### 你将学到什么

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

### 课程概况

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.

### 课程大纲

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

### 预备知识

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