## Mathematics - Key Stage 4

The Mathematics department offers three qualifications at Key Stage 4.

- IGCSE Mathematics
- GCSE Statistics
- Free Standing Mathematics Qualification (FSMQ) Additional Mathematics

All students complete the Edexcel IGCSE Mathematics course. This course is broader and has a higher algebraic component, enabling us to prepare the students more effectively for further study of mathematics as the majority of students choose to study the subject at A level.

The Statistics GCSE qualification is available to sets 2, 3 and 4. This course runs alongside the IGCSE Mathematics course and in many instances overlaps it. This course enables students to further enhance their mathematical skills and help with the interpretation and manipulation of data in coursework and in other subject areas.

The FSMQ Addition Mathematics qualification is only available to the Fast Track group and is specially written for those students who are successful in taking the IGCSE Mathematics course early. Students will complete the FSMQ in year 11 as a stand alone subject having already completed the IGCSE Mathematics course in year 10.

## IGCSE Mathematics

The IGCSE Mathematics qualification is a two year course which is a recognised internationally. The qualification is assessed at the end of the course with all candidates taking two examinations, which are each two hours long. All students are entered for the higher tier with grades A*, A, B, C, or D available.

The course is structured into five main units:

- Number
- Algebra
- Graphs and Sequences
- Shape and Space
- Handling Data

### Year 10

Module | Contents |
---|---|

Number | Number 1: Simplifying fractions; Percentages; Standard form; Signifcant figures. Number 2: Standard form with negative indices; Four rules of fractions; Ratio; Direct proportion. Number 3: Compound percentages; Multiples, factors and primes; Highest Common Factor (HCF); Lowest Common Multiple (LCM). Number 4: Inverse percetages; Rounding; Upper and lower bounds; Estimating. Number 5: Proportion; Positive indices; Recurring decimals. |

Alegbra | Algebra 1: Simplifying algebraic equations; Solving linear equations; Standard form; Signifcant figures. Algebra 2: Simplifying fractions; Solving equations; Positive integer indices, Inequalities. Algebra 3: Simple factorising; Equations with fractions; Simultaneous equations. Algebra 4: Changing subject; Using formulae. Algebra 5: Multiplying brackets; Factorising quadratic equations; Solving quadratic equations by factorisation; Problems leading to quadratic equations. |

Graphs & Sequences | Graphs 1: Gradient of a straight line; Straight line graphs. Graphs 2: Simultaneous equations; Inequalities. Graphs 3: Travel graphs. Graphs 4: Drawing quadratic graphs; Solving quadratics graphically. Sequences 5: Finding a formula for a sequence (nth term). |

Shape & Space | Shape & Space 1: Basic principles, Constructions; Loci. Shape & Space 2 & 3: Trigonometric ratios; Inequalities. Shape & Space 4: Circles; Similar triangles; Pythagoras' Theorem. Shape & Space 5: Transformations; Combining transformations; Englargement. |

Handling Data | Handling Data 1: Venn diagrams. Handling Data 2: Statistical investigation; Collecting data; Frequencey tables; Averages; Displaying data. Handling Data 3: Extending frequency tables into calculation tables. Handling Data 4: Probability Handling Data 5: Distributions; Quartiles; Measures of spread; Cumulative frequency. |

### Year 11

Module | Contents |
---|---|

Number | Number 1: Inverse proportion; Recurring decimals. Number 2: Negative and fractional indices. Number 3: Financial arithmetic. Number 4: Irrational numbers; Surds. Number 5: Directed numbers; Standard forms; Recurring decimals; Percentages; Ratio. |

Alegbra | Algebra 1: Proportion. Algebra 2: Solving quadratic equations; Problems leading to quadratic equations. Algebra 3: Solving two simultaneous equations - one linear and one non-linear; Functions. Algebra 4: Algebraic fractions; Equations with fractions. Algebra 5: Algebraic manipulation; Formulae; Linear equations; Inequalities. |

Graphs & Sequences | Graphs 1: Cubic graphs; Reciprocal graphs. Graphs 2: Using graphs to solve equations; Inequalities. Graphs 3 & 4: Differentiation; Tangents; Turning points; Motion of a particle in a straight line. Sequences 5: Straight line graphs; Distance/speed time graphs; Sequences; Gradients of curves. |

Shape & Space | Shape & Space 1: Congruents; Circles; Intersecting chords and tangents. Shape & Space 2: Converting measurements; Circles, semicircles and quadrants; Surface areas and volumes of solids; Areas of similar shapes; Volumes of similar shapes. Shape & Space 3: Vectors; Vector geometry. Shape & Space 4: Trigonometric ratios for angles upto 180° Sine and Cosine rule; Area of a non-right angled triangle; 3D trigonometry. Shape & Space 5: Compass constructions; Transformations; Circle theorems; Graphs of Sin, Cos and Tan; Arcs, sectors and segments; Vectors. |

Handling Data | Handling Data 1: Problems involving sets; Identifying sets by shading; Set-builder notation. Handling Data 2, 3 & 4: Compound probability; Histograms; More probability. Handling Data 5: Sets; Probability; Handling data; Histograms; Cumulative frequency. |

The above topics are returned to on numerous occasions during the IGCSE course and students are assessed on a regular basis.

