# 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!

**Subject Leader: Mrs C Spring (cspring@fortpitt.medway.sch.uk)**

# Curriculum Content

**Exam Boards:**

**Level 2 Further Maths – AQA**

**KS4 – Edexcel GCSE Maths, Algebra and Statistical Methods awards**

## 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.

### 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.

## Key Stage 4

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 to be delivered within this framework. It is intended 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.

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.

In 2015-16 all students will also sit the Edexcel Algebra award at level 2, with some EAA students sitting at level 3. Following this course will strengthen their algebraic skills in preparation for their GCSE next year.

### 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.

Current Year 11 students are following a mixture of courses designed for those who passed their GCSE last year. These are the AQA Further Maths Award and the Edexcel Algebra and Statistical methods Awards

## Key Stage 5

**Exam Board – AQA**

We currently use the AQA examination board for AS/A2 studies. We follow courses for both Mathematics and Further Mathematics in the sixth form.

### Year 12

### AS Mathematics

**Core 1**

Surds, quadratics, inequalities, simultaneous equations, coordinate geometry, factor and remainder theorems, differentiation and its applications, integration and area, and circles.

**Core 2**

Transformations of graphs, indices, Binomial expansion, radians, solving trigonometric equations, trigonometric identities, area of sectors and arc lengths, exponentials and logarithms, arithmetic and geometric series, further differentiation and integration, and the trapezium rule.

**Statistics 1**

Collecting and processing data, variance and standard deviation, probability, the Binomial distribution, the Normal distribution, sampling distribution of the mean, confidence intervals, linear regression, and correlation using the product moment correlation coefficient.

### AS Further Mathematics

**Further Pure 1**

Roots and coefficients of quadratic equations, series, matrices, transformations using matrices, graphs of rational functions, conics, complex numbers, differentiation from first principles, improper integrals, general solutions of trigonometric equations, interval bisection, linear interpolation, the Newton-Raphson method, step-by-step solutions to differential equations, and reduction to a linear form.

**Decision 1**

Graphs, networks and matrices, minimum spanning trees, shortest path, route inspection, travelling salesman problem, bipartite graphs, sorting algorithms, linear programming, and efficiency of algorithms.

**Mechanics 1**

Modelling, kinematics in one and two dimensions, statics and forces, Newton’s laws of motion, linear momentum, and projectiles.

### Year 13

### A2 Mathematics

**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 (ex, 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.