Further Mathematics


Post 16 at WG6


Year 13



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 


  1. Exponential form of complex numbers 

  1. Multiplying and dividing complex numbers 

  1. De Moivre’s theorem 

  1. Trigonometric identities 

  1. Sums of series 

  1. Nth roots of a complex number 

  1. 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