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### 2013 Syllabus vs. 1993 Syllabus

Edit: On 14 May 2014, The Malaysian Examination Council released a notice to declare that 956 Further Mathematics will be removed as a subject from STPM from 2015 onwards. The following information may not be relevant any more, but still, read it if you're interested.

Here are the contents of the 2013-2014 956 Further Mathematics syllabus:

 SEMESTER 1: Discrete Mathematics SEMESTER 2: Algebra & Geometry SEMESTER 3:Calculus 1. Logic & Proofs 1.1 Logic1.2 Proofs 7. Relations 7.1 Relations7.2 Binary Operations 13. Hyperbolic &        Inverse Hyperbolic        Functions 13.1 Hyperbolic &          Inverse Hyperbolic          Functions13.2 Derivatives &          Integrals 2. Sets & Boolean      Algebras 2.1 Sets2.2 Boolean Algebras 8. Groups 8.1 Groups8.2 Cyclic Groups8.3 Permutation Groups8.4 Isomorphism 14. Techniques &       Applications of       Integration 14.1 Reduction Formulae14.2 Improper Integrals14.3 Applications of         Integration 3. Number Theory 3.1 Divisibility3.2 Congruences 9. Eigenvalues &     Eigenvectors 9.1 Eigenvalues &       Eigenvectors9.2 Diagonalisation 15. Infinite Sequences &       Series 15.1 Sequences15.2 Series15.3 Taylor Series 4. Counting 10. Vector Spaces10.1 Vector Spaces10.2 Bases & Dimensions10.3 Linear          Transformations 16. Differential        Equations 16.1 Linear Differential         Equations16.2 Numerical Solution          of Differential          Equations 5. Recurrence      Relations 11. Plane Geometry 11.1 Triangles11.2 Circles11.3 Collinear Points &         Concurrent Lines 17. Vector-valued       Functions 17.1 Vector-valued         functions17.2 Derivatives &          Integrals17.3 Curvature17.4 Motion in Space 6. Graphs 6.1 Graphs6.2 Circuits & Cycles6.3 Isomorphism 12. Transformation        Geometry 18. Partial Derivatives 18.1 Functions of 2          Variables18.2 Partial Derivatives18.3 Directional          Derivatives18.4 Extrema of          Functions

WHAT HAPPENED TO THE CHAPTERS OF THE OLD FURTHER MATHEMATICS T?

Sections which had been moved over to the new Mathematics T:
1. Properties of determinants
2. Augmented matrices, uniqueness of system of linear equation, Gaussian elimination
3. de Moivre’s theorem
4. Vector products
5. 3D coordinate geometry
6. Differentiation of inverse trigonometric functions
7. Integrating factor for differential equations
8. Maclaurin series
9. Entire Sampling & estimation chapter
10. Entire Hypothesis Testing chapter (exclude Type I & Type II errors)
11. Entire Chi-squared Tests chapter (exclude Yates correction)

I would say, the new STPM Mathematics T paper is more challenging. First of all it has 18 chapters compared to 16 last time, and even with 16, we could hardly finish our syllabus on time, I’m really curious how it can be done. Secondly, calculus is only taught in the second semester, when the physics students need it for their kinematics. I feel sorry for the physics teachers, they will need to teach some elementary calculus on top of their usual classes. But on the other hand, students should be glad that there’s now more statistics than before, as statistics are generally easier to score. That awful Analytical Geometry chapter is now given to the Further Mathematics students to suffer.

Sections which had been moved over to the new Mathematics M:
1. Entire Correlation & Regression chapter
Actually it has been there all the while, because last time Further Mathematics T and Mathematics S share the same 2 chapters, this one and Sampling & Estimation. What I’m most impressed is that there is a whole new set of 5 to 6 chapters on financial mathematics. Good or bad, I’m not sure, but definitely the workload will be greater.

Chapters which remained in the new Further Mathematics paper:
1. Logic & Proof. Everything’s the same, except that now you need to know how to use the rules of inferences.

2. Number Theory. This time the syllabus explicitly states that you are definitely required to now how to use the Chinese remainder theorem and Fermat’s little theorem.

3. Recurrence Relations. Still the same, as hard as before.

4. Graphs. In addition to before, you are required to know what are regular graphs and planar graphs. You are also explicitly told to study isomorphism of graphs too.

