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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.

Engage in practical and experimental activities in order to appreciate principles of probability. There is no coursework

unit overview 

Subject: Units 1 - 4:  Algebra and Functions

Skills

  • Understand and use the laws of indices for all rational exponents.
  • Use and manipulate surds, including rationalising the denominator.
  • Work with quadratic functions and their graphs.
  • The discriminant of a quadratic function, including the conditions for real and repeated roots.
    Completing the square.
  • Solution of quadratic equations, including solving quadratic equations in a function of the unknown.
  • Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.
  • Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions.
  • Express solutions through correct use of ‘and’ and ‘or’, or through set notation.
    Represent linear and quadratic inequalities such as y > x + 1 and y > ax2 + bx + c graphically.
  • Manipulate polynomials algebraically, including expanding brackets, collecting like terms and factorisation and simple algebraic division; use of the factor theorem.
  • Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, y =  and y =  (including their vertical and horizontal asymptotes).
  • Interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations.
  • Understand the effect of simple transformations on the graph of y = f(x) including sketching associated graphs:
    • y = af(x),   y = f(x) + a,   y = f(x + a),  y = f(ax) .

Knowledge

By the end of the unit, students should:

  • be able to perform essential algebraic manipulations, such as expanding brackets, collecting like terms, factorising etc;
  • understand and be able to use the laws of indices for all rational exponents;
  • be able to use and manipulate surds, including rationalising the denominator.
  • be able to solve a quadratic equation by factorising;
  • be able to work with quadratic functions and their graphs;
  • know and be able to use the discriminant of a quadratic function, including the conditions for real and repeated roots;
  • be able to complete the square. e.g. ;
  • be able to solve quadratic equations, including in a function of the unknown.
  • be able to solve linear simultaneous equations using elimination and substitution;
  • be able to use substitution to solve simultaneous equations where one equation is linear and the other quadratic.
  • be able to solve linear and quadratic inequalities;
  • know how to express solutions through correct use of ‘and’ and ‘or’ or through set notation;
  • be able to interpret linear and quadratic inequalities graphically;
  • be able to represent linear and quadratic inequalities graphically.
  • understand and use graphs of functions;
  • be able to sketch curves defined by simple equations including polynomials;
  • be able to use intersection points of graphs to solve equations.
  • understand the effect of simple transformations on the graph of y = f(x);
  • be able to sketch the result of a simple transformation given the graph of any function y = f(x).

Rationale

Algebra is the basis of all higher mathematics. It allows for mathematics to be done with variables in place of numerical values, and so allows for solving and the expression of relationships with regard to these variables. In addition, it is often quicker for more complicated numerical problems to be solved algebraically instead. Algebra has many applications over a wide range of fields. For instance, it is utilised in finance, chemistry, physics and environmental science.

In particular, functions are defined by a process that changes an input into an output. Functions are widely used in all aspects of engineering and control theory, where transfer functions define the manufacturing or production process.

Algebra also develops modelling, logic, and rationalisation skills. These can be widely applied to other areas that do not have a direct application of algebra.

knowledge organisers

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.