** CBSE Sample Papers**

# (Syllabus) CBSE Class 10th - Mathematics : Year 2013

## Syllabus CBSE Class 10th

Mathematics

**UNIT VII : STATISTICS AND PROBABILITY : (18) Periods**

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

CLASS-X

**UNITS MARKS**

II. ALGEBRA (Contd.) 23

III. GEOMETRY (Contd.) 17

IV. TRIGONOMETRY (Contd.) 08

V. PROBABILITY 08

VI. COORDINATE GEOMETRY 11

VII. MENSU RATION 23

**Total Marks : **90

**UNIT II : ALGEBRA (Contd.)
**3. QUADRATIC EQUATIONS (15) Periods

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. Problems related to day to day activities to be incorporated.

**4. ARITHMETIC PROGRESSIONS (8) Periods
**Motivation for studying AP. Derivation of standard results of finding the
nth term and sum of first n terms and their application in solving daily life
problems.

**UNIT III : GEOMETRY (Contd.) **

**2. CIRCLES (8) Periods
**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 (8) Periods
**1. Division of a line segment in a given ratio (internally)

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 (8) Periods
**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.

## UNIT V : STATISTICS AND PROBABILITY

**2. PROBABILITY (10) Periods
**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) (14) Periods
**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 (12) Periods
**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.)

**2. SURFACE AREAS AND VOLUMES (12) Periods
**(i) 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.

(ii) 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.)

**RECOMMENDED BOOKS
**1. Mathematics - Textbook for class IX - NCERT Publication

2. Mathematics - Textbook for class X - NCERT Publication

3. Guidelines for Mathematics laboratory in schools, class IX - CBSE Publication

4. Guidelines for Mathematics laboratory in schools, class X - CBSE Publication

5. A hand book for designing mathematics laboratory in schools - NCERT Publication

6. Laboratory manual - Mathematics, secondary stage - NCERT Publication.