As I always say, you cannot ever get rid of mathematics. So if you don’t like mathematics, try altering your approach towards the subject or you will have to pay heavily for your mistake. It doesn’t matter if you take sciences or commerce; you will have to study mathematics in both the streams until and unless you take up arts or medical stream. The success mantra to mathematics is very simple and that is sheer hard work, nothing is difficult in mathematics, it’s just that sometimes you may need to put in more time and effort. But once you are done with the hard part of clearing your basics, rest is easy going and you just to have to revise periodically to retain everything. All the best, word hard and success is all yours.

Download CBSE 2010 Class X Mathematics Sample Papers

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CBSE Syllabus Class 10 for 2010 : Mathematics

Mathematics : CBSE syllabus class 10 for March 2010 examinations.

Course Structure

Mathematics

Class X

One Paper Time : 3 Hours Marks : 80

UNIT  –MARKS

I. Number System –04

II. Algebra –20

III. Trigonometry –12

IV. Coordinate Geometry –08

V. Geometry –16

VI. Mensuration –10

VII. Statistics and Probability –10

Total Marks –80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (15) Periods
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 decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

UNIT II : ALGEBRA

1. POLYNOMIALS (6) Periods
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.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods
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.

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 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.

4. ARITHMETIC PROGRESSIONS (8) Periods
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.

UNIT III : Trigonometry

1. TRIGONOMETRIC RATIOS (12) Periods
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.

2. TRIGONOMETRIC IDENTITIES (16) Periods
Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

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 IV : COORDINATE GEOMETRY

1. LINES (In two-dimensions) (15) 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 V : GEOMETRY

1. TRIANGLES (15) Periods
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 parallel 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 triangle.

2. CIRCLES (8) Periods
Tangents to a circle motivated by chords drawn from points coming closer and 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 VI : MENSURATION

1. AREAS OF PLANE FIGURES (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.)

UNIT VII : STATISTICS AND PROBABILITY

1. STATISTICS (15) Periods
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

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.

INTERNAL ASSESSMENT 20 Marks
Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks