Course description
A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods
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.
Upcoming start dates
1 start date available
Training content
Syllabus
Module 1Indices 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
- 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
- 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
- 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
- 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
- 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
- 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
Course delivery details
This course is offered through Imperial College London, a partner institute of EdX.
2-4 hours per week
Costs
- Verified Track -$49
- Audit Track - Free
Certification / Credits
What you'll learn
- 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
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