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Calculus (Weightage 25%)  

Topics from Calculus

  • Integral as limit of a sum, fundamental theorem of calculus (4 concepts)
  • Determining areas of the regions bounded by simple curves in standard form (9 concepts)
  • Properties of definite integrals, evaluation of definite integrals (21 concepts)
  • Integral as an anti-derivative, fundamental integrals algebraic, trigonometric, exponential and logarithmic functions (37 concepts)
  • Integration by substituion using trigonometric identities (14 concepts)
  • Graphs of simple functions, limits, continuty and differentiability. (56 concepts)
  • Differentiation of the sum, difference, product and quotient of two functions (16 concepts)
  • Differentiation of trigonometric, inverse trigonometric, logarithmic exponential, composite and implicit functions (16 concepts)
  • Derivatives of order upto two (1 concepts)
  • Apllications of derivatives monotonic, maxima and minima of functions of one variable, tangents and normals (34 concepts)
  • Monotonic- increasing and decreasing functions (8 concepts)
  • Rolle's and Lagrange's Mean Value theorems (5 concepts)
  • Ordinary differential equations, their order and degree (8 concepts)
  • Formation of differential equations (2 concepts)
  • Solution of differential equations by the method of separation of variables (12 concepts)
  • Solution of homogeneous and linear differential equations (26 concepts)
  • Limits and their Importance (17 concepts)
  • Differentiation (17 concepts)
  • Continuity and Differentiability (12 concepts)
  • Application of Derivatives (8 concepts)
  • Monotonicity and Maxima-Minima of Functions (12 concepts)
  • Indefinite Integral (21 concepts)
  • Definite Integral (9 concepts)
  • Area (2 concepts)
  • Differential equations (11 concepts)
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