This is a good resource!

I will start with Chapter 2 as I've pretty much covered all the concepts in Chapter 1 in form four. I think it has its advantages over KhanAcademy as there are more practice problems and the pace is faster, and the topics are arranged in digestible chunks.

Hmmm... I'm not that sure, really.
But it does affect me in a way. I can't really comment on the early night part, but I can safely say that I work the same way as he did. I disliked working in groups, I skipped school to catch up on my studies alone, and in doing that, I was stressed out at times. During SPM, I think I broke down. It was too much. I didn't take any time off my studies, not even a single day. I started to decline invites from my friends to go out on weekends, telling myself that it would all be worth it. But was it worth it? I think it wasn't, I would probably have done better if I wasn't so hard on myself.

I am still hard on myself. I'm not even sure what my goal is anymore, working on Physics and Maths. What am I trying to achieve? I don't know. I'm not sure. Maybe I think it would all be worth it, again? But it won't, it won't if I continue being so hard on myself.

I'm looking forward to getting my driving license in a couple of weeks, telling myself that I can't stop worrying after obtaining my license. But would it stop me from worrying? There is still SPM results, college decision, university. It goes on and on, and if I think I can continue making decisions and planning my future, hoping that things would work out the way I want them to be, I will continue to worry.

Then again, my mum told me this and I'll always remember it:

'船到桥头自然直'

My goal, when I start college, is to try to take things lightly.

I don't understand the proof, but I respect the fact that you've arrived at it.

Also, the 2 questions you gave me ( the pendulum and the banked road problem ), I've solved them after learning Circular Motion. However, I still have several questions left unsolved. Firstly, it's about the classic bucket whirl problem. The question is why doesn't the water in the bucket fall out of the bucket when it's at the top of the circle?

My book says that since the centripetal force is R+mg, hence R+mg = mv^2/r => R = (mv^2/r) - (mg) . For the water to not fall out of the bucket, the centripetal force must be > mg, thus, R > 0 so the water doesn't fall. But I can't grasp the intuition behind the equation. Why doesn't the water fall out when the reaction force is greater than zero? Also, the minimum value of v should be such that mv^2/r = mg => v = √rg. What does it mean that the centripetal force is equal to the weight? R in this case would be 0, but still, the water doesn't fall out. I've searched online but arrived at contradicting answers. Some referenced inertia, some said centrifugal force ( which doesn't exist ).

Thanks !

At the top, the water is acted upon by gravity, and the normal reaction force. Thus, mg and R. This provides the centripetal force, v^2/r.

I had the intuition after thinking about it, reflecting on ninty's explanation. Your explanation reinforced my understanding. Thank you, and welcome back!

Hi, now that I'm done with my driving test I can finally relax and spend time studying Physics and Maths. I was worried and nervous about my driving, couldn't really concentrate on other things.

Critical_Fallacy If you mean Analytic Geometry in AS, then yes, it was covered in SPM. If you mean STPM's Analytic Geometry then no, haven't started with it, yet.

I passed the test yesterday.

So I'm very relieved right now, I can get back to work. I will definitely catch up with Lagrangian but I've seen that it requires partial differentiation.

Oh sorry. My driving made me forget a lot of things. Will get back to it!

Critical_Fallacy

Sorry for my absence. I'll admit it, no progress has been made. I'd also like to admit that my knowledge of trigonometry needs brushing up. Serious work has to be done in many parts of Maths, I'm still average in most of it.

But I'd like to update you guys on what I've been doing. Recently I've been going back to my school to teach form four students Add Maths and Physics for their Alumni Program. I took great care to ensure that what I'm teaching is very sound, conceptually. For Add Maths, I taught elementary functions. Emphasis was placed on decomposing composite functions and inverse functions because many requested a lesson on those concepts. I presented to them multiple ways to tackle the composite functions problem from Critical_Fallacy's previous tutorial when I was in form five, and consulted ninty to confirm. And I made sure I fully understood those concepts before teaching them.

As for Physics, I taught Kinematics. My aim was to clear the air on the sign conventions used in Kinematics, especially on the usage of g, gravitational acceleration. I also discouraged the use of deceleration and asked them to be comfortable with positive and negative acceleration instead as it will come in handy in future concepts. Derivation of the equations were done without the use of calculus.

Hence, I've been a little bit busy. I've also been driving a lot to make sure I'm very comfortable with my car.

