A-Level Further Mathematics for Year 12 - Course 2: 3 x 3 Matrices, Mathematical Induction, Calculus Methods and Applications, Maclaurin Series, Complex Numbers and Polar Coordinates
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Brief Introduction
Develop your thinking skills, fluency and confidence in A-level further maths and prepare for undergraduate STEM degrees.
Description
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:
- 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 eight modules, you will be introduced:
- The determinant and inverse of a 3 x 3 matrix
- Mathematical induction
- Differentiation and integration methods and some of their applications
- Maclaurin series
- DeMoivre’s Theorem for complex numbers and their applications
- Polar coordinates and sketching polar curves
- Hyperbolic functions
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.
Knowledge
- 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.
A-Level Further Mathematics for Year 12 - Course 2: 3 x 3 Matrices, Mathematical Induction, Calculus Methods and Applications, Maclaurin Series, Complex Numbers and Polar Coordinates
- 0.0
-
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Develop your thinking skills, fluency and confidence in A-level further maths and prepare for undergraduate STEM degrees. These skills include: Over eight modules, you will be introduced:...
