Mathematics

Introduction

Maths is a vital part of a student's education and here at Northolt we have a thriving department which operates across Key Stages 3, 4 and 5.

Key Stage 3

The Key Stage 3 Maths course aims to build upon the foundations laid at primary school whilst fostering a love for the subject as students approach their GCSE course.

With the course split into Number, Algebra, Stats, Geometry and Probability there is something for everybody. Students consolidate the skills they have already gained at the same time as they discover Maths that they have never seen before.

We look to engage students in problem solving and puzzle activities.

YEAR 7

Here in the Northolt Maths Department we are strong believers in the spiral curriculum model. This is the idea that, rather than, for example, studying geometry to a high level before beginning algebra, students should cover all areas of maths every academic year and, ideally, every term.

First the basics of each topic are covered before each area is then revisited again and again throughout a student's school career, each time reviewing what was learnt the last time before then taking the next step within that topic. As such, year 7 students will be able to reach new heights in maths whilst still being able to relate their learning to what they studied during Key Stages 1 and 2.

YEAR 8

The spiral curriculum approach is, of course, carried forward into year 8 where we aim to ensure that students have all the building blocks required to tackle the GCSE course. Year 8 also sees a greater focus on problem solving using the myriad skills developed and attained in year 7.

Key Stage 4

Edexcel GCSE Mathematics (1MA1)

A pass in GCSE Mathematics will keep open the doors to whatever you want to achieve in life. On top of this, the syllabus enables you to see how maths can be and is used in the everyday situations you face outside of school.

The current GCSE was launched in 2015 and was first examined in the summer of 2017. The new exams look to build and assess the logic and problem-solving skills that will enable students to learn complex skills and deal with challenging situations. Questions are set in contexts that students will see in the real world such as decorating a room or designing a garden; or perhaps paying bills or sorting out rotas for shop staff.

The content of our GCSE Mathematics specifications has been grouped into the topic areas of Number, Algebra, Geometry, Statistics and Probability.

In comparison to it's predecessor, the course places a renewed emphasis on problem solving, functionality and mathematical thinking.

GCSE Mathematics is vital for getting into Sixth Form, College or employment. If you achieve a grade 6 or above you can also study Maths at A level, which will give you the opportunity to explore maths further and to follow a number of fascinating degree courses at top universities.

It is now statutory that a student must remain in education until the age of 18 if they have not acquired at least a grade 4 in Maths and English.

YEAR 9

From the beginning of Year 9 we dive straight into the GCSE material. The topics at the beginning of the course are not necessarily easier than those covered in Years 10 and 11. We believe that it is good for students to be exposed to the harder material as early as possible so that they can master it over an extended period of time.

The units covered in Year 9 are:

  • 1a. Calculations, checking and rounding
  • 1b. Indices, roots, reciprocals and the hierarchy of operations
  • 1c. Factors, multiples and primes
  • 1d. Standard form and surds
  • 2a. Algebra: the basics
  • 2b. Setting up, rearranging and solving equations.
  • 2c. Sequences
  • 3a. Averages and range
  • 3b. Representing and interpreting data
  • 3c. Scatter graphs
  • 4a. Fractions
  • 4b. Percentages
  • 4c. Ratio and proportion
  • 5a. Polygons, angles and parallel lines
  • 5b. Pythagoras' theorem and trigonometry
  • 6a. Graphs: the basics and real-life graphs

    YEAR 10

    Our aim in Year 10 is to finish the year in a position where each student is almost ready to sit their GCSE and perform well. In order to reach this goal we get through the bulk of the course by the end of year 10 and ensure that throughout the year students are being thoroughly assessed on their learning so teachers and students are aware of precisely where the gaps lie in student understanding and knowledge.

    The units covered in Year 10 are:
  • 6b. Linear graphs and coordinate geometry
  • 6c. Quadratic, cubic and other graphs
  • 7a. Perimeter, area and circles
  • 7b. 3D forms and volume, cylinders, cones and spheres
  • 7c. Accuracy and bounds
  • 8a. Transformations
  • 8b. Constructions, loci and bearings
  • 9a. Solving quadratic and simultaneous equations
  • 9b. Inequalities
  • 10. Probability
  • 11. Multiplicative reasoning
  • 12. Similarity and congruence in 2D and 3D
  • 13a. Graphs of trigonometric functions
  • 13b. Further trigonometry

YEAR 11

In Year 11 we cover all remaining material by the end of the Autumn term at the same time as thoroughly preparing our students for the conditions they will face during their GCSE exams. This includes two periods of Pre-Public Examinations (PPEs): one in November and the second in March.