5. Eigenvalues & Eigenvectors. Now you are told explicitly that you should know how to diagonalize a matrix. The rest still applies.

6. Transformation Geometry. It seems you are supposed to use 3 × 3 matrices this time. Rotations in 3D can be really confusing, seriously.

7. Hyperbolic & Inverse Hyperbolic Functions. Now that they took inverse trigonometric functions into Maths T, this chapter is only left with the hyperbolics.
Chapters with major modifications that remain in Further Mathematics:
1. Techniques & Applications of Integration. Reduction formulae, length of arc, surface area of revolution are still here. But now there’s more: you learn improper integrals (integrals with infinite limit or discontinuous integrands) and you learn how to use calculus in polar coordinates.

2. Infinite Sequence & Series. You still can’t run away from that remainder theorem. But now there’s more: you are explicitly told that you need use L’Hospital’s rule (read as ‘lo-pi-ters’), and probably D’Alembert’s ratio as well. You learn the p-series, harmonic seris and alternating series. Harder than before.

3. Differential Equations. You are now explicitly told that you need to know how to transform an unsolvable differential equation into a 2nd order differential equation, with substitution. besides, now you are required to use Taylor series to help you to find numerical solutions. Euler’s method is new too.

NEW STUFF IN THE NEW FURTHER MATHEMATICS PAPER!

1. Sets & Boolean Algebras
You probably already know what sets are. In fact, this sets thingy came from the old Maths T, so I don’t think you’ll have any problem with it. Boolean algebra is interesting. It works with only 2 numbers: 1 and 0, true and false. It is the fundamentals of logic gates, and has some similarity with logic. Not hard, don’t worry.

2. Counting
This chapter contains some advanced combination & permutation techniques. If you have a hard time doing logic, this will be harder. Pigeonhole principle is interesting too, but the generalized one might confuse you. Put some effort into it.

3. Relations
This chapter is about relationships, how do two numbers, variables relate to one another. They have their own new notations, so you have to get used to it, and it is more on memorizing and proofing. I’m not sure about binary operations though. It’s some calculations involving 2 operands, you might want to check it out further.

4. Groups
Guess what, I just learned this in my second year of university! You study about the different types of groups, abelian, cyclic, permutation etc. Not hard, trust me, just need to know what they are, and able to prove them, and play around with their tables. Lots of definitions.

5. Vector Spaces
This is another one chapter, which is also from second year linear algebra. You will be surprised that the word ‘vector’ doesn’t necessarily mean a bracket with 3 numbers in it. You will need to know what it takes to be a vector, even integrals, polynomial expressions can be vectors too! All the best to you guys, especially when it comes to change of basis. I am still confused with that, as of now.

6. Plane Geometry
Not really new actually, this is another chapter that came from Maths T, except that you learn a few new theorems, Apollonius’, Ptolemy’s, Menelaus’ and Ceva’s theorem. I can imagine you talking in alien language to your classmates about these theorems, and they will probably worship you as a Mathematics God or something.

7. Vector-valued Functions
This is not hard, trust me. Just imagine putting 3 different algebraic expressions in the 3 columns of a vector, and it is a vector-valued function. Now your function has a direction, it is not a scalar anymore. You differentiate it, integrate it as usual. But curvature may be new, even I didn’t learn that either. Motion in space is not hard, it was from the old Maths T syllabus, just change the variables from x to t, differentiate them you get velocity and acceleration.

8. Partial Derivatives
Ever wondered how do you differentiate stuff if there are more than 3 variables? Yes, you partial differentiate them, with respect to one variable at a time. Partial derivatives is the starting of multivariable calculus, you should be glad that the double integrals and triple integrals are not in your syllabus. You realise that in a 3 dimensional world, differentiation in  different directions end up differently. You find the extrema of function of 2 variables using the Lagrange multiplier. This is just the start of the ‘real stuff’ that calculus is all about!

I’m a quite excited to see how the new Further Mathematics students will do in STPM. Seriously, if you can score A for this paper, I will call you a GENIUS! I’ve no idea what is the Malaysian government trying to do with your brain, but if you really master this paper, you’re really the man. You deserve full respect from me. Do your best and have no regrets, all your hard work will be worthwhile.