13 - Curriculum Development Centre, Kalamassery

Definition of trigonometric functions of an angle in any quadrant, Signs of trigonometricfunctions of related angles, Given a trigonometric functions of an angle and its quadrant findothers. Find the values of the trigonometric functions between 0˚ and 360˚.UNIT – II2.1 Properties of trigonometric functionsAddition formulae, Multiple and Sub-multiple formulae, Sum and Product formulae, simpleproblems.2.2 Properties of trianglesState and prove Sine rule, Cosine rule and projection formula. State and prove Napier’s formulaand simple problems relating to this.2.3 Solution of triangleSolve the triangle given1. Three sides2. Two sides and the included angle (use Napier’s formula)2.4 Co-ordinate geometryStraight line-Slope, Equations of a straight line in the forms1) Y = mx + C,2) y-y ı = m(x-x ı ),3) y-y ı = x-x ıy ı -y 2 x ı -x 24) x + y = 1a bPoints of Intersection of two lines, Angle between two lines, Conditions for two lines, Conditionsfor two lines to be parallel and predicator.UNIT – III3.1 Function and LimitsDefinition, some problems for finding limits, PropertiesLimit x n -a n = na n-1 and limit Sinǿ = 1 (statements only),x -> a x-a φ -> 0 φGeneral definition of continuous functions.3.2 Methods of Differentiation IDefinition of derivative of x n , Sin x, Cos x etc by using first principle, find derivatives of e x andlog x, Fundamental formulas, product and Quotient rules (statement only). Derivatives of othertrigonometric functions, Simple problems.3.3 Methods of Differentiation IIFunction of a function rule, Differentiation of implicit and parametric equations, problems ondifferentiation of functions involving these forms, second order derivatives, Simple problems.UNIT – IV4.1 Application of DifferentiationGeometrical meaning of derivatives, Slope, Tangent, Normal and Equation of a straight line, Rateof change.Problems connecting Area and Volume, Velocity and Accelerations.4.2 Maxima and MinimaIncreasing and Decreasing functions, Turning points, Finding Maximum and Minimum values ofa function by using derivatives, Conditions for Maximum and Minimum, Simple problems.4.3 Indefinite IntegralDefinition of integration, Fundamental formulas, Problems, Integration by substitution, functionof the form ∫ f (g (x) g¹ (x) dx, ∫ f (ax + b) n dxUNIT – V5.1 Integrates by parts21