CBSE Class 10 Math Syllabus for 2014-15

The syllabus for students of class 10, studying in CBSE schools is formatted according to the guidelines of CCE, the pattern being followed by the Board. The CBSE Class 10 Maths syllabus encompasses the necessary topics for the Board examinations in 2015, in a simplified manner. In other words, Class 10 Maths syllabus for CBSE students is divided into equal units, chapters and topics for every term. As a result, it becomes easier for students to cover greater portions of their CBSE Class 10 syllabus. The marks for each topic as well as the ideal number of periods to be taken in completing the syllabus has also been mentioned.

First Term Units (SA-I) Marks
I. Number System 11
II. Algebra 23
III. Geometry 17
IV. Trigonometry 22
V. Statistics 17
  Total 90
Second Term Units (SA-II) Marks
II. Algebra (contd.) 23
III. Geometry (contd.) 17
IV. Trigonometry (contd.) 8
V. Probability 8
VI. Co-ordinate Geometry 11
VII. Mensuration 23
  Total 90

FIRST TERM UNITS (SA-I):

UNIT I : NUMBER SYSTEMS

1. 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 Ö2, Ö3, Ö5, 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.

2. 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 a pair of linear equations in two variables algebraically - by substitution,

  • by elimination and by cross multiplication method

  • Simple situational problems must be included. Simple problems on equations

  • reducible to linear equations may 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 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.

UNIT IV : TRIGONOMETRY

1. 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 0° and 90°

Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships

between the ratios.

2. TRIGONOMETRIC IDENTITIES 2

Proof and applications of the identity sin A + cos A = 1

Only simple identities to be given

Trigonometric ratios of complementary angles

UNIT V : STATISTICS AND PROBABILITY

1. STATISTICS

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

SECOND TERM UNITS (SA-II):

UNIT II : ALGEBRA (Contd.)

3. QUADRATIC EQUATIONS

  • Standard form of a quadratic equation ax2 + bx + c = 0, (a 1 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

Motivation for studying Arithmetic Progression 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

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 (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

  • Simple and believable problems on heights and distances

  • Problems should not involve more than two right triangles

  • Angles of elevation / depression should be only 30°, 45°, 60°

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

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

2. SURFACE AREAS AND VOLUMES

(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.)

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