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Mathematics

 

SUBJECT overview

Mathematics can be applied in practical tasks, real life problems and within mathematics itself. The aim of the course is to develop mathematical vocabulary, improve mental calculation and use a range of methods of computation and apply these to a variety of problems.

The course of study should help you whether working individually or collaboratively to reason logically, plan strategies and improve your confidence in solving complex problems.

During Maths lessons you will learn how to:-

  • Use and apply maths in practical tasks, real life problems and within mathematics itself.
  • Develop and use a range of methods of computation and apply these to a variety of problems.
  • Develop mathematical vocabulary and improve mental calculation.
  • Consider how algebra can be used to model real life situations and solve problems.
  • Explore shape and space through drawing and practical work using a range of materials and a variety of different representations.
  • Use statistical methods to formulate questions about data, represent data and draw conclusions.

Unit overview

Subject: Unit 1 (Part 1):   Algebraic and partial fractions

Skills

  • Simplify rational expressions including by factorising and cancelling, and algebraic division (by linear expressions only).
  • Decompose rational functions into partial fractions (denominators not more complicated than squared linear terms and with no more than 3 terms, numerators constant or linear).

Knowledge

By the end of the unit, students should:

  • be able to add, subtract, multiply and divide algebraic fractions;
  • know how to use the factor theorem to shown a linear expression of the form  is a factor of a polynomial;
  • know how to use the factor theorem for divisors of the form ;
  • be able to simplify algebraic fractions by fully factorising polynomials up to cubic.
  • be able to split a proper fraction into partial fractions;
  • be able to split an improper fraction into partial fractions, dividing the numerator by the denominator (by polynomial long division or by inspection).

Rationale

Algebraic manipulation is a key skill in any further mathematical studies, as well as fields that make frequent use of mathematical models. This includes finance, economics, engineering, and most forms of science.

Algebraic and partial fractions is an important part of this algebraic manipulation toolkit.

Being able to split and simplify fractions can in turn reduce complicated fractional functions into much easier to solve in implement mathematical models, which can be introduced into

Full models linearly in sections rather than all at once.

In the field of computer programming (or applied programming to finance or science) it is essential to be able to individually test and isolate different parts of the function. This can be achieved through partial fractions.

knowledge Organiser

A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and A-Level exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments, and calculations.

We encourage all pupils to use them by doing the following:

  • Quiz themselves at home, using the read, write, cover, check method.
  • Practise spelling key vocabulary
  • Further researching people, events and processes most relevant to the unit.