This article is an introduction of the subject Further Mathematics in STPM Baharu by a friend of mine. In Form 6, there are very few people that take up Further Maths and I am really lucky to have a friend who took this subject and is willing to share his experience in this subject. Well, read on!

STPM FM is introduced for those who has intense interest in math and wish to challenge
themselves in STPM. It can be only be taken with Maths (T). Being a 100%
written test, you don’t have to do any assignment or project.
Since there are less than 30 candidate taking it each year, there are no any
reference book selling in the market and no teacher teaching it in school (as
far as I know). You can only learn it by yourself or going for tuition. The reference
book recommended by MPM is hardly found in normal bookstore. You may order it
from MPM or online but they are really expensive (each book cost about RM 200)
and you may need 4 different books for the whole STPM. Most of us like me will
just download the e-books or borrow the books from college/university and
photostat it. Since the books are university-typed book, it is more on theory
and have less examples. A-level reference book is not sufficient to cover all
the syllabus but they are good for reference also.

__Semester 1: Discrete Mathematics__
This semester will be useful especially for those who are
going to study for computer science. There are only two new chapter compare to
the old syllabus:

**Sets and Boolean Algebras**and**Counting**. This sem requires a lot memory works and the questions are mainly proving, so you have to memorize plenty of law and theorem to answer the question.**Counting**is easy to learn but the question can be very tough and complicated. If you are a person with logical thinking mind then this semester will not be a problem for you. The sad thing that I always faced in this semester is I know a statement is obviously true but I don’t know how to prove it.

__Semester 2: Algebra and Geometry__

I think this is the hardest semester. There are four new
chapter (

**Relation**,**Groups**,**Vector space**and**Plane geometry**) and two old chapter (**Eigenvalue & eigenvector**and**Transformation geometry**). Overall,**Relation**and**Groups**is not that hard except for some subtopic which is quite abstract. Luckily this two chapter are A-level old syllabus so I can refer to a lot past year questions.**Eigenvalue and eigenvectors**is easy and same as A-level. The hardest chapter is**Vector space**. It is a huge chapter and I found it difficult to understand.**Plane geometry**is quite easy to learn although it has 8 theorems and plenty of properties but the question always disappoint me. I don’t even know how to start and just left blank for it. Although**Transformation geometry**is an old chapter (only involving 2D), in the new syllabus it consist of 2D and 3D. Transformation in 3D is really confusing, I can’t imagine how it undergoes.

__Semester 3: Calculus__
In this semester you will learn about hyperbolic function,
further integration, infinite sequences and series, differential equation,
vector-value function and partial derivative. This is the easiest semester, easy to
learn and the questions are straight forward. All these chapters are useful
especially for those who want to take up engineering. Although

**vector-value function**and**partial derivative**are new chapters but they are not too complicated. The only thing I don’t know is sketching the graph for vector-value function and function of two variables. I wonder if they want us to sketch a 3D graph in exam?

__Comparison with A-level further maths__
There is a big difference between STPM further math (
STPM FM ) and A-level further math. STPM FM is deeper and wider than A-level (if compared with pure FM only). There are about 10 or 11 chapters out of 18
chapters which is not include in A-level syllabus especially discrete math
chapters. But STPM FM do not have mechanics and statistic (statistics chapter
brings to Maths (T) already) chapters which I think they are rather important.
Some of chapter in STPM like

**Relation**and**Groups**are actually appear in A-level old syllabus.

__Toughness__

Taking STPM FM is really not an easy task. Some of the
topics are very abstract and difficult to understand and the worst thing is I
don’t have enough examples to refer. There are not much calculation and most of
it are based on theory and proving. I heard from a senior that some of the
topic is in first year of math degree. The syllabus set are too wide and we
don’t know what they want. For example, in the syllabus they say “use the
properties of cyclic quadrilateral” but there are plenty of properties and we
don’t know which properties they want/mean.

__Advice__

I do not encourage those who don’t like maths to take
FM. Those who take must manage your time properly because there are lots of new
things need to learn. Since there are less examples for certain chapter, you
have to search it from other sources like International Baccalaureate and
A-level old syllabus past year question. There is a useful blog and a group in
Facebook where you can refer to and discuss the question with ex-FM candidates
and teacher.

*Useful Blog: http://furthermathematicst.blogspot.com/p/new-syllabus-vs-old-syllabus.html*

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