A level H2 maths question spotting thoughts for AY2013
November 11 and 13 of 2013: Monday and Wednesday. H2 maths students will definitely know why they are such important dates.(or you are really in deep trouble son.) Last lap, last round of prep work, last minute prayers.....the list is endless. Parents and students alike probably want nothing more than a god-sent menu of tremendously accurate predictions regarding what questions will (or will not) surface in this year's A Level papers; however this too damn good of a thing is never going to happen. So here I am sharing my expectations for specific topics/areas, and in the process hopefully hit the bull's eye in some department. Let's take a look shall we?
Abstract problems are in vogue. If you are still not thoroughly acquainted with the various dot/cross product formulations and their canons of adaptations, head back to your notes for another round of internalization.Make that stuff stick in the back of your head. A sample problem you say? Try this:
Formulation of Conjecture/Mathematical Induction
This is a classic instance of "one leads to another" ; should you fail to devise the correct description for the nth term of a recurrence relation, it is possible you may not be able to proceed to verify the conjecture by means of Mathematical Induction. The number one peeve of students is exactly that: "I can't for the love of god see any pattern let alone create a conjecture!" My advice? Cultivate a certain sensitivity to the notion of numbers. For example, 120 is equivalent to 5! , 1024 is equivalent to 2^10 etc. Only then can you "crack the code" with greater ease.
Try this: if the first, second, third, fourth and fifth terms of a sequence are 0, 1, 5, 23 and 119 respectively, can you find an expression for the nth term in terms of n? I have planted a very obvious hint in the preceding paragraph.
(I have previously written some material related to this; you can check it out over at my supplementary site the Mathematical Sharpener.)
System of Linear Equations ( S-O-L-E)
If memory serves me right, this little rascal of a topic has been]making lesser appearances in recent prelim papers. Still, it pays to remain frosty-when the storyline of a particular problem starts to go all weird, alarm bells should ring, because chances are you are staring right at a S-O-L-E question.
Remember the periodicity problem which first sprung a nasty surprise in the 2009 paper?
Could something similar happen in 2013? Why not? After all it's been quite a long while since it last happened yes?
What else for functions-related problems then? Three items.
(a) Solving f(x) =f ^-1 (x)
There are "genuises" out there who still feel the need to work out the actual expression for
f ^-1 (x), and subsequently solve the mess resulting from this. Remember and remember it well: simply evaluate f(x)= x !
(b) Finding a function based on given composite functions
Prototype problem: If hg(x)= (sin x)^2 + 4 and g(x)=sin x, find h(x). Did you manage to arrive at x^2 + 4 by yourself?
(c) Modulo Functions
When tasked to find the inverse of a modulo function, say f(x) = |(x-1)/ (x+1)| , x >3, ensure you have dismantled the modulo apparatus appropriately based on the specified domain set before moving forward to work out x in terms of y. A close examination of the graph describing the function is seriously useful.
Many students will probably find this section pretty "mundane and boring"- I guess they aren't wrong. GC (Graphic Calculator) action and more GC action. Essentially finger discipline when punching those keys. However, marks can be lost for seemingly trivial qualitative stuff, such as articulating the characteristics of a Binomial distribution,or explaining what exactly is a least squares regression line of y on x by means of a properly labelled diagram. So make it a point to memorize them definitions. You will bleed less, trust me on this.
And that's a wrap folks, do remember to take care of your health and get sufficient sleep. Everything will over in a flash, and an upcoming long holiday break (for most) beckons. So just hang in there.
Good luck kids. Peace.