P2 Course content
FUNCTIONS AND ALGEBRA: Simplification of rational functions, definitions, domain, range, composite, inverse, graphs and sketches, modulus, geometrical interpretation, simple transformations: y = af(x), y = f(ax), y = f(x) + a, y = f(x + a).
SEQUENCES, SERIES AND PROOF: Recurrence relations, binomial expansion, n! nCr, methods of proof including contradiction and counter-example.
TRIGONOMTERY: secx, cosecx, cotx, inverse trigonometric functions, further identities, sin(A + B), rcos(x + a), use of identities in equations and integration.
EXPONENTIALS AND LOGARITHMS: exp(x), lnx, exponentials, graphs, laws of logarithms, solution of equations in the form a^x = b.
DIFFERENTIATION: differentiation of exp(x), lnx, applications to tangents and normals.
INTEGRATION: exp(x), 1/x, volume of revolution.
NUMERICAL METHODS: location of roots, change of sign, use of iterative methods to solve equations, trapezium rule.
Course Programme
0915 Coffee
0930 INTRODUCTION AND SESSION I: Exponentials, logarithms, Differentiation and Integration
1115 Coffee
1130 SESSION II: Trigonometry, Functions
1300 Lunch
1345 SESSION III: Sequences and Series, Proof, Numerical Methods
1515 Tea and depart
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