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.
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.
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.