# Mathematics

Our team of Maths teachers is dedicated to ensuring our students fulfil their potential in one of the curriculum’s most rewarding subjects. Mathematics is not just about ‘doing sums’; it is about challenging the mind to solve problems, and it is these problem solving skills that are so useful as our students move on to the world of work.

A qualification in Mathematics can lead to a number of careers. These include careers in engineering, finance, ICT and computer design, scientific research, medicine and architecture, to name but a few key examples. Most importantly, a good qualification in Mathematics tells a potential employer that you are a good problem solver!

**Enrichment**

We run a weekly Maths Surgery in order to support our students across all the Key Stages. At Maths Surgery we have a qualified member of staff and several Sixth Form Maths prefects in order to be able to help everybody who attends.

Within the department there is also a weekly chess club. Our chess players are able to enter school competitions.

As a department we also run a comprehensive range of Revision sessions for our GCSE and A-Level Students. These come in a variety of formats, covering different elements from the syllabus and different examination techniques.

**trips and events**

Every year we participate in the NSPCC Number day in February. Students raise money to have a fun ‘number based’ Maths lesson rather than following the usual restraints of the curriculum.

We are in the process of collaborating with the Computing department to organize a curriculum based visit to Disneyland Paris with our Sixth Form students.

We enter Maths Team Challenge events and also hold Junior and Intermediate Individual Maths Challenge competitions within school.

**Subject Leaders: Mrs E Brownridge (ebrownridge@fortpitt.medway.sch.uk ) **

**Curriculum Content**

**Key Stage 3**

**Year 7**

Basic skills are the focus for Year 7, ensuring students from different schools are equipped with the skills needed to move forward in their Mathematics learning. These focus on the early parts of the Foundation level GCSE.

Topics included for this year are:

Probability (including mutually exclusive events), algebraic shorthand, collecting like terms, powers, roots, prime factors and HCF/LCM, alternate and corresponding angles, area, sequences, angles in triangles and quadrilaterals, geometric proof, fractions, decimals and percentages, expanding brackets, index notation with algebra, y=mx + c, real-life graphs, constructions, solving equations (including negatives), stem and leaf diagrams, pie charts, congruent shapes, transformations, scatter graphs and correlation.

In Year 7 all students also embark on their Numeracy journey, starting off with Numeracy Ninja. These are weekly challenges where they aspire to become a black belt before the end of the year.

**Year 8**

In Year 8, students continue to study topics that will be examined at GCSE, but at the lower grades. This gives them a firm foundation on which to build towards their GCSE. Topics covered include:

Arithmetic with fractions, decimals and percentages, prime factors, HCF and LCM, negative numbers, compound interest, reverse percentages, ratio, time, distance and speed, proportion, best buys, density, standard form, area (including circles, sectors and trapezia), volumes of prisms (including cylinders), solving linear equations, trial and improvement, rules of indices, multiplying out pairs of brackets, Pythagoras’ theorem, right-angled trigonometry, angles in polygons, construction and loci, transformations, averages, grouped data, surveys, sampling methods.

Many of these topics will be revisited and developed in each of the subsequent years.

The Numeracy Challenges also continue, with Numeracy Samurai.

**Key Stage 4 GCSE 9-1 Mathematics**

**Exam board: Edexcel**

The main GCSE syllabus will be covered as a three-year plan, with students sitting their GCSE at the end of Year 11. The examination board is Edexcel. As previously, topics are revisited on a regular basis, with reinforcement and developmental activities delivered within this framework. It is expected that all students will take their GCSE at the higher level. Syllabus coverage is heaviest in Years 9 and 10 to give ample time to revise thoroughly for the examination in Year 11. Throughout the three year course we ensure our students are familiarized regularly with Problem Solving elements, ensuring they are able to efficiently apply numerical reasoning and logic to the most demanding exam questions.

We begin a programme of regular ‘Whole-year’ Assessments, with the frequency increasing as they progress through to the end of year 11. We believe this prepares them more fully for the examinations that they will sit at the end of year 11.

The main topics for each year are:

**Year 9**

Simultaneous equations – elimination and substitution, rearranging formulae, Pythagoras’ theorem and trigonometry in three dimensions, circle theorems, combined transformation geometry, congruent triangles, further constructions and loci, bearings, powers, standard form and surds, reciprocals and rational numbers, averages, frequency tables, grouped data, histograms, moving averages, sampling, expanding brackets, quadratic factorisation, solving quadratics (by factorising, by the formula and by completing the square), area (parallelograms and kites), and volumes of cones and pyramids.

**Year 10**

Distance-time graphs, velocity-time graphs, real life graphs, similar triangles, areas and volumes of similar shapes, sine, cosine and tangent graphs, solving simple trigonometric equations, the sine rule, the cosine rule, area of a non-right angled triangle, linear graphs, y = mx + c, parallel and perpendicular lines, drawing straight line graphs – tables of values, gradient and intercept method and cover-up method, solving simultaneous equations graphically, quadratic graphs, square-root and reciprocal graphs, cubic and exponential graphs, stem and leaf diagrams, scatter diagrams, cumulative frequency graphs, box plots and measures of dispersion.

