CIE Mathematics - Further Maths - Pure Math 01 - 9231
CIE Mathematics - Further Maths - Pure Math 01 - 9231 Math

Course                                : CIE Further Maths – Pure Math 01  9231


Period                                 : 12 weeks


Features                             :


Ö      Lecture Notes,

Ö      Lecture PPT,

Ö      Related video link

Ö      Suggested Experiment


Course Meeting Time :


Discussion            : 2 sessions / week, 1 hour / session

Recitation              : 1 session / week, 1 hour / session


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Pre-requisite                   :


Being confident, responsible, reflective, innovative, and engaged intellectually, socially, with information and ideas to make a difference on facing future challenges with the ability to learn knowledgeably of AS/A-Level Pure Maths units P1 and P3, under code 9709 CIE Mathematics and AS/A-Level Mechanics especially units M1 and M2, with Probability and Statistics units S1 and S2 under Mathematics code 9709. It’s a mandatory course you have taken before you try out on this course.

Prerequisite: None
Author: alberttls
Course Length: 12 weeks

 Course Descriptions  :


Cambridge International Examination A Level Further Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding.  This CIE A-Level Further Maths course is designed to give you a deeper understanding of mathematical principles, 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, recognizing when and how a situation may be represented mathematically, and as a solid foundation for further study, on typed of topics like:


·      Polynomials and rational functions

·      Polar Coordinates

·      Summation of series

·      Mathematical induction

·      Differentiation and integration

·      Differential equations

·      Complex numbers

·      Vectors

·      Matrices and linear spaces


The course is designed for CIE A-Level Further Maths enthusiasts in all levels, beginner, intermediate, expert, who want to understand the conceptual laws and physical processes that govern the sources, extraction, transmissions, storage, conversion, and end uses of Calculus.


Course Goal                    :


The basic objective of CIE A-Level Further Maths is to relate technique 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:


01.  Understand relevant mathematical concepts, terminology, and notation.

02.  Develop their mathematical knowledge and skills in a way that encourages confidence and provides satisfaction and enjoyment.

03.  Recall accurately and use successfully appropriate manipulative techniques

04.  Recognize the appropriate mathematical procedure for a given situation

05.  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

06.  Apply combinations of mathematical skills and techniques in solving problems. The use of mathematics as a means of communication with an emphasis on the use of a clear expression.

07.  Present mathematical work, and communicate conclusions, in a clear and logical way. To acquire the mathematical background necessary for further study in this or related subjects.


Course Structure          :


This course, designed for independent study, has been organized to follow the sequence of topics covered in the learning course on CIE A-Level Further Maths Syllabus and Scheme of Works. The content is organized into nine main pure math major continued units:


1.     Mathematical Induction

2.     Summation of Series

3.     Polynomials and Rational Functions

4.     Polar Coordinates

5.     Complex Numbers

6.     Vectors

7.     Differential and Integration

8.     Matrices and Linear Spaces

9.     Differential Equations


Each of the units has been further divided into parts (A, B, C, etc.) with each part containing a sequence of sessions. Because each session builds on knowledge from previous sessions, it’s important you progress through the sessions in order. Each session covers an amount you might expect to complete in one week.


Within each unit you will be presented with sets of problems at strategic points, so you can test your understanding of the material. As you begin each part of a unit, review the problem set at its end so that you may work toward solving those problems as you learn new material.


AT.LS expects its learner to spend about 100 hours on this course. More than half of that time is spent preparing for class and doing assignments. It’s difficult to estimate how long it will take you to complete the course, but you can probably expect to spend an hour or more working through each individual session.


Lecture PPT                     :


Most sessions include ppt and hopefully audio from lectures of Albert Tan teaching CIE A-Level Further Maths, recorded live in the office room in the spring of 2020. The PPT was carefully segmented to take you step-by-step through the content. The PPT is accompanied by supporting course notes, and audio.


Recitation PPT               :


This course includes a dozen of recitation PPT – brief problem-solving sessions taught by an experienced learner – developed and recorded especially for you, the independent learner.


Assignments and Exam:


No textbook is required for this course.


