Debrief - 9740 Mathematics
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i wrote from 6 to 13 leh..Originally posted by teraexa:Ok now let me recall all the various questions...
Qn 11)
I got the graph wrong by including the bottom part too. 1 mark gone. Anyway for the 2nd part, it is possible to show the expression although the step is tedious (I did and cancelled my original answer twice. Did in pencil on the qn paper before copying the solution onto my paper later on). Integration one was rather easy. Just need to eliminate the cos t term by multiplying by dt/du which is 1/cos t.
Qn 10)
I believe the majority were asking about the values for n which S > 4a. Ok at first, u have to find ur d in terms of a. Use ur ar - a = 3d to get the result that d = -1/9 a. Then sub this expression back into the inequality. You will get a quadratic inequality of something like an^2 - 19an + 72a < 0. You can divide by a as a > 0 as defined by the question. Therefore u get n^2 - 19n + 72<0. Solve for n which should be in the range of (5+,13+), therefore n should be 5 to 13 as n is an integer.
Qn 9)
2nd part: When X1=0, X will increase towards alpha. X1 = 1, X will decrease towards alpha. X1 = 2, X will increase to infinity.
3rd part: Proving that X(n+1)>Xn for Xn between values of alpha and beta. To prove it, first express X(n+1)-Xn = 1/3 * e^(Xn) - Xn. Let Xn be x, therefore expression will give you 1/3 of the equation of the graph (e^x - 3x). When Xn is between alpha and beta, e^x - 3x is always less than zero. Since 1/3 * anything negative is less than zero, therefore X(n+1) - Xn < 0, X(n+1) < Xn. You can prove the other case using this method too.
That's all for qn 9, 10 and 11.
cos 5 not included rite? -
this is h2 math right?
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Yes Uncle. 9740 Mathematics = H2 Maths.Originally posted by unclebutcher:this is h2 math right?
Anyway, I found the odd-numbered pages of the paper to be easy. Q11 part 2 was very tedious though. But stick close to what you need to prove is vital here.
For me, in Q11 part 2, I expanded the entire terms, till I have something like sin^5 (t), before factorising. (teraexa, what method did you use?)
Q1 Inequalities
Some mistakes included completing the square in the denominator to prove that the denominator is always positive, but it isn't. In fact, it is factorisable.
Q3 Complex Number in (a + bi) form
I splattered on this one. Didn't realise that w = x + yi (and likewise w*= x - yi) and solve.
Q9 Recurrence
Parts (i) and (ii) were relatively straightforward.
Part (iii) requires me to use my GC. For X1 = 0 and 1, the series is convergent to alpha. For X1 = 2, it is divergent (tends to infinity).
Part (iv) was the hardest in my opinion, but it's worth only two marks. For the first sub-part, I tried to prove from the graph drawn in (i). I left the 2nd sub-part blank.
Part (v) was a conclusion from (iii) and (iv).
anyway ... Expected topics to come out on Pure Maths section of 9740/02
1. Integration by Parts
2. Area Under Curve / Volume of Revolution
3. Summation of Series (with Mathematical Induction I suppose
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4. Graphing Techniques
5. Binomial Theorem and Maclaurin Series -
so what is the correct answer for qn 1?
i got sumthing like x<-3, x>7 -1 -
Oh yea paiseh i wrote 6 to 13. Mistake cos I was distracted last night reading something else.Originally posted by club18:i wrote from 6 to 13 leh..
cos 5 not included rite?
Really sry for the mistake. -
yep.Originally posted by th3m0ment:so what is the correct answer for qn 1?
i got sumthing like x<-3, x>7 -1 -
Last Qn, Qn 11. the last part answer for the area is 2/5!!!
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yeah.Originally posted by akinos:Last Qn, Qn 11. the last part answer for the area is 2/5!!! 
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KNN!Originally posted by Ignorance:Yo guys
I am still enjoying my post promos holidays 