# A-level Further Mathematics for Year 12 - Course 1

## Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors

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 to

complex numbers, their modulus and argument and how they can be represented diagrammatically

matrices, their order, determinant and inverse and their application to linear transformation

roots of polynomial equations and their relationship to coefficients

series, partial fractions and the method of differences

vectors, their scalar produce and how they can be used to define straight lines and planes in 2 and 3 dimensions.

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.

What you'll learn

- 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
- matrices, their order, determinant and inverse and their application to linear transformation
- roots of polynomial equations and their relationship to coefficients
- series, partial fractions and the method of differences
- vectors, their scalar produce and how they can be used to define straight lines and planes in 2 and 3 dimensions.
- The definition of a complex number
- Solving simple quadratic equations
- Addition, subtraction and multiplication of complex numbers
- Complex conjugates and division of complex numbers
- Radian measure
- Representing complex numbers on the Argand diagram
- Addition and subtraction of conformable matrices
- Matrix multiplication
- The identity matrix
- Matrix transformations in 2 and 3 dimensions
- Invariant lines and lines of invariant points
- The relationship between roots and coefficients in a polynomial equation
- Forming a polynomial equation whose roots are a linear transformation of the roots of another polynomial equation
- Writing complex numbers in modulus argument form
- square matrix.
- The inverse of a
- square matrix
- Using matrices to solve simultaneous equations (5)
- The geometrical interpretation of the solution of a system of equations
- Separating algebraic fractions into partial fractions
- The method of differences
- Partial fractions and method of differences
- The vector and Cartesian forms of an equation of a straight line in 2 and 3 dimensions
- Solving geometrical problems using vector equations of lines
- The dot product and the angle between two lines
- The vector equation of a plane
- Solving geometrical problems with lines and planes using vectors
- The intersection of a line and a plane
- Perpendicular distance from a point to a plane

## Get a Reminder

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Length | 7 weeks |

Effort | 2 - 4 hours per week |

Starts | On Demand (Start anytime) |

Cost | $49 |

From | Imperial College London via edX |

Instructors | Philip Ramsden, Phil Chaffe |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

## Get a Reminder

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Rating | Not enough ratings |
---|---|

Length | 7 weeks |

Effort | 2 - 4 hours per week |

Starts | On Demand (Start anytime) |

Cost | $49 |

From | Imperial College London via edX |

Instructors | Philip Ramsden, Phil Chaffe |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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