### About this course

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:

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.

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.

### 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

**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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