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St. George’s Mathematics Department A Level Mathematics Long Term Scheme Of Work 2004 General Course Information The OCR Mathematics Advanced level is aimed at students who have obtained a minimum of a Grade B at GCSE at the Higher level. Sessions are held in January and June. Students may be accredited with the following certificates, depending on the course followed: Certification Title and Number Advanced Subsidiary GCE Mathematics (3890) Advanced Subsidiary GCE Pure Mathematics (3891) Advanced Subsidiary GCE Further Mathematics (3892) Advanced GCE Mathematics (7890) Advanced GCE Pure Mathematics (7891) Advanced GCE Further Mathematics (7892) Units Required C1 & C2 together with one of M1, S1, D1 C1, C2 and FP1 FP1 together with two other units which may not include any of C1, C2, C3, C4 C1, C2, C3, C4 together with either two from M1, S1 D1 or M1, M2 or S1, S2 or D1, D2 C1, C2, C3, C4, FP1 and either FP2 or FP3 FP1 together with FP2 or FP3 or both, plus three or four other units as appropriate. Weighting of each unit is equal and all units are externally assessed by a written examination of duration 1 hour 30 minutes with 72 marks available on each paper. Question papers will be designed to have a gradient of difficulty with the more demanding questions towards the end of the paper Calculators No calculators may be used in answering unit C1; for all other units candidates may use a graphic calculator if they wish. Computers, and calculators with computer algebra functions, are not permitted in answering externally assessed units. Coursework Requirements There is no requirement for coursework associated with any of the units. Module Content Summary New sections and notes comparing to the 2000 syllabus are highlighted in blue; sections that have changed location are highlighted in red. Pure Mathematics Core Mathematics 1 (C1) (4721) (AS) Indices (laws of indices & rational indices) & Surds (including rationalising the denominator of the form a b - change); Polynomials (expansion of brackets, quadratics, quadratic inequalities, simultaneous equations, completing the square); Coordinate Geometry & Graphs A Level – Long term scheme – 2004 Page 1 Core Mathematics 2 (C2) (4722) (AS) (C1 knowledge assumed) Core Mathematics 3 (C3) (4723) (A2) (C1 & C2 knowledge assumed) Core Mathematics 4 (C4) (4724) (A2) (C1, C2, C3 knowledge assumed) Further Pure Mathematics 1 (FP1) (4725) (AS) (C1, C2 knowledge assumed) Further Pure Mathematics 2 (FP2) (4726) (A2) (C1-C4 & FP1 knowledge assumed) Further Pure Mathematics 3 (FP3) (4726) (A2) (C1-C4 & FP1 knowledge assumed - but not FP2) (new: circle equation (x-a)2 + (y-b)2=r2 and x2 + y2 + 2gx + 2fy + c = 0); Differentiation; (Integration & Trigonometry gone!) Trigonometry (Sine & cosine rules, ½ab sin C, radians, graphs, elementary identities, surd values); Sequences and series (now including sigma notation); expansion of (a + b)n; Factor & Remainder theorems; Logarithms; Integration (same as P1 + trapezium rule) Algebra & Functions (all the P2 material + transformation of graphs from P1); Trigonometry (no calculus of trig functions); Differentiation & Integration (P2 material + product, quotient & chain rule); Numerical methods (new – Simpson’s rule) Rational functions and graphs; Binomial expansion; Differentiation & Integration (now calculus of trig functions); First order differential equations; vectors (including dot product etc.) Summation of series; Proof by induction (including finding the nth power of a 2x2 matrix); Roots of polynomial equations; Complex numbers (no polar form); Matrices (including transformation matrices & solution of 3 simultaneous equations with 3 unknowns) Rational functions & Graphs; Polar coordinates (including integration); Hyperbolic functions; Differentiation & Integration(arc length and surface area have gone); Numerical methods (including Newton-Raphson method) Differential equations; Vectors (including vector product etc.); Complex numbers (including de Moivre’s theorem); Groups Mechanics – as before Mechanics 1 (M1) (4728) (AS) Mechanics 2 (M2) (4729) (A2) Mechanics 3 (M3) (4730) (A2) Force as a vector; Equilibrium of a particle; Kinematics of motion in a straight line; Newton’s laws of motion; Linear momentum. Centre of mass; Equilibrium of a rigid body; Motion of a projectile; Uniform motion in a circle; Coefficient of restitution and impulse; Energy, work and Power. Equilibrium of rigid bodies in contact; Elastic strings and springs; Impulse and momentum in two dimensions; Motion in a vertical circle; Linear motion under a variable force; Simple Harmonic Motion. Statistics – as before Probability and Statistics 1 (S1) Representation of data; Probability; Discrete Random Variables; (4732) (AS) Bivariate data Probability and Statistics 2 (S2) Continuous Random Variables; The Normal Distribution; The (4733) (A2) Poisson Distribution; Sampling and Hypothesis testing. Probability and Statistics 3 (S3) Continuous random variables; Linear combinations of random (4734) (A2) variables; Confidence intervals and the t distribution; Difference of population means and proportions; the chi squared test. Discrete Mathematics – as before Discrete Mathematics 1 (D1) Algorithms; Graph Theory; Networks; Linear Programming. (4736) (AS) A Level – Long term scheme – 2004 Page 2