A-level Mathematics for Year 13 - Course 1: Functions, Sequences and Series, and Numerical Methods
Imperial College London via edX
Overview
This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level maths exams.
The course is most appropriate to the Edexcel, AQA, OCR and OCR(MEI) papers. 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:
You’ll also be encouraged to consider how what you know fits into the wider mathematical world.
The course is most appropriate to the Edexcel, AQA, OCR and OCR(MEI) papers. 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
You’ll also be encouraged to consider how what you know fits into the wider mathematical world.
Syllabus
Module 1: Algebra and Functions
- The difference between a mapping and a function
- Function notation
- Domain and range of a function
- Composition of functions
- Inverse functions
- How to define a sequence by an nth term rule
- How to define a sequence by an inductive rule
- Arithmetic sequences
- Geometric sequences
- The sum of n terms of an arithmetic and a geometric sequence
- Series and the sigma notation
- The binomial expansion for positive integer n
- The general binomial expansion
- Properties of sequences
- Radian measure
- Circle calculations
- Small angle approximations
- Circular functions
- The reciprocal trigonometric functions
- Inverse trigonometric functions
- Addition and double angle formulae
- Trigonometric identities
- An introduction to numerical methods
- The trapezium rule
- Numerical solution of equations
- The Newton-Raphson method
- Fixed point iteration
Taught by
Philip Ramsden and Phil Chaffe
Related Courses
-
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
-
A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations
-
A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods
5.0 -
A-level Further Mathematics for Year 12 - Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors
-
A-level Mathematics for Year 12 - Course 2: Calculus, Newton’s Laws and Hypothesis Testing
5.0 -
Fundamentals of Engineering Exam Review
Never Stop Learning!
