Class 10 Syllabus

Course Structure

Maths Syllabus for class 10

Three Hours Max. Marks -90

First Term (SA-I)

Units Marks
I. Number System 11
II. Algebra 23
III. Geometry 17
IV. Trigonometry 22
V. Statistics 17
Total 90

Second Term (SA-II)

Units 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

  • Euclid’s division lemma, Fundamental Theorem of Arithmetic.
  • Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating and non-terminating recurring decimals.
  • Zeros of a polynomial
  • Relationship between zeros and coefficients of quadratic polynomials.
  • Statement and simple problems on division algorithm for polynomials with real coefficients.
  • 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.
  • Problems on equations reducible to linear equations.
  • (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.
  • If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
  • If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
  • If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
  • 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.
  • 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.
  • Trigonometric ratios of an acute angle of a right-angled triangle.
  • Proof of their existence; 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.
Proof and applications of the identity sin2A + cos2A = 1.
Trigonometric ratios of complementary angles.
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

Second Term Syllabus

  • Standard form of a quadratic equation ax2+bx+c=0, (a ≠ 0).
  • Solution of quadratic equations 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.
Motivation for studying Arithmetic Progression, Derivation of the nth term and sum of the first n terms of A.P.

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.


  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.
  1. Simple problems on heights and distances.
  2. Angles of elevation / depression should be only 30°, 45°, 60°.
Classical definition of probability. Simple problems on single events.
  • The area of a circle; area of sectors and area of segments of a circle.
  • Problems based on areas and perimeter / circumference of the above said plane figures.
  • Plane figures involving triangles, simple quadrilaterals and circle.
(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.)

Practise This Question

A function f such that f(a)=f′′(a)=......f2n(a)=0 and f has a local maximum value b at x = a, if f (x) is