This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level further 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 eight modules, you will be introduced:
Your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A-level further mathematics course. You’ll also, be encouraged to consider how what you know fits into the wider mathematical world.
How to find the determinant of a complex number without using a calculator and interpret the result geometrically.
How to use properties of matrix determinants to simplify finding a determinant and to factorise determinants.
How to use a 3 x 3 matrix to apply a transformation in three dimensions
How to find the inverse of a 3 x 3 matrix without using a calculator.
How to prove series results using mathematical induction.
How to prove divisibility by mathematical induction.
How to prove matrix results by using mathematical induction.
How to use the chain, product and quotient rules for differentiation.
How to differentiate and integrate reciprocal and inverse trigonometric functions.
How to integrate by inspection.
How to use trigonometric identities to integrate.
How to use integration methods to find volumes of revolution.
How to use integration methods to find the mean of a function.
How to express functions as polynomial series.
How to find a Maclaurin series.
How to use standard Maclaurin series to define related series.
How to use De Moivre’s Theorem.
How to use polar coordinates to define a position in two dimensional space.
How to sketch the graphs of functions using polar coordinates.
How to define the hyperbolic sine and cosine of a value.
How to sketch graphs of hyperbolic functions.
How to differentiate and integrate hyperbolic functions.
Module 1: Matrices - The determinant and inverse of a 3 x 3 matrix
Module 2: Mathematical induction
Module 3: Further differentiation and integration
Module 4: Applications of Integration
Module 5: An Introduction to Maclaurin series
Module 6: Complex Numbers: De Moivre's Theorem and exponential form
Module 7: An introduction to polar coordinates
Module 8: Hyperbolic functions
* Differentiating and integrating hyperbolic functions
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