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A-level Mathematics for Year 12 — Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods

  • Job DurationedX
  • Job Duration7 weeks long, 2-4 hours a week
  • Job DurationFree Online Course (Audit)

Project detail


Overview

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.

Syllabus

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

Languages required