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LoginDebrief - 9740 Mathematics
34 posts
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Originally posted by dragoncloud:TMD
tio owned
....my own fault...never study...i did soooooooo badly that i'll
fail...Anyone knows if i can retake only math next year, then use
the second year's result combine wth this year de result? My other
subjects still ok... How can ?
I think the last 2-3 questions were really a bummer.
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Originally posted by dxdx:did anyone manage to prove the ans for the last ques area of triangle: the (1/12) (sin theta) (blah blah bah)...
and the last part which was 2 integrate ( cos t)^3 (sin t) ? dam sht man. i got -2 integrate ( cos t) ^3 (sin t) instead.i can prove the area of triangle
but not the integration one
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Originally posted by striderz_o405:somehow i just play around with the calc and all the values seem to be moving towards 0.619 for numbers below 1.512
Wah you long term memory, the numbers remember until so exact.
My friend tell me plot graph for that question. How did you play around with the calculator? That's the question I didn't know how to do in the paper. Horrorrr. Question 9 (iii) and (v). They are linked, so too bad for me =/ I know how to do (iv) though.
Then I also spotted a careless mistake after the paper.
Question 11, the sketching of the graph. I went to draw both the graph below and above the x-axis when you're only required to draw the one above. Sigh =/
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Originally posted by tangjing:Wah you long term memory, the numbers remember until so exact.
My friend tell me plot graph for that question. How did you play around with the calculator? That's the question I didn't know how to do in the paper. Horrorrr. Question 9 (iii) and (v). They are linked, so too bad for me =/ I know how to do (iv) though.
Then I also spotted a careless mistake after the paper.
Question 11, the sketching of the graph. I went to draw both the graph below and above the x-axis when you're only required to draw the one above. Sigh =/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
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.
*EDIT* Range of values for n should be 6 to 13, not 5 to 13. Sorry if I made anyone panic.Edited by teraexa 03 Nov `07, 11:25AM
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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
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.*clap clap*
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Originally posted by RaaRaa:7 also is complex no. Was dam turned of once I turn to the last 2 pages! Especially the last question.
standard. In O level, they are supposed to put the questions from easiest to hardest. (roughly).
This is so that pple dont give up when they see the first 3 questions. 16 years old still considered young. If you put 3 difficult questions in front, young students will panic and screw up whole paper.
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sorry noahie