**Year 11**

Graphs of trigonometric functions, two-way tables, mutually exclusive and exhaustive events in probability, addition rule, combined events, tree diagrams, independent events and conditional probability, algebraic fractions, non-linear simultaneous equations, sequences (including quadratics and nth term rules), changing the subject of a formula, dimensional analysis, direct and indirect variation, limits of accuracy – lower and upper bounds, solving inequalities, graphical inequalities, and vectors.

**Key Stage 5 – Mathematics**

**Exam board: Edexcel**

**Year 12 – ****Level 3 Advanced GCE in Mathematics (9MA0)**

Students will follow the new specifications for A-Level Mathematics. Students follow a two year programme of Study culminating in three externally examined papers. All 3 papers must be taken in May/June in any single year (at the end of year 13). Papers 1 and 2 may contain questions on any topics from the Pure Mathematics content. Paper 3 will contain questions on the Statistics and Mechanics topics. Throughout the two-year course we endeavour to ensure all students develop their problem solving and reasoning skills by teaching them to a deeper level of understanding and engaging them with rich activities.

Core Content:

- Proof
- Algebra and Functions
- Co-ordinate Geometry in the (x,y) plane
- Sequences and Series
- Trigonometry
- Exponentials and Logarithms
- Differentiation
- Integration
- Numerical Methods
- Vectors

Statistics Content:

- Statistical Sampling
- Data Presentation and interpretation
- Probability
- Statistical distributions
- Statistical hypothesis testing

Mechanics content:

- Quantities and Units in Mechanics
- Kinematics
- Forces and Newtons Laws
- Moments

Students have the option of taking the AS in Mathematics at the end of year 12. The majority of students will, however continue studying in Year 13 and achieve their A-Level.

**Level 3 Advanced GCE in further Mathematics (9FM0)**

Students will follow the new specification for A-Level Mathematics. Students follow a two-year programme study culminating in four externally examined papers. All Papers must be completed in May/June of any single year. All 4 papers are 90 minutes long. Papers 1 and 2 are the Core Mathematics Papers. For Paper 3 we have chosen to study Further Mechanics 1 and for Paper 4 we have decided to study Decision Mathematics. Throughout the two-year course we endeavour to ensure all students develop their problem solving and reasoning skills by teaching them to a deeper level of understanding and engaging them with rich activities.

The content will be covered over the two-year course and will cover the following:

Core Content:

- Proof
- Complex Numbers
- Matrices
- Further Algebra and Functions
- Further Calculus
- Further Vectors
- Polar Coordinates
- Hyperbolic Functions
- Differential Equations

Mechanics Content:

- Momentum and Impulse
- Work, Energy and Power
- Elastic Strings and springs and elastic energy
- Elastic collisions in one dimension
- Elastic collisions in two dimensions

Decision Mathematics content:

- Algorithms and graph Theory
- Algorithms on Graphs
- Critical Path Analysis
- Linear Programming

**Year 13 – **A2 Mathematics (2016 Specification)

### Exam board: AQA

**Core 3**

Functions, modulus function, inverse trigonometric functions, sec, cosec and cot, natural logarithms and ex, differentiation of ex, lnx and trigonometric functions, product and quotient rules, integration (e^{x}, sinx, cosx and 1/x), integration by substitution and parts, standard integrals, solids of revolution, numerical methods (such as mid-ordinate, Simpson’s rules and use of staircase and cobweb diagrams), proof.

**Core 4**

Rational expressions, partial fractions, parametric equations, circles and ellipses, the Binomial theorem, addition and double angle formulae for trigonometric functions, differential equations, parametric differentiation, integration using partial fractions and double angle formulae, vectors.

**Statistics 2**

Discrete random variables, the Poisson distribution, continuous random variables, estimation using the Normal and t- distribution, hypothesis testing, and Chi-squared tests.

### A2 Further Mathematics

**Further Pure 2**

Complex numbers, Argand diagrams and loci, roots of polynomial equations, summation of finite series by method of differences and induction, proof by induction, De Moivre’s theorem, inverse trigonometric functions, hyperbolic functions-graphs, identities, Osborne’s rule, differentiation and integration, arc length, and area of surface of revolution.

**Further Pure 3**

Series and limits, polar coordinates, differential equations – order, general and particular solutions, numerical methods to solve first order differential equations – Euler’s formula, mid-point formula, error analysis, and second-order differential equations.

**Mechanics 2**

Calculus in kinematics, velocity at an instant, motion in two and three dimensions, moments, equilibriums, centres of mass, centres of gravity, work, energy and power, elasticity – springs and strings, circular motion, and differential equations.