Karnataka Board SSLC Class 10 Mathematics Syllabus – Part 1

• Arithmetic Progressions
  Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.
• 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 of 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 angle.
• Pair of Linear Equations in Two Variables
  Pair of linear equations in two variables and graphical method of their
  solution, consistency/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. Simple problems on equations reducible to linear
  equations.
• Circles
  Tangent to a circle at, point of contact
  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 a circle are equal.
• 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.)
• Constructions
  1. Division of a line segment in a given ratio (internally).
  2. Tangents to a circle from a point outside it.
  3. Construction of a triangle similar to a given triangle.
• Coordinate Geometry
  Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula.
  Section formula (internal division). Area of a triangle.
• 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
  irrationality of √2, √3, √5 Decimal representation of rational numbers in terms of
  terminating/non-terminating recurring decimals.

Karnataka Board SSLC Class 10 Mathematics Syllabus – Part 2

• 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.
• Quadratic Equations
  Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). Solutions of 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.
• 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.
• Some Applications Of Trigonometry
  Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given.Trigonometric ratios of complementary angles.
• Statistics
  Mean, median and mode of grouped data (bimodal situation to be avoided).Cumulative frequency graph.
• Probability
  Classical definition of probability. Simple problems on single events (not using set
  notation).
• Surface Areas And Volumes
  1. 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.
  2. 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).
• Proofs In Mathematics
• Mathematical Modelling

Source and Credits:
All the data of Karnataka Science Syllabus for Class 10 is taken from Karnataka Board . LearnFatafat is not responsible for any changes in the 10^th syllabus.