# Mathematics

## Head of Faculty:

Mr S Marriott – smarriott@oriel.w-sussex.sch.uk

## KS5 Leader

Mr M Pearce – mpearce19@oriel.w-sussex.sch.uk

## Numeracy Leader

Ms R Angus – bangus2@oriel.w-sussex.sch.uk

## Teaching Staff

Miss C Wilson – cwilson@oriel.w-sussex.sch.uk

Mrs C Hossack – chossack@oriel.w-sussex.sch.uk

Mrs H Freeman – hfreeman@oriel.w-sussex.sch.uk

Mrs C Carter- ccarter@oriel.w-sussex.sch.uk

Mr S Withell – swithell@oriel.w-sussex.sch.uk

Ms D Mayhew – dmayhew@oriel.w-sussex.sch.uk

Miss A Frasi – afrasi@oriel.w-sussex.sch.uk

**“Go down deep enough into anything and you will find mathematics.” ~Dean Schlicter**

The Mathematics teachers at Oriel aim to provide every student in our care with the opportunity to master the fundamentals of number in order that they become abstract thinkers and independent problem solvers. We work closely with other faculties in the school to ensure that skills, knowledge and vocabulary are widely transferable and consistent.

Our curriculum ensures that pupils understand basic concepts thoroughly and then builds on these skills throughout the year so that they gain a cumulative knowledge. We spend longer on topics so that pupils become fluent in them.

Problem-solving is integrated throughout every topic we study. Pupils of all standards are required to select, understand and apply the relevant mathematics principle. They represent concepts mathematical models, objects and pictures, and by making connections between different representations. This gives them the confidence, resilience and ability to tackle any problem rather than repeating routines without grasping the principles.

Lessons are not simply taught from text books, but utilise a wide ranging and varied set of classroom resources, intended to keep the subject interesting and engaging for all. These range from hands on worksheets and appropriate puzzle activities to eLearning resources, including the MyMaths and Mangahigh websites as well as our area on the school Moodle Virtual Learning Environment.

## Key Stage 3 Curriculum

In Year 7, students begin a programme of study tailored specifically to their attainment in year 6. They are put on a pathway that aims to take their existing knowledge and understanding of mathematics and develop them further into abstract thinkers and independent problem solvers.

We work closely with our locality schools to ensure a consistent approach to teaching key concepts as well as ensuring a deep collective understanding of the latest developments in the national curriculum.

## Key Stage 4 Curriculum

In KS4 students are increasingly encouraged to develop good patterns of study and independent learning. Classroom work focuses on guiding students to reach their full potential in Mathematics, and we offer Edexcel entry level examinations and Edexcel Linear GCSE (specification A 1MA0) at both Foundation and Higher levels. For that extra challenge for our more able students we also study the Further Maths GCSE course.

Edexcel GCSE Specification A is a linear course. This means that all examinations are taken at the end of the course, namely in the summer of Year 11. The examination is split into two papers, and the first is a non calculator examination.

Calculators are allowed for the second paper. We recommend the Casio FX85GTPlus which is available in most supermarkets and stationers and online stores.

http://www.edexcel.com/quals/gcse/gcse10/maths/maths-a/Pages/default.aspx

## Key Stage 5 Curriculum

In years 12 and 13 students have the opportunity to study Mathematics AS and A2 level and Further Mathematics AS and A2 level. In Year 12 students study Core 1, Core 2 and Statistics 1. In Year 13 they study Core 3, Core 4 and Decision 1.

If students choose to study Further Mathematics they are required to study another 6 modules. This will include Further Pure 1 and 2, Mechanics 1 and 2, and Statistics 2 and 3.

Year Group: 12 | Topics | Core 1, Core 2 and Statistics 1(Core 1 non-calculator examined January year 12) |

C1 | Algebra and functions | Laws of indices for all rational exponents. Use and manipulation of surds. Quadratic functions and their graphs. The discriminant of a quadratic function. Completing the square. Solution of quadratic equations. Simultaneous equations: analytical solution by substitution. Solution of linear and quadratic inequalities. Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Graphs of functions; sketching curves defined by simple equations. Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations. Effect of simple transformations. |

C1 | Coordinate geometry in the (x, y) plane | Equation of a straight line. Conditions for two straight lines to be parallel or perpendicular to each other. |

C1 | Sequences and series | Sequences, including those given by a formula. Arithmetic series, including the formula for the sum of the first n natural numbers. |

C1 | Coordinate geometry in the (x, y) plane | Equation of a straight line. Conditions for two straight lines to be parallel or perpendicular to each other. |

C1 | Differentiation | The derivative of f(x) as the gradient of the tangent to the graph of y = f (x) at a point; the gradient of the tangent as a limit; interpretation as a rate of change; second order derivatives. Differentiation of xn, and related sums and differences. Applications of differentiation to gradients, tangents and normals. |

C2 | Integration | Indefinite integration as the reverse of differentiation. Integration of xn. |

C2 | Coordinate geometry in the (x, y) plane | Coordinate geometry of the circle using the equation of a circle. |

C2 | Sequences and series | The sum of a finite geometric series; the sum to infinity of a convergent geometric series. Binomial expansion of (1+ x)n for positive integer n. |

