﻿ Further Mathematics - Subjects - Wilmington Grammar School for Girls

# 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    Exponential form of complex numbers  Multiplying and dividing complex numbers  De Moivre’s theorem  Trigonometric identities  Sums of series  Nth roots of a complex number  Solving geometric problems 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