The units covered in year 11 are:

  • 14a. Collecting data
  • 14b. Cumulative frequency, box plots and histograms
  • 15. Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics
  • 16a. Circle theorems
  • 16b. Circle geometry
  • 17. Changing the subject of complex formulae, algebraic fractions, rationalising surds and algebraic proof
KS4 Assessment & Examinations
The new GCSE follows the two-tier model introduced in 2006: Foundation tier, where grades 1 up to 5 may be achieved, and Higher tier, where grades 3 up to 9 are possible.

The course is assessed entirely by written examination, which means that no coursework will be expected from any student.

All 3 papers are taken at the end of the course (usually, but not always, at the end of Year 11) and any part of the specification can be tested on any paper. Paper 1 is a non-calculator exam whereas calculators are permitted for papers 2 and 3.

Key Stage 5

Mathematics is the study of Quantity (Numbers), Structure (Algebra), Space (Geometry), and Change (Calculus). In mathematics we use patterns to formulate new conjectures (conclusions), and then prove the truth or falsity of these new conjectures using mathematical proof. In fact when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

Pure Mathematics is the study of abstract entities with respect to their intrinsic nature. One central concept in pure mathematics is the idea of generality, where generality can facilitate connections between different branches of mathematics.

Mechanics is an area of science concerned with the behaviour of physical bodies when subjected to forces or displacements; it is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light.

Statistics is the study of the collection, analysis, interpretation, presentation, and organisation of data; it deals with all aspects of data ncluding the planning of data collection in terms of the design of surveys and experiments.

YEAR 12

Year 12 is fantastically refreshing for students as for the first time in maths lessons they find themselves surrounded solely by peers who have a passion for maths. We first ensure that all gaps in understanding from GCSE are filled before studying a range topics structured into the following units:

Pure Maths

  • 1. Algebraic Expressions
  • 2. Quadratics
  • 3. Equations and Inequalities
  • 4. Graphs and Transformations
  • 5. Straight Line Graphs
  • 6. Circles
  • 7. Algebraic Methods
  • 8. The Binomial Expansion
  • 9. Trigonometric Ratios
  • 10. Trigonometric Identities and Equations
  • 11. Vectors
  • 12. Differentiation
  • 13. Integration
  • 14. Exponentials and Logarithms

Statistics

  • 1. Data Collection
  • 2. Measures of Location and Spread
  • 3. Representations of Data
  • 4. Correlation
  • 5. Probability
  • 6. Statistical Distributions
  • 7. Hypothesis Testing

Mechanics

  • 1. Modelling in Mechanics
  • 2. Constant Acceleration
  • 3. Forces and Motion
  • 4. Variable Acceleration

There are no public exams at the end of year 12 unless students wish to complete only an AS level rather than the full A level.

YEAR 13

In Year 13 students prepare for their exams and build on their learning from year 12. The course is structured into the following units:

Pure Maths

  • 1. Algebraic Methods
  • 2. Functions and Graphs
  • 3. Sequences and Series
  • 4. Binomial Expansion
  • 5. Radians
  • 6. Trigonometric Functions
  • 7. Trigonometry and Modelling
  • 8. Parametric Equations
  • 9. Differentiation
  • 10. Numerical Methods
  • 11. Integration
  • 12. Vectors

Statistics

  • 1. Regression, Correlation and Hypothesis Testing
  • 2. Conditional Probability
  • 3. The Normal Distribution

Mechanics

  • 1. Moments
  • 2. Forces and Frictions
  • 3. Projectiles
  • 4. Applications of Forces
  • 5. Further Kinematics
KS5 Assessment & Examinations
The course is assessed with 3 exams at the end of year 13. Papers 1 and 2 are on Pure Maths and Paper 3 is split into Section A on Statistics and Section B on Mechanics. All 3 papers are equally weighted and a calculator can be use for all papers.

Extra Curricular Opportunities

Every year across the year groups we enter students into the United Kingdom Mathematics Trust (UKMT) Maths Challenges at Junior, Intermediate and Senior levels. Students revel in the problem solving style of questions and enjoy the out-of-lesson support they receive to prepare for the challenge. Each year students receive a range of Bronze, Silver and Gold certificates and it is always exciting when students are asked to take part in the next level up: The European Maths Challenge!