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

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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.

What you will 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

Skills you learn

• Basic Math
• Language Construct
• Applied Mathematics

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

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 4Coordinate 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

Auto Summary

Achieve A* in A-level Maths with this 12-week course focusing on algebraic methods, graphs, and applied mathematics. Ideal for Year 12 students aiming for STEM degrees, it builds thinking skills, fluency, and confidence. Offered by edX, with professional and starter subscription options.