Further Mathematics
Post 16 at WG6
Year 13
|
Topic |
Learning Outcomes |
Term 1 |
Decision 5: The travelling salesman problem
Core Pure 3: Methods in calculus
Core Pure 2: Series
Core Pure 1: Complex Number |
5.1 The classical and practical travelling salesman problems 5.2 Using a minimum spanning tree method to find an upper bound 5.3 Using a minimum spanning tree method to find a lower bound 5.4 Using the nearest neighbour algorithm to find an upper bound 3.1 Improper integrals 3.2 The mean value of a function 3.3 Differentiating inverse trigonometric functions 3.4 Integrating with inverse trigonometric functions 3.5 Integrating using partial fractions 2.1 The method of differences 2.2 Higher derivatives 2.3 Maclaurin series 2.4 Series expansions of compound functions
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Term 2 |
Decision 2: Graphs and networks
Core Pure 4: Volumes of Revolution
Further Stats 3: Geometric and Negative Binomial
Further Stats 4: Hypothesis Testing |
2.5 The planarity algorithm 4.1 Volumes of revolution around the x-axis 4.2 Volumes of revolution around the y-axis 4.3 Volumes of revolution of parametrically defined curves 4.4 Modelling with volumes of revolution 3.1 The geometric distribution 3.2 Mean and variance of a geometric distribution 3.3 The negative binomial distribution 3.4 Mean and variance of the negative binomial distribution 4.3 Hypothesis testing for the parameter p of a geometric distribution 4.4 Finding critical regions for a geometric distribution |
Term 3 |
Decision 4: Route Inspection
Core Pure 5: Polar coordinates
Core Pure 6: Hyperbolic Functions |
4.3 Networks with more than four odd nodes
5.1 Polar coordinates and equations 5.2 Sketching curves 5.3 Area enclosed by a polar curve 5.4 Tangents to polar curves
6.1 Introduction to hyperbolic functions 6.2 Inverse hyperbolic functions 6.3 Identities and equations 6.4 Differentiating hyperbolic functions 6.5 Integrating hyperbolic functions |
Term 4 |
Decision 7: This simplex algorithm
Further Stats 5: Central Limit Theorem
Further Stats 6: Chi Squared Tests
Further Stats 7: Probability Generating Functions
Further Stats 8: Quality of Tests |
7.1 Formulating linear programming problems 7.2 The simplex method 7.3 Problems requiring integer solutions 7.4 Two-stage simplex method 7.5 The Big-M method 5.1 The central limit theorem 5.2 Applying the central limit theorem to other distributions 6.6 Apply goodness-of-fit tests to geometric distributions 7.1 Probability generating functions 7.2 Probability generating functions of standard distributions 7.3 Mean and variance of a distribution 7.4 Sums of independent random variables 8.1 Type I and Type II errors 8.2 Type I and Type II errors using the normal distribution 8.3 Calculate the size and power of a test 8.4 The power function |
Term 5 |
Core Pure 7: Methods in differential equations
Core Pure 8: Modelling in differential equations |
7.1 First-order differential equations 7.2 Second-order homogeneous differential equations 7.3 Second-order non-homogeneous differential equations 7.4 Using boundary conditions 8.1 Modelling with first-order differential equations 8.2 Simple harmonic motion 8.3 Damped and forced harmonic motion 8.4 Coupled first-order simultaneous differential equations |
Term 6 |
Revision & Preparation
External Examinations |
Review of previously taught topics in preparation for summer examination. Individual teachers to teach specific content to their class based on gap analysis of their class / groups within their class as a result of recent assessment |