CBSE 10th Class Mathematics Syllabus



Course Structure

I Term Units Topics Marks
I Number System 11
II Algebra 23
III Geometry 17
IV Trigonometry 22
V Statistics 17
Total 90
II Term Units Topics Marks
II Algebra 23
III Geometry 17
IV Trigonometry 8
V Probability 8
VI Co-ordinate Geometry 11
VII Mensuration 23
Total 90

First Term Course Syllabus

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 √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

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

Unit III: Geometry

1. Triangles

  • Definitions, examples, counter examples of similar triangles

  • (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

  • (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side

  • (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar

  • (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar

  • (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

  • (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

  • (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides

  • (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides

  • (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 0o and 90o

  • Values (with proofs) of the trigonometric ratios of 30o, 45o and 60o

  • Relationships between the ratios

2. Trigonometric Identities

  • Proof and applications of the identity sin2A + cos2A = 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 Course Syllabus

Unit II: Algebra

3. Quadratic Equations

  • 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

  • Situational problems based on quadratic equations related to day to day activities to be incorporated

4. Arithmetic Progressions

  • Motivation for studying Arithmetic Progression Derivation of the 9th term and sum of the first ā€˜nā€™ terms of A.P. and their application in solving daily life problems.

Unit III: Geometry

2. Circles

  • Tangents to a circle motivated by chords drawn from points coming closer and closer to the point

  • (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact

  • (Prove) The lengths of tangents drawn from an external point to circle are equal

3. 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

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 30o, 45o, 60o

Unit V: Statistics and Probability

2. Probability

  • Classical definition of probability
  • Simple problems on single events (not using set notation)

Unit VI: Coordinate Geometry

1. Lines (In two-dimensions)

  • Concepts of coordinate geometry, graphs of linear equations
  • Distance formula
  • Section formula (internal division)
  • 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 60o, 90o and 120o only

  • Plane figures involving triangles, simple quadrilaterals and circle should be taken

2. Surface Areas and Volumes

  • Problems on finding surface areas and volumes of combinations of any two of the following −

    • Cubes

    • Cuboids

    • Spheres

    • Hemispheres

    • 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.)

To download pdf Click here.

Advertisements