Answer to what problem as 0? Please show me.

You don't have a reason make y equals to 0. Look at the following theorem. It is known as the Euclidean Division Theorem.

The Division Theorem is prequel to the Remainder Theorem (you learned in STPM).

That's a good thing to hear. Keep practicing and they will never look at themselves quite the same way!

The gravitational forces exerted by the Planet on the two satellites hold them in the same orbit but moving in the opposite direction (v and –v) around the Planet. Without thinking any complicated situation, this question is best answered using VECTOR ADDITION.



When v = 0, then a_θ = 0. Therefore, a = a_R.

Try this:



It looks a kind of arithmetico-geometric sequence.

For ideal gases, the calculation for the internal energy is fairly straight forward.



An error is detected in the question. Helium (He) is a monatomic gas. Hydrogen (H₂) is a diatomic gas. The given answers cannot be accepted.

This post has been edited by Critical_Fallacy: Oct 15 2014, 01:06 AM

For Q4a, it is fairly easy to show



Please list the relevant formulas for dealing with complex numbers.

This post has been edited by Critical_Fallacy: Oct 15 2014, 01:17 AM

Please show your workings, so that your peers can comment.

I think the answer in the textbook may be wrong.

What you need to show is that the gravity g decreases with altitude h as one rises above the Earth's surface because W ∝ 1/r². From that, you can find the relationship between the gravity g at altitude h and the surface gravity g₀ (h = 0).



********************************************************************
A mathematically intuitive physicist will do this, but you can skip this step if you want.



********************************************************************

The next stage is to determine the altitude that yields the percent error, δ = 1%, or the relative error, η = 0.01.

The formula for relative error η is given by



Applying the formula to the problem, we have



So, writing the result correct to 1 significant figure

h = 30 km

Displacements are vectors. And you know that the norms |PQ| ≠ |QR| ≠ |RS| ≠ |ST|. This reason alone is suffient to reject (A).

And kinetic energy too...

I worry that it might send the wrong idea to other math-loving students.

It is true that you don't have the luxury of time to think deeply about every question in the exam.

Therefore, if you practice enough, solving math problems becomes second nature. Good intuitively problem-solving skill comes from many hours of practice.

As a tactician by nature, I'm sure you can plan your strategy well to solve almost any math problems at STPM level.

I suspect that the problem you are facing is that you don't have enough time to complete the paper that requires deep thinking.

What kind of questions do you frequently get stuck at?

I don't know the divide between A-level and STPM. But I want to know the basic mathematical knowledge taught to STPM students in these two topics.

TRIGONOMETRY

Are you able to

(1) plot the graphs of trigonometric functions,

(2) find the particular solutions and general solutions of trigonometric equations,

(3) apply the sine rule and cosine rule to solve non-right-angled triangle,

(4) covert angles from degrees to radians and vice versa,

(5) find the amplitude, period, frequency and phase of a wave,

(6) determine the time displacement between two waves

(7) use some trigonometric identities to show various engineering results, and

(8) rewrite the function as ?

VECTORS

Are you able to

(1) apply vector addition and subtraction,

(2) apply vectors to problems in mechanics,

(3) write vectors of two dimensions in i and j unit vector notation,

(4) find the resultant vector,

(5) write vectors of three dimensions in i, j and k unit vector notation,

(6) find the magnitude of a vector in 3D,

(7) evaluate a unit vector,

(8) determine the work done by a force vector F through a displacement r using a scalar product, and

(9) determine the moment vector M, about the origin O, of a force F, passing through the point with position vector r using a cross product?

Bravo!

Now your