# Mathematics

The Mathematics department aims to promote the appreciation of the power and beauty of Mathematics within each student and to enable each student to develop their mathematical skills and understanding to the limit of their capability. As mathematics is an essential prerequisite for many other subjects within the school curriculum, the department aims to provide each student with the mathematical background that they require to be able to apply their mathematics successfully in other areas. Also it aims to ensure that all students are aware of the power of a mathematical argument and the need for clear, logical arguments. In an academic school, the need for each student to attain the highest exam result possible for their ability is very important. With this in mind the department tries to ensure that all students are fully aware of the demands of the subject and have experienced a variety of teaching styles to facilitate their learning and can apply their mathematics in examination situations.

## Lower School

#### Year 6

Pupils in Year 6 are taught in a mixed ability form group (or groups). They follow the KS2 National Curriculum in general with an emphasis on formal written methods. The aim of the year is to bridge the gap from the mathematics they have studied in their many different primary schools to the rigour required in the senior school. They are prepared for a SATs style exam at the end of the year. The following material will be covered:

**Number**- Using and applying number through problem solving and communicating using precise mathematical language and reasoning. Understanding of numbers and the number system including place value, factors, multiples, prime numbers, fractions, ratios, percentages, integers and negative numbers. Calculations using the four rules of arithmetic with whole numbers and decimals.**Algebra**- Using formulae in words and symbols. Introduction to simple linear equations.**Shape and Space**- Names of 2D and 3D shapes. Correct use of geometrical notation and vocabulary. Properties of shapes including parallel and perpendicular lines and knowledge of basic angle facts. Use of a protractor to draw and measure angles accurately. Reflective and rotational symmetry and simple transformations. Finding the perimeter and area of simple 2D shapes. Understand the concept of volume. Units of measurement including units of length, mass, capacity and time.**Handling Data**- Interpreting data from charts and graphs. Collection and display of data using frequency tables, bar charts and pie charts. Calculation of mean, mode, median and range for a set of numbers. Introduction to probability.

#### Year 7

Pupils in Year 7 are taught in mixed ability form groups. The aim of the year is to ensure that all pupils have covered the basic building blocks of mathematics in a rigorous way. The following material will be covered:

**Number**- Four rules of arithmetic with positive whole numbers, negative numbers, fractions and decimals. Converting between fractions and decimals. Finding the Highest Common Factor and Lowest Common Multiple of sets of numbers.**Algebra**- Solution of linear equations (including those with the variable on both sides). Simplification of additive expressions. Substitution of whole numbers into simple formulae. Introduction to set notation.**Shape and Space**- Plane geometry (including angle problems involving triangles, quadrilaterals and parallel lines). Construction of triangles using ruler, compasses and protractor. Co-ordinates in 4 quadrants. Area of rectangles, triangles, parallelograms and compound shapes.**Handling Data**- Creating and interpreting bar charts and pie charts. Finding the mean and range of a set of numbers.

**Year 8**

Pupils in Year 8 (and upward) are taught in 6 or 7 ability sets. The initial setting arrangement is based on performance in Year 7 but is reviewed regularly to ensure that all pupils are being taught at a level and pace appropriate to their individual needs with extension/revision as required. The following material will be covered:

**Number**- Evaluation of terms in index form involving positive and negative integral indices. Multiplication and division of terms in index form. Conversion of numbers to and from standard form. Percentages (including simple percentage increase and decrease). Simple calculations involving ratio and proportion.**Algebra**- Multiplication of a bracket by a single term. Linear equations involving brackets. Multiplication of two brackets. Substitution into formulae. Drawing straight line graphs from a formulae. Finding the gradient of a line between two points.**Shape and Space**- Angle properties of polygons. Pythagoras’ Theorem. Construction of angle and line bisectors and special angles using compasses and ruler. Area and circumference of a circle and of simple sectors. Volumes of cuboids and compound cuboids. Volumes of prisms (including cylinders). Similar triangles.**Handling Data**- Probability (including sample space diagrams and simple tree diagrams). Mean, median and mode of a set of values. Problems involving means.

#### Year 9

The following material will be covered:

**Number**- Evaluation of terms in index form involving fractional and negative indices. Manipulation of terms in index form. Standard form and calculations involving standard form. Percentage increase and decrease and inverse percentages.**Algebra**- Solving linear equations involving brackets. Creating and rearranging formulae. Solving a pair of linear simultaneous equations. Factorisation of quadratic expressions. Solution of quadratic equations by factorisation. Solving linear inequalities.**Shape and Space**- Trigonometry – finding lengths and angles in right-angled triangles. Circle theorems.**Handling Data**- Calculating means from frequency tables and grouped frequency tables. Drawing histograms.

## GCSE

In Years 10 and 11, pupils study for the Edexcel IGCSE in Mathematics. All pupils take Higher Level and achieve great success with an average of 59% of all pupils obtaining A* grades and 87.5% obtaining at least an A grade over the last 5 years.

As well as extending the ideas covered during Years 7 to 9, the following new material will be covered over the course of the two years:

**Number**- Set Theory. Simplification and manipulation of surds. Upper and lower bounds.**Algebra**- Solution of quadratic equations using different methods. Simplification and manipulation of algebraic fractions. Drawing and using graphs to solve equations. Sequences. Introduction to calculus. Function notation and finding composite and inverse functions. Vectors. Solving quadratic inequalities.**Shape and Space**- Calculation of Volumes and Surface areas of common solid shapes. Tangent properties of circles. Areas and Volumes of similar shapes. Trigonometry in non right-angled triangles. Transformations.**Handling Data**- Cumulative frequency curves and calculations.

For the last four years, the pupils in the top two sets have also had the chance to sit the AQA Level 2 Certificate in Further Mathematics which provides greater challenge for able mathematicians without accelerating pupils into A level work. The results they have achieved have been very pleasing with 82/194 obtaining A** grades and 97/194 obtaining A* grades.

Those taking this qualification also cover the following material:

**Algebra**- Quadratic identities. Completing the square. The factor theorem. Drawing piecewise continuous graphs and using such graphs to solve equations. Algebraic proof. Limiting values of sequences. Further calculus. Introduction to matrices and matrix transformations.**Shape and Space**- Equations of circles. Solving geometric problems involving circles and straight lines. Geometric proof. Three dimensional trigonometry. Graphs of trigonometric functions. Solving trigonometric equations. Simplification and application of trigonometric identities.

## A level

Mathematics is the most popular subject in the Sixth Form with between 60 and 90 students opting to study it every year. It is also one of the most successful with an average of 28.8% of students obtaining A* grades and 87% A* to B grades over the last five years.

Students studying Mathematics will study four compulsory modules of Pure Mathematics (called C1 – C4). These contain the following material:

**Core 1**- Manipulation of algebra and solution of equations. Co-ordinate geometry and curve sketching. Arithmetic Sequences. Differentiation and Integration.**Core 2**- Trigonometric equations and identities. Radian measure. Logarithms. Geometric Sequences. Further Differentiation and integration.**Core 3**- Algebraic Fractions. Functions and transformations of graphs. Numerical solution of equations. Further Trigonometry. Differentiation of advanced functions.**Core 4**- Further Algebraic Fractions. Parametric co-ordinates and differentiation. Binomial Theorem. Vectors. Integration of advanced functions.

They will also study two further modules of Applied Mathematics from one of the following three areas:

**Mechanics**- The study of moving objects including motion under constant acceleration. Systems of forces. Momentum and Impulse.**Statistics -**Analysis of data. Probability. Theoretical probability distributions. The Normal distribution. Simple hypothesis testing. Regression and correlation.**Decision Mathematics**- The study of algorithms to study real-world problems such as the shortest route between two points, profit optimisation, linear programming, critical path analysis, traffic flow and other transportation problems.

Students who are particularly interested in Mathematics and who are wishing to study highly numerate subjects such as Mathematics, Physics, Engineering, Computing and Economics at top universities, can also choose to study a second A level in Mathematics known as Further Mathematics. Students who study this subject will spend half their curriculum time on Mathematics and so a desire to learn and an ability in the subject is required. This is reflected in the excellent results these students achieve with 45.8% obtaining A* grades over the last five years.

Students studying Further Mathematics will complete the standard A level course with an Applied option of Mechanics during the Lower Sixth and then in the Upper Sixth they will study three compulsory modules of Further Pure Mathematics (called FP1 – FP3) and three modules of Mechanics (M3 –M5). There may also be an opportunity to cover one of the Statistics or Decision Mathematics modules as well.

Some students studying Mathematics A level may also be given the opportunity to complete an extra AS in Further Mathematics over the course of their two years in the Sixth Form. This will consist of two Applied Mathematics modules, one from each of the two areas they have not already decided to study, and a compulsory module of Further Pure Mathematics. By studying this extra material, students get the chance to widen their mathematical experience and knowledge without restricting their choices of other subjects across the curriculum.

## Extra-curricular

The Mathematics Department believes that all pupils should be able to think about how to apply their knowledge of mathematical topics to solve problems. All pupils have the chance to take part in the UKMT Mathematics Challenges (All Year 8 and selected Year 7 in the Junior Challenge, all Year 10 and top set Year 9 in the Intermediate Challenge and all Lower Sixth Maths students and any Upper Sixth Maths students who opt to take it in the Senior Challenge). The department also sends teams to the Team Maths Challenge competitions and in 2012/13 our Junior Team qualified for the National Final and our Year 10 team qualified for the Midlands Final, in 2013/14 our Senior Team qualified for the National Final and our Year 10 team won the Midlands Final and in 2015/16, our Senior Team again qualified for the National Final.

## Other

The department organises a Year 6 Team Maths Challenge for local primary schools each November.

The department is an Institutional member of the Mathematical Association and is represented on the UKMT Challenges Committee.