Tuesday 01 September, 2020 CBSE 10th Class

CBSE 10th Class Mathematics

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 ‘n’ 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.)