## GCSE Statistics

The GCSE Statistics qualification offers a course of study which complements the IGCSE in Mathematics, and provides a background for the study of statistics at A level. It is based on good practice in statistics, emphasising the theoretical, practical and applied nature of the subject. Most of our students go on to university and would be expected to undertake some form of research, following this statistics course should enable them to be better prepared to undertake this research and interpret the outcomes.

The GCSE Statistics course is structured into four main branches of study:

- Planning and data collection
- Processing, representing and analysing data
- Reasoning, interpreting and discussing results
- Probability

Module | Contents |
---|---|

The Collection of Data | Types of data; Collecting data; Sampling; Questionnaires, Experimental design; Accuracy; Presentation of data; Bivariate data. |

Representing and Processing | Discrete Data: Tally charts and frequency tables; Grouping data; Two-way tables; Pictograms; Bar charts and vertical line graphs; Pie charts, Stem and leaf diagrams. Continuous Data: Frequency tables for continuous data; Rounded data; Frequency polygons; Histograms; Stem and leaf; Population pyramids; Using line graphs to predict trends; Choropleth maps. |

Summarising Data | Mode, median and mean; Transformations; The weighted and geometric mean; Index numbers, Range, quartiles and percentiles; Using a cumulative frequency polygon; Variance and standard deviation; Standardised scores; The normal distribution. |

Scatter Diagrams & Time Series | Scatter Diagrams: Scatter diagrams; Recognising correlation; Causal relationships; Using scatter diagrams and lines of best fit; Using ICT to plot scatter diagrams and lines of best fit; Fitting a line of best fit to a non-linear model of the form y = ax^{n} + b and y = ka^{x}; Spearman's rank correlation coefficient. Time Series: Line graphs, time series and trend lines; Variations in a time series; Moving averages; Estimating seasonal variations; Making predictions; Calculating the equation of a trend line; Quality assurance. |

Probability | Probability: The probability of an event; Experimental probability; Sample space, Venn diagrams; Mutually exclusive outcomes; Exhaustive events; The multiplication law for independent events; Conditional probability. Probability of Distributions: Probability distributions; The discrete uniform distribution; The bonomial distribution; Normal distributions; Standard deviation of a normal distribution; Variance of a normal distribution. |

The assessment is by one 2 hour examination worth 75% and one piece of controlled assessment worth 25%. The examination will take place at the end of Year 11 and the controlled assessment will be completed in the autumn term of Year 11.

## Free Standing Mathematics Qualification (FSMQ) Additional Mathematics

This course provides candidates with an introduction to the Mathematics studied in AS and A Level GCE modules. It is designed for those students who have taken Higher IGCSE in year 10 and who wish to pursue the study of mathematics further. As an advanced level qualification FSMQ Additional mathematics carries UCAS points.

The content consists of four areas in Pure Mathematics:

- Algebra
- Co-ordinate Geometry
- Trigonometry
- Calculus

Module | Contents |
---|---|

Algebra | Review: Linear expressions; Solving linear equations; Changing the subject of an equation; Quadratic expressions; Solving a quadratic equation that factorises; Completing the square; Simultaneous equations. Techniques: Linear inequalities; Solcing quadratic inequalities; Manipulating algebraic fractions; Solving equations involving fractions; Simplifying expressions containing square roots. Polynomials: Operations with polynomials; The factor theorem; The remainder theorem. Applications: The binomial expansion; The binomial distribution. |

Coordinate Geometry | Coordinate Geometry: Parallel and perpendicular lines; The distance between two points; Midpoint of a line joining two points; The equation of a straight line; Drawing a line given its equation; Finding the equation of a line; Intersection of two lines; The circle. Applications: Inequalities; Using inequalities for problem solving. |

Trigonometry | Trigonometry: Using trigonometry in right-angled triangles; Trigonometrical functions for angles of any size; Solving trigonometrical equations; Identities involving Sin, Cos and Tan; The Sine and Cosine rules. Applications: Application of the Sine and Cosine rules in 2D; Height and distance problems in 3D; 3D problems involving solids. |

Calculus | Differentiation: Finding the gradient of a curve; Differentiating by using standard results; Tangents and normals; Stationary points; Curve sketching. Integration: Reversing differentiation; Using integration to find areas. Applications to Kinematics: Variable acceleratin problems; The formulae for constant acceleration. |

The assessment is by a single 2 hour examination in the summer of each year, with grades A, B, C, D or E available. There is no coursework.