The notes that accompany the PPT present their content slightly more formally than the lecture does. If you are wondering exactly 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.


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


Some worked examples will be accompanied by a Mathletes. 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 at each course. As you start each part, familiarize yourself with the problems in the problem set. This 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 to you. Do not hesitate to work any problem that piques your interest).


Textbook                           :


[Author]. Cambridge International AS & A Level – Further Mathematics – Further Pure Mathematics 1. Hodder Education [Date] [ISBN:]


[Author]. Cambridge International AS & A Level – Further Mathematics – Coursebook. Cambridge University Press


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


During the course, I have resource lists that can be filtered to show all resources or just those which are endorsed by CIE. The resource lists include further suggestions for resources to support learning.


Homework and Exams          :


In this course of CIE A-Level Further Math’s – Section of Pure Maths, all candidates will have 11 questions of different marks and lengths. Candidate should answer all questions except for the final question (worth 12-14 marks) which will offer two alternatives, only one of which must be answered.


Before the exams started, you may have a calculator with standard “scientific” functions for use in the examination. Graphic calculators may be used but obtaining results solely from graphic calculators without supporting working or reasoning will not receive credit. Computers, and calculators capable of algebraic manipulation, are not permitted. All the regulations in the Cambridge Handbook apply with the exception that, for examinations on this syllabus only, graphic calculators are permitted.


Make-up Exams             :


If you miss or fail an exam, you make take a make-up exam at certain arranged times. You will be notified by an e-mail soon after taking an exam if you have failed it so that you can plan for the make-up. make-ups for failed exams can boost your grade only up to the lowest passing score (C-), which will be announced. Make-ups for full credit are permitted with a medical excuse. If you must be absent for other reasons, such as team sports, you must arrange to be excused in advance.


Grading                              :




Eight Problem Sets

50 each (note: the lowest problem set score will be dropped)

Five in-class 1-hour exams

100 each

Final exam






Outline                                :




Chapter 1 – Mathematical Induction

Chapter 2 – Summation of Series

Chapter 3 – Polynomials and Rational Functions

Chapter 4 – Polar Coordinates

Chapter 5 – Complex Numbers




Chapter 6 – Vectors

Chapter 7 – Differentiation and Integration

Chapter 8 – Matrices and Linear Spaces

Chapter 9 – Differential Equations


Format                                :


Rather than follow the traditional format of theory followed by an experiment, we will integrate fundamental mechanics with practical applications to some topic in the systems of contemporary relevance throughout the course. If you complete this course, you should be equipped with the technical tools and perspective to enable you to start to evaluate mathematical application choices objectively and quantitatively both at a community and a personal level.


Additional Comment  :


This course includes features that do not display correctly in a random browser. For best results, I would like to recommend viewing this course with the latest Firefox, or Google Chrome.


Our public learning reference contains a list of endorsed textbooks for each course. Many of our syllabuses are supported by a range of different endorsed textbooks and sources to ensure that learners have a choice. Guider is advised to choose the textbook that best suits their course.


Endorsed resources go through a rigorous quality-assurance process to make sure they closely reflect the syllabus and are appropriate for learners worldwide. Resources may be endorsed for full syllabus coverage or endorsed to cover specific sections, topics or approaches. Look for the specific “references” on here.


NOTE: This is a course only for Pure Math section in CIE Further Math, for a section of Statistics and Mechanics, please sign up to another related course in this site, under the name CIE Further Maths – Statistics 3, and CIE Further Maths – Mechanics 3


The Understanding of Syllabus and Procedures


Learner Name             : _______________________________        Date: _______________


I, _______________________________ have read the AP Physics 1 Syllabus and Procedures with my parents/guardian/supervisor (P/G/S). I fully understand the rigor of the course and understand that I must maintain an 85% or above during each exam to remain in the class. I further understand that if I am failing at the course, I will be removed from the course and placed in the very beginning.

I will abide by the online course rules in, the field safety rules, and the ethics of learnings to the best of my ability. I understand there are consequences for misbehavior, especially during the learning.


Learner Signature       : _______________________________        Date: _______________



P/G/S Signature          : _______________________________        Date: _______________


P/G/S E-mail              : _______________________________________________________