Besides that, since I have a lot of free time, I've read extensively on different fields. Accounting, psychology, philosophy and economics. It's been very satisfying, indulging in my different interests without the pressure to score in examinations. I'm truly 'studying' and 'learning' right now according to my pace and interests. I don't think I'll have this opportunity when my holiday's over.

Kudos to you guys for keeping this thread active. Will be back to contribute ( not sure if I can contribute much ) to this thread when the time is right.

As of now, I can't attempt this. I've got a lot of work cut out in order to be competent in college-preparatory Mathematics. Unfortunately, when there are no tests and exams, being disciplined to learn Mathematics is not as easy as it seems. But I guess I deserve a little bit of room to explore other things for now given the amount of work I've put in for my SPM.

Anyway, your previous question is interesting, a little bit paradoxical. What's your take on it?

v1n0d, Critical_Fallacy, ninty, ystiang, kingkingyyk

I would like to see how you attempt these questions. You can either provide multiple solutions or one favoured workaround. Thanks!

1. Ali is 3 times as tall as Kumar. Kumar is 30cm shorter than Ah Chong.Their total height is 330cm. How tall is Ali, Kumar and Ah Chong?

2. Ali completed 32 pages of his homework on Monday. On Tuesday he finished 1/6 of the remainder. Then he still had half of the book to complete. Find the total number of pages he still has to complete.

3. The number of cattle in a ranch is four times the number of horses. After 280 heads of cattle were sold, the were twice as many horses as cattle. How many cattle and horses were there initially?

This post has been edited by maximR: Mar 12 2014, 04:51 PM

Thank you gentlemen for your responses.

However, these are Year Five questions. How do I approach the questions without using algebra and matrices?

Thank you so much for sharing this. Do you know how can I purchase the hard copy version of this book?

Also, I'm stuck with this question:

I'm not attacking chapters based on which PreU they come from.

I want to completely master Counting, up to STPM FM T Counting so I won't have problems with A-Level Counting. I used to get questions wrong even for SPM Counting as I didn't have enough time to completely master it. So I'm looking for good notes/books to help me with this.

By the way, after seeing your Math M results jumping from C to A, I feel that nothing is impossible.

So you like working things out algebraically?

I also observed that you like older academic books, like me in the past. Have you searched for the books you wanted in libraries? My college library has all the books you want. Even the bookshop has them. I'm given a free copy of Bostock/Chandler's Pure Mathematics book because I'm taking Further Mathematics, and it's a good book.

Good! Keep the questions coming. I liked the post about proving identities with methods like these:

RHS-LHS = 0
RHS/LHS = 1

Getting zero marks in a Trigonometry test because the teacher doesn't accept this is totally worth it!

Anyway, after reading 80's/90's STPM Matematik Tulen books and HSC books, I disagree that the newer Mathematics (T) is harder than the older curriculum.

I have a fat HSC past-years book. The epic moment when one of the P/C questions is like an introductory Olympiad-style counting problem...

Will PM you tomorrow if I have the time.

One humble note though, if you're planning to do Maths at uni, you might want to do more than working out problems involving algebraic manipulations using A-Level books, because uni Maths is a whole different beast altogether. It's about creativity, experience and insight, and reasoning. Books to watch out for are Art and Craft of Problem Solving or the collection of AoPS books on Intermediate Algebra, Intermediate Number Theory and Intermediate Counting and Probability, as well as Calculus which contains stuff beyond normal undergraduate calculus, like Putnam problems.

Firstly, the question is wrong. The answer should be T(c+1)/(log c)^(c+1), where c is the gamma function. When c is a positive integer, T(c+1) = c!, where T is the gamma function. So the answer is c!/(log c)^(c+1). Otherwise, there is no closed-form answer.

Credits to a friend of mine.

This post has been edited by maximR: Aug 12 2014, 10:35 PM

Say you have the terms T1, T2 and T3. How many steps should you take from T1 to arrive at T3?

Edit, I didn't look at the question. I think it has something to do with the fact that you're summing from k = 2, but I might be wrong.

This post has been edited by maximR: Aug 27 2014, 03:05 PM

I just got back from college. Back to home sweet home. Thank you for the challenge, and 'without doing a Google search' is a wonderful way of challenging us!

Incidentally I have wondered and read about this a few years ago, probably in form two/form three. But I've forgotten enough of it to be able to occupy myself with this.

I'll struggle on my own first, and if I can't progress further I'll discuss it with my classmates.