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ST. FRANCIS' CANOSSIAN COLLEGE MATHEMATICS DEPARTMENT 2009/2010 CURRICULUM PLANNING Subject: Pure Mathematics Class: F. 7 Sc Subject Teacher(s): Ms Q. Kwok Month Aug 2009 Ch. Alg. 6 Sept 2009 Alg. 8 BASIC CONTENT / OBJECTIVES System of Linear Equations - to acquire skills in solving system of linear equations Inequalities - to study the various techniques used in proving inequalities DETAILED CONTENT 1. simple treatment in solving system of linear equations - use of Cramer's rule 2. more detailed treating in solving system of linear equations - Gaussian elimination 1. elementary properties of inequalities 2. idea of intervals 3. triangle inequalities 4. A.M. G.M. 5. Cauchy-Schwarz inequality 6. general techniques in proving inequality - by proving increasing / decreasing function - by locating max / min of function - working backwards -1- REMARKS Month Oct Ch. Cal. 7 Nov Cal 9 Dec Alg.1 3 BASIC CONTENT / OBJECTIVES Limit of a Sequence - to understand the definition of limit of a sequence - to investigate properties of limit of a sequence DETAILED CONTENT 1. 2. 3. 4. 5. 6. Introduction Convergent and Divergent Sequences Operations on Limits of Sequences Sandwich Theorem for Sequences Monotonic Sequences The Number e Theory of Differential & Integral Calculus - to study various theories of differential and 1. Mean Value Theorem integral calculus and their applications 2. Comparison of Definite Integrals 3. Differentiation of Integrals Complex Number - to investigate the various properties of complex number - to study the De Moivre's theorem and to use it in factorizing polynomials - to study complex value function as an example of function mapping from a two dimensional space to another two dimensional space 1. idea of complex number 2. operations with complex numbers 3. conjugate / properties of conjugates and its relation with modulus 4. polar form 5. geometric representation of complex number / Argand diagram 6. geometric interpretation of the operations of complex number 7. Complex value function 8. De Moivre's Theorem 9. Nth root of unity / of a complex number 10. Factorization of polynomial -2- REMARKS Month Ch. Jan 2010 Cal. 1 Jan Feb 10 (Cal) BASIC CONTENT / OBJECTIVES Polar Coordinates - to recognize polar coordinates Conic Sections - to introduce the idea of matrices and determinants - to understand of idea of transformation and to equip with skills in relating transformation with matrices DETAILED CONTENT 1. Fundamental Concepts 2. Polar Equations 3. Relation between rectangular and polar coordinates 4. Sketch of Graphs in Polar Coordinates 5. Intersection of Two Curves in Polar Coordinates 6. Slope of a Tangent 1. Basic Formulae 2. Loci 3. Parametric Equations 4. Straight Lines 5. Circles 6. General Conics in Two Dimensional Plane 7. Pair of Straight Lines 8. Parabolae 9. Ellipses 10. Hyperbola MOCK EXAM -3- REMARKS