C2 | Trigonometry | Sine and cosine rules, and the area of a triangle in the form 1/2ab sin C. Radian measure, including use for arc length and area of sector. Sine, cosine and tangent functions. Their graphs, symmetries and periodicity. Knowledge and use of tan x¸ = sin x¸/cos x¸, and sin^{2}x¸ + cos^{2}x¸ = 1. Solution of simple trigonometric equations in a given interval. |

C2 | Exponentials and logarithms | y = ax and its graph. Laws of logarithms The solution of equations of the form ax = b. |

C2 | Integration | Evaluation of definite integrals. Interpretation of the definite integral as the area under a curve. Approximation of area under a curve using the trapezium rule. |

C3 | Algebra and functions | Simplification of rational expressions including factorising and cancelling, and algebraic division. Definition of a function. Domain and range of functions. Composition of functions. Inverse functions and their graphs. The modulus function. Combinations of transformations. |

S1 | Representation and summary of data | Histograms, stem and leaf diagrams, box plots. Measures of location — mean, median, mode. Measures of dispersion — variance, standard deviation, range and interpercentile ranges. Skewness. Concepts of outliers. |

S1 | Probability | Elementary probability. Sample space. Exclusive and complementary events. Conditional probability. Sum and product laws. Use of tree diagrams and Venn diagrams. Sampling with and without replacement. |

S1 | Correlation and regression | Scatter diagrams. Linear regression. Explanatory (independent) and response (dependent) variables. Applications and interpretations. The product moment correlation coefficient, its use, interpretation and limitations. |

S1 | Discrete and Random Variables | The concept of a discrete random variable. The probability function and the cumulative distribution function for a discrete random variable. Mean and variance of a discrete random variable. The discrete uniform distribution. The mean and variance of this distribution. |

S1 | The Normal Distribution | The Normal distribution including the mean, variance and use of tables of the cumulative distribution function. |

Year 13: | Topics | Core 3, Core 4 and Decision 1(Core 3 examined January Year 13) |

C3 | Trigonometry Exponentials and logarithms | Knowledge of secant, cosecant and cotangent and of arcsin, arccos and arctan. Their relationships to sine, cosine and tangent. Understanding of their graphs and appropriate restricted domains. Knowledge and use of double angle formulae; use of formulae for sin (A ± B), cos (A ± B) and tan (A ± B). The function ex and its graph. The function ln x and its graph; ln x as the inverse function of ex. |

C3 | Differentiation Numerical methods | Differentiation of ex, ln x, sin x, cos x, tan x and their sums and differences. Differentiation using the product rule, the quotient rule and the chain rule. The use of dy/dx = 1/(dx/dy)Location of roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x in which f(x) is continuous. Approximate solution of equations using simple iterative methods, including recurrence relations of the form xn+1 = f(xn). |

C4 | Algebra and functions. Coordinate geometry in the (x, y) plane. Sequences and series | Rational functions. Partial fractions (denominators not more complicated than repeated linear terms). Parametric equations of curves and conversion between Cartesian and parametric forms. Binomial series for any rational n. |

C4 | Differentiation and Integration | Differentiation of simple functions defined implicitly or parametrically. Exponential growth and decay. Formation of simple differential equations. Integration of ex, 1/x , sinx, cosx. Evaluation of volume of revolution. Simple cases of integration by substitution and integration by parts. These methods as the reverse processes of the chain and product rules respectively. Simple cases of integration using partial fractions. Â Analytical solution of simple first order differential equations with separable variables. Numerical integration of functions. |

C4 | Vectors | Vectors in two and three dimensions. Â Magnitude of a vector. Algebraic operations of vector addition and multiplication by scalars, and their geometrical interpretations.ÂPosition vectors. The distance between two points. Vector equations of lines. The scalar product. Its use for calculating the angle between two lines. |

D1 | Algorithms | The general ideas of algorithms and the implementation of an algorithm given by a flow chart or text. Bin packing, bubble sort, quick sort, binary search. |

D1 | Algorithms on graphs | The minimum spanning tree (minimum connector) problem. Prim’s and Kruskal’s (greedy) algorithm. Dijkstra’s algorithm for finding the shortest path. |

D1 | The route inspection problem (Chinese Postman) | Algorithm for finding the shortest route around a network, travelling along every edge at least once and ending at the start vertex. The network will have up to four odd nodes. |

D1 | Critical Path Analysis | Modelling of a project by an activity network, from a precedence table. Completion of the precedence table for a given activity network. Algorithm for finding the critical path. Earliest and latest event times. Earliest and latest start and finish times for activities. Total float. Gantt (cascade) charts. Scheduling. |

D1 | Linear Programming | Formulation of problems as linear programs. Graphical solution of two variable problems using ruler and vertex methods. Consideration of problems where solutions must have integer values. |

D1 | Matchings | Use of bipartite graphs for modelling matchings. Complete matchings and maximal matchings. Algorithm for obtaining a maximum matching. |

http://www.edexcel.com/quals/gce/gce08/maths/Pages/default.aspx

## Useful Study links

Every student will have been given a log in for the mymaths website www.mymaths.co.uk

**We have subscriptions with the following sites which have useful links and work sheets to help students with their maths **

**http://justmaths.co.uk/online/**

**We also suggest that students use these links as well to further**** their understanding**

**http://www.examsolutions.net/maths-revision/syllabuses/Edexcel/period-1/specification.php**