A-level Mathematics forYear 12 - Course 1:Algebraic Methods, Grap

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This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level maths exams.

You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:

  • Fluency - selecting and applying correct methods to answer with speed and efficiency
  • Confidence - critically assessing mathematical methods and investigating ways to apply them
  • Problem solving - analysing the unfamiliar' and identifying which skills and techniques you require to answer questions
  • Constructing mathematical argument - using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others
  • Deep reasoning - analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied

Over seven modules, your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A
-level course. You'll also be encouraged to consider how what you know fits into the wider mathematical world.

Program Benefits


  • Improve fluency and accuracy when using laws of indices and surds in a variety of calculations
  • Learn how to solve the types of inequalities you'll encounter at A-level and various ways to represent these
  • Discover how to divide any polynomial by either a linear or quadratic polynomial
  • Learn about the information found in different forms of the Cartesian equation of a circle and use these to solve coordinate geometry problems
  • Investigate the main transformations of graphs; translation, enlargement and reflection, and use these transformations to sketch new graphs
  • Understand the constant acceleration formulae through travel graphs illustration, speed, velocity, distance and displacement against time
  • Explore statistical sampling methods and weigh up the advantages and disadvantages of each one
  • Learn how to interpret data presented in a variety of forms including box plots, cumulative frequency curves, histograms and bar charts


Philip Ramsden

*Program faculty is subject to change


Module 1  Indices and Surds
  • Recognise and use the laws of indices for all rational exponents
  • Use and manipulate surds, including rationalising the denominator
  • Solve a variety of problems that include surds and indices
Module 2  Inequalities
  • Solve linear and quadratic inequalities in a single variable and interpret these solutions graphically
  • Express the solutions to linear and quadratic inequalities usingnumber lines and inequality notation, and using the terms ‘and'and ‘or'and set notation
  • Represent linear and quadratic inequalities in two variables graphically, using standard A-level conventions
Module 3  The Factor Theorem & Algebraic Division
  • Manipulate polynomials algebraically, using the factor theorem to write a polynomial as the product of linear factors or a combination of linear and quadratic factors
  • Divide one polynomial by another of a lower order by equating coefficients
Module 4  Coordinate Geometry 
  • Solve problems using the coordinate geometry of the circle
  • Complete the square to find the centre and radius of a circle from its equation
  • Solve problems using the properties of the angle in a semicircle, the perpendicular from the centre to a chord, and a tangent from a poin
Module 5  Graphical Transformation and Curve Sketching
  • Use curve sketching techniques based on the the shapes and symmetries of standard curves
  • Identify key features of a curve from its equation and transform the equations of linear, quadratic, rational and trigonometrical curves using translations, rotations and stretches
  • Use knowledge of the symmetry and asymptotes of standard curves to create sketches
Module 6  An Introduction to Mechanics
  • Interpret and accurately use the term distance, speed, displacement, velocity, and acceleration
  • Interpret graphs to do with speed against time, distance against time, velocity against time and acceleration against time, and solve problems involving motion in a straight line with constant acceleration
  • Apply the formulae for constant acceleration to solve problems involving motion in a straight line
Module 7  An Introduction to Statistics
  • Identify the ideas of a population and a sample and use simple sampling techniques to draw informal inferences about populations
  • Apply critical thinking to issues of representative sampling
  • Interpret histograms to draw informal inferences about univariate data
  • Interpret scatter diagrams, regression lines and the ideas of correlation to draw informal inferences about bivariate data


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