# Further Mathematics

Mr S Robinson (Head of Team) | srobinson@conyers.org.uk | Mr J Downs | jdowns@conyers.org.uk |

Mr K Anderson | kanderson@conyers.org.uk | Mrs K Gray | kgray@conyers.org.uk |

Miss L Allanson | lallanson@conyers.org.uk | Mr M Black | mblack@conyers.org.uk |

Mr P Dixon | pdixon@conyers.org.uk | Mr A Pach | apach@conyers.org.uk |

Mr M Taylor | mtaylor@conyers.org.uk | Mx A Taylor | ataylor@conyers.org.uk |

Mrs J White | jwhite@conyers.org.uk |

## Key Stage 5 Curriculum Map

**Curriculum Intent**

To engage students and extend their curiosity for Mathematics by extending their range of mathematical skills and techniques and to use their knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts; communicating the rationale for these decisions clearly.

To give students an insight into other areas of Mathematics by studying Decision Maths – this will help to further complement other A levels and potential career paths.

**Key Knowledge and Skills **

Construct and present mathematical arguments through appropriate use of diagrams using the correct mathematical language and definitions

Improve their problem solving techniques: specifying the problem, identifying the underlying mathematics within the problem, collecting information, processing and representing information and interpreting results

Understand the use of modelling and create a suitable model while understanding assumptions, its limitations and the context of the situation

Improve data analysis skills using real data collected and collated within the large data set. Understanding problems, limitations, terminology and drawing conclusions

**Sequence Discussion**

The Core element is compulsory and represents 50% of the content. For the remaining 50% we have chosen Further Mechanics and Decision. The Core element requires full understanding of the pure topics from AS and A2 Maths so these topics are taught in the first half term of each year. Further Mechanics extends the Mechanics elements taught beforehand. The Statistics elements and using the data set are still required for Maths and are therefore taught throughout year 2 as in the normal maths curriculum. All Year 13 topics depend upon a secure understanding of Year 12 Maths and Further Maths topics and therefore a large emphasis is placed on practising and revisiting sills in the form of mini tests, starter questions and weekly skills based homeworks throughout both years.

### Year 12

#### Half Term 1

Algebra and Functions

Co-ordinate Geometry

Trigonometry

Differentiation

Vectors

Integration

Further Algebra – polynomials and Binomial expansion

Algorithms on Graphs 1 & 2:

#### Half Term 2

Exponentials and

Logs

Vectors

Complex Numbers

Further Complex Numbers

Further Algebra & Functions

Quantities and Units

Kinematics

Forces and Newton’s Laws

Linear Programming

Graph Theory

#### Half Term 3

Series

Further Calculus

Further Complex Numbers

Matrices

Further Vectors

Kinematics

Momentum and Impulse

Work, Energy, Power

Forces and Newton’s Laws

Algorithms

Critical Path Analysis

#### Half Term 4

Matrices

Proof

Further Vectors

Elastic Collisions

Work, Energy, Power

Statistical Sampling

Introduction to and using the Large Data Set

Data Presentation and Interpretation

#### Half Term 5

Correlation and Regression

Probability

Statistical Distributions

Hypothesis Testing

Elastic Collisions

#### Half Term 6

__Year 13 content__

Series and Sequences

Algebraic and Partial

Fractions

Functions and modelling

Binomial Theorem

Data Set

Proof

Complex numbers

Moments

### Year 13

#### Half Term 1

Trigonometry

Integration

Differentiation

Numerical Methods

Proof

Functions and modelling

Integration

Algorithms

#### Half Term 2

Parametric Functions

Complex Numbers

Further Integration

Further Series

Forces and Friction

Further Kinematics

Projectile, Forces

Regression and Correlation

Algorithms and Graph Theory, Probability

#### Half Term 3

Further Calculus

Further Kinematics

Polar Coordinates

Momentum and Impulse

Elastic Collisions in 2D

Probability

Normal Distribution

Algorithms 2

#### Half Term 4

Differential Equations

Hyperbolic Functions

Elastic Collisions in 2D

Elastic Springs and Energy

Linear Programming

Critical Path Analysis

#### Half Term 5

Differential Equations

Elastic Springs and Energy

Critical Path Analysis