Algebra
(i) Elementary Topics in Algebra: Remainder and Factor Theorems; Indices; Surds; Logarithms and their Properties (including change of base). Problems based on Properties.
(ii) Quadratic Equations and Quadratic Functions: Solution of ax 2 +bx+c = 0 OR reducible to this form by factorisation and formula method; Theory of Quadratic Equations, Nature of Roots, Sum and Product of Roots, Value of Symmetric Functions. Forming Quadratic
Equations with given roots. To find the condition when a relation between the two roots is given; Common roots; Quadratic Functions - Graph of Quadratic Function ax 2 +bx+c, a ¹ 0 - Sign of Quadratic Function ax 2 +bx+c - Maximum/minimum value of a Quadratic Function - Quadratic Inequalities and their solutions; solutions of inequations of the form f(x)/g(x) </> 0 where f(x) and g(x) have linear factors only; Range of Values of Quadratic Fractions (ax 2 +bx+c)/(px 2 +qr+r), x Î R.
(iii)Finite and Infinite Sequences: T n and S n of AP, GP - Insertion of Arithmetic and Geometric means between two Numbers. Sum to Infinity of a G.P. Sum to Infinite of G.P. (|r| < 1). Recurring Decimals as G.P.; H.P. Insertion of H.M. between two Numbers; Special Sums i.e. n S n, n S n 2 and n 1 S n 3 where n Î N.
(iv) Partial Fractions. Rational Functions of the form f(x)/g(x), where f and g are polynomials (including monomials) in x.
CASE I degree of numerator < degree of the denominator
Type 1 Non repeated Linear Factors, Type 2 Repeated Linear Factors, Type 3 Quadratic Factors (may not be factorisable).
CASE II degree of numerator > degree of the denominator
Type 1 Non-repeated Linear Factors, Type 2 Repeated Linear Factors.
Trigonometry
(i) Angles and Arc Lengths: Angles – Convention of sign of angles - Magnitude of an angle - Measures of angles - Circular measures; T ratio of angles of any magnitude. The relation S = r q , where q is in radians. Relationbetween radians and degrees; Arc length and area of a sector of circle.
(ii) Trigonometrical Functions: Trigonometric ratios; relationship between trigonometric ratios; proving simple identities; signs of trigonometric ratios; limits of trigonometric ratios; trigonometric ratios of standard angles; trigonometric ratios of allied angles.
(iii) Compound and Multiple Angles: Addition and subtraction formulas; sin (A ± B), cos (A ± B), tan (A ± B); sum and difference as products sinC + sinD = 2sin[(C+D)/2]. cos[(C-D)/2]; product to sum or difference 2sinA.cosB = sin(A+B) + sin(A-B) etc.; double angle formula; triple angle formula; half and one third angle formula; conditional identities (involving the angles of a triangle).
(iv) Trigonometric Equations: Solution of Trigonometric Equations (General solution and solution in a specified range).
Types (i) Equations in which only one function of a single angle is involved.
(ii) Equations expressible in terms of one trigonometric ratio of the unknown angle.
(iii) Equations involving multiple angles.
(iv) Equations involving compoundangles.
(v) Inverse Trigonometric Functions: Meaning of inverse trigonometric functions; Principle value interval; Properties of inverse trigonometric functions (without proof); Use of the properties to represent inverse trigonometric functions in the simplest form.
Coordinate Geometry
(i) Points and their Coordinates in 2D: Cartesian system of coordinates - distance formula - section formula (internal and external) - centroid of a triangle - incentre of a triangle; area of a triangle using the three vertices of a triangle; area of a quadrilateral; slope/gradient of a straight line; angle between two lines; Conditions for lines to be parallel and perpendicular; slope/gradient of a line joining two points.
(ii) Locus and its Equation: Definition of a locus; illustrations of the equation of locus; methods to find the equation of a locus.
(iii) The Straight Line: Various forms of the equation of a line - slope intercept form - point slope form - two points form – two intercept form - perpendicular/normal form - parametric form - general equation of a line - distance of a point from a line; equation of the perpendicular bisector of a line segment - distance between parallel lines - equations of lines bisecting the angle between given lines; families of lines - lines parallel to ax+by+c = 0 are the form ax+by+k = 0 – lines perpendicular to ax+by+c = 0 are the form ay-bx+k = 0 - any line through intersection of two lines L 1 and L 2 is of the form L 1 +KL 2 = 0 where K Î R; Solution of simultaneous linear inequations in one or two unknowns e.g. 3x+2y >5, y >2; 3x+2y< 5,x+y > 1.
(iv) Circles
(a) Equation of circles in - standard form - diameter form - general form - parametric form.
(b) Given the equation of a circle to find the centre and radius.
(c) Finding the equation of a circle - given 3 non-colinear points - given other sufficient data; condition for tangency - equations of tangents to a circle at a point on the circumference from an external point - equation of a normal - length of a tangent to a circle from an external point - finding the equation of a circle given the centre and tangent line.
Calculus
(i) Differential Calculus: Functions/limits and continuity - concept of real valued functions.
Domain and Range of a function - classification of functions - sketches of graphs of exponential functions, logarithmic functions and mod functions, trigonometric functions, namely sinx, cosx and tanx; notion and meaning of limits - fundamental theorem on limits - evaluation of limits of algebraic functions and trigonometric functions - problems on algebraic functions based on factorisation, rationalisation with x ® 0, x ® a, x ® ¥ only.
Problems on trigonometric functions based on limits x ® 0, sinx/x, cosx and tanx/x only; continuity - continuity of a function at a point x=a and in an interval; differentiation - meaning and geometrical interpretation of derivative - derivatives of simple algebraic and trigonometric functions - derivatives of sum/difference product and quotient of function - derivatives of composite functions implicit functions parametric functions - derivatives of 2nd order; application of derivative - equation of tangent and normal - approximation - rates measure.
(ii) Integral Calculus: Indefinite integral (anti derivative) - integration as the inverse of differentiation, anti derivative of polynomials and the functions (ax+b) n , sinx, cosx, secx.tanx, sec 2 x, cosec 2 x – trigonometric transformations; simple substitutions - indefinite integrals of the form sin 2 xdx, sin 3 xdx, cos 2 xdx, cos 3 xdx, f ¢ (x) [f(x)] n dx.
Ratio and Proportion
Simple Interest and Compound Interest
Stocks and Shares
Depreciation: emphasis on industrial and commercial applications e.g. insurance.
Statistics
(i) Data representation: classification and tabulation of data; graphical representation of data.
(ii) Measures of central tendency: mean, mode, median.
(iii) Quartiles and Percentiles: estimation of median/quartiles from the ogive .
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