Division of a line segment in a given ratio (internal y)
2.    Tangent to a circle from a point outside it.
3.    Construction of a triangle similar to a given triangle.
 
UNIT IV : TRIGONOMETRY
3.    HEIGHTS AND DISTANCES
 
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation

UNIT V : STATISTICS AND PROBABILITY
 
2.  PROBABILITY
 
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.

UNIT VI : COORDINATE GEOMETRY
 
1. 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.

UNIT VII : MENSURATION
 
1. AREAS RELATED TO CIRCLES

2. 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.

SURFACE AREAS AND VOLUMES    
(i)    Problems on finding surface areas and volumes of combinations of any two of the fol owing: cubes,
cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(i) Problems involving converting one type of metal ic solid into another and other mixed problems.