OK Lor:

Hi,


Please evaluate
http://www.postimage.org/

Thanks.

Let u=tan(x). Rewrite it in term of u, it would become an integral of an elementary function in form of

http://lh6.ggpht.com/_nr85VD4DdiA/TPjKaT7U5HI/AAAAAAAAAE0/jSSE2KNWb9E/s800/elementary-function-integral.png\">

Bounty:

I am back again. Thank you for your all your help.

I have spoken to my daughter’s school Prinicpal. I have the option of doing the subject privately as an additional subject and the school will register her for the O Level exam through the school. This is what MOE also told me.
So now, could anyone recommend me a good teacher who can teach her the complete school curriculum on a one-to-one tuition at home (or any other suggestions)? And the rates of course. I live in Woodlands.

Hi Bounty,

I can give her a try. As a professional math trainer, I look forward to taking the challenge to help every student for a better change.

Some student hate math while others are scary of math. Some seriously lack the background of previous classes while others simply need a change in learning attitude (but making such a change is never simple though). These initial obstacles have to be dealt with before going to the next step which includes strategic theory review and practise questions. What does “strategic” mean? It means 2 things:
(i) most important subjects which carry high mark portions have to be carefully highlighted and addressed
(ii) the preparation need to be individualized to deal with particular background weaknesses of each student.

Indispensably, every student needs to know by heart the tips to identify, analyze a new question as a known question and thinking process to solve it.

Feel free to send your daughter in for a FREE workshop & an assessment test.

http://mathqa.blogspot.com/2010/11/free-revision-workshops-for-gce-o-level.html

http://mathqa.blogspot.com/2010/11/test-question-for-senior-olympiad.html

http://mathqa.blogspot.com/2010/11/sat-i-math-collection-of-medium-to-hard.html

worriedparent:

Original Title: Failed Maths & Science Subjects


My son has done very badly in his Sec 3 Mid-Year Exam, esp in his core subjects of E. Maths, A. Maths, Physics and Chemistry.

Can anyone help?

I can give him a try. As a professional math trainer, I look forward to taking the challenge to help every student for a better change.

Some student hate math while others are scary of math. Some seriously lack the background of previous classes while others simply need a change in learning attitude (but making such a change is never simple though). These initial obstacles have to be dealt with before going to the next step which includes strategic theory review and practise questions. What does “strategic” mean? It means 2 things:
(i) most important subjects which carry high mark portions have to be carefully highlighted and addressed
(ii) the preparation need to be individualized to deal with particular background weaknesses of each student.

Indispensably, every student needs to know by heart the tips to identify, analyze a new question as a known question and thinking process to solve it.

You can send him in for a FREE workshop & an assessment test.

http://mathqa.blogspot.com/2010/11/free-revision-workshops-for-gce-o-level.html

http://mathqa.blogspot.com/2010/11/test-question-for-senior-olympiad.html

http://mathqa.blogspot.com/2010/11/sat-i-math-collection-of-medium-to-hard.html

mathqa:

Details for FREE O Level workshops now available


http://MathQA.blogspot.com

http://mathqa.blogspot.com/2010/11/free-revision-workshops-for-gce-o-level.html

http://mathqa.blogspot.com/2010/11/test-question-for-senior-olympiad.html

http://mathqa.blogspot.com/2010/11/sat-i-math-collection-of-medium-to-hard.html

OK Lor:

Hi,


Function f is defined by f(x) = { ax² + bx – 2, x ≤1; 2 – 1/x², x > 1
where a and b are constants. If f(x) is differentiable at x = 1, find the values of a and b.
Ans: a = -1, b = 4

Thanks.

1. f(x) is differentiable at x=1 -> f'(1-) = f'(1+) -> 2a+b=2
( 1+ denotes right hand side of 1,
1- denotes left hand side of 1,)

2. since f(x) is differentiable at x=1, it is continous at x=1 (please note that the converse is not true)
f(1-)=f(1+) -> a+b-2=1

3. In summary, 2a+b=2, a+b=3 -> Ans.

Details for FREE O Level workshops now available


http://MathQA.blogspot.com

1: Free Senior Singapore Mathematics Olympiad (SMO) training:


This is an invitation to students who are preparing for SMO 2011, 2012 to take 2 round tests and top scorers will get free weekly training by MathQA.

MathQA can help prepare you better for the challenging competition.

Round 1: Online test, submit your answer on the blog website, deadline 20-Nov-2010

Round 2: Paper test by invitation to those score well in the round 1.

Details on the tests can be found at http://MathQA.blogspot.com

2: Free holiday revision workshop for 2011 GCE O level students:

Details coming soon.


MathQA Mint Tan

GuzHo:

Can you suggest Maths Olympiad Training centres @ North?

You can visit http://MathQA.blogspot.com. The place is in the North.

Currently, there is a selection process in which top scorers can get free weekly training to prepare for SMO 2011, 2012.

MathQA

mramk:

iFruit:

[quote=\"mathqa\"]

If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt² - 6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.

The solution is is posted at my blog. Cannot post it here due to oversize images.

http://mathqa.blogspot.com/2010/11/nonhomgeneous-differential-equations.html

MathQA

Hi MathQA,

Nice working. But I think there is a small mistake in it. You can't apply initial conditions to the homogeneous equation (equation 6) as they are initial conditions for non-homogeneous equation. That's why your solution doesn't tally back for initial conditions. Also particular solution C = -11/4

The solution after applying initial conditions to the general equation should be (pi = π)

x(t) = ((1-2π)/4) e^t cos(t/√3) - (√3(1+2π)/4) e^t sin(t/√3) - 11/4

Regards.

Thanks MathQA for volunteering your time to help solve this tough question.
Small mistake does not matter. It is just + or - of a constant value.
Overall steps posted on blog are well defined and easily followed.
But may I suggest you try to post the images of your works here. The forum does support [img] tag.

@iFruit: we need steps to understand how to solve the question, not just final answer. How to solve the problem is much more important than final answer. Appreciate if you could be more elaborate next time then :). Thanks!!!

Best regards,
Mr AMK.[/quote]Thanks Mr AMK, and iFruit for your feedbacks and kind words

iFruit:

OK Lor:

Hi,


I'm not taking A-level Maths this year, but interested to know the solution for part (b):

If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt² - 6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.

Thanks.

Hi OK Lor,

Is this A-level question? AFAI can see, The equation is a non-homogeneous linear differential equation, so it needs some background to understand the solution..

iFruit is right to point out that this question is non-homogeneous linear differential equation. But it is nice to have for A level since it would test students's competence in many areas at once.

The solution is is posted at my blog. Cannot post it here due to oversize images.

http://mathqa.blogspot.com/2010/11/nonhomgeneous-differential-equations.html

MathQA