**As Taught in:**

2017/2018

**Level**:

High School A-Level

**Learning Resource Types:**

=> Problem Sets

=> Lecture PPT

=> Reading Resources

**Course Descriptions:**

Universities and employers accept International Examination A-Level Further Mathematics as proof of mathematical knowledge and understanding. This A-Level Further Maths course is designed to give learners a deeper understanding of mathematical principles and the further development of mathematical skills, including the use of applications of mathematics in the context of everyday situations with the ability to analyze problems logically, recognize when and how a situation may be represented mathematically, and as a solid foundation for further study.

**Course Goal:**

The basic objective of A-Level Further Maths is to relate techniques with applications. After completing this course, the learner will able to demonstrate an understanding of the large-scale as a cumulative sum, of the small-scale as a rate of change, and of the inverse relationship between them, and competency in:

- Understand relevant mathematical concepts, terminology, and notation.
- Develop their mathematical knowledge and skills in a way that encourages confidence and provides satisfaction and enjoyment.
- Recall accurately and use successfully appropriate manipulative techniques.
- Recognize the appropriate mathematical procedure for a given situation
- Develop the ability to analyze problems logically, recognize when and how a situation may be represented mathematically, identify and interpret relevant factors, and, where necessary, select an appropriate mathematical method to solve the problem.
- Apply combinations of mathematical skills and techniques in solving problem. Using mathematics as a means of communication emphasizes using a clear expression.
- Present mathematical work and communicate conclusions clearly and logically.

**Course Meeting Time:**

Discussion – 2 sessions 1 hour / week

Recitation – 1 session 1 hour / week

**Prerequisite:**

Being confident, responsible, reflective, innovative, and engaged intellectually and socially, with information and ideas to make a difference in facing future challenges with the ability to learn knowledgeably of combination of AS/A-Level Mathematics – Pure Maths, Mechanics, and Statistics. It is a mandatory course you have taken before you try out on this course.

**Lecture PPT:**

Most units include PowerPoint slides and hopefully with an audio guide recorded. The PowerPoint was carefully segmented to take you step-by-step through the content. The PowerPoint is accompanied by supporting course notes and an assignment review.

**Recitation PPT:**

This course includes a dozen recitation PowerPoint – brief problem-solving sessions chosen carefully – developed and recorded, especially for you, the independent learner.

**Practice – Assignment:**

“Worked Examples” present a problem or problems to be solved; many of these problems have appeared on practice assignments in the course. After solving these problems, you can check your answer against a detailed solution per illustrative examples of the learner’s work at different performance levels.

A Mathletes will accompany some worked examples. These interactive learning tools will improve your geometric intuition and illustrate how changes in certain factors affect the results of different calculations.

Problem sets occur at the end of each part; these were taken directly from the homework assigned in each course. As you start each part, familiarize yourself with the problems in the problem set. That will enable you to work on each problem as you gain the knowledge you need to solve it. Once you have completed the problem set, you can check your answers against the solutions provided. (The problem sets are carefully selected from a longer list of questions available. Do not hesitate to work on any problem that piques your interest).

**Textbook**:

This course is self-contained, and no textbook is required. If you need some resources, I recommend resources endorsed by Cambridge. Go through the details here. It will be a useful companion to this course, although you might have to deal with slight differences in terminology and notation.

In addition, the notes that accompany the PowerPoint present their content more formally than the lecture. If you are wondering what conditions must hold for a statement to be true or if you wish to see the details of the calculations displayed on the slides, check the notes. Here is some roughly recommended book if you need it:

2003. *Cambridge International AS & A Level Further Mathematics – Further Pure Mathematics 1. *Published by Hodder Education.

2005. *Cambridge International AS & A Level Further Mathematics Coursebook*. Published by Cambridge University Press.

Finally, during the course, I have resource lists that can be filtered to show all resources or just those most International Examinator endorses. The resource lists include further suggestions for resources to support learning.

In order to help build a solid foundation for the learner, this course is designed for A-Level Further Mathematics enthusiasts at all levels with prerequisite mastered, who want to understand the conceptual laws and physical processes that govern the sources, extraction, transmission, storage, conversion, and end uses of Calculus. Therefore, this course will cover the most general topics in foundation mathematics, as pointed out below:

- Mathematical Induction
- Summation of Series
- Polynomials and Rational Functions
- Polar Coordinates
- Complex Numbers
- Vectors
- Differential and Integration
- Matrices and Linear Spaces
- Differential Equations

Each unit has been further divided into parts – A, B, C, and more – with each part containing a sequence of sessions. Because each session builds on knowledge from previous sessions, the learner must progress through the sessions in order. Each session covers an amount the learner might expect to complete in one to two weeks.

Within each unit, learners will be presented with sets of problems at strategic points to test their understanding of the material. As the learner begins each part of a unit, review the problem sets at their end so that the learner may work toward solving those problems as they learn new material.

“AT.LS” education expect their educator to spend about 100 hours on this course. More than half of that time is spent preparing for class and doing selected assignments. Estimating how long the learner will take to complete the course is difficult, but the learner can expect to spend an hour or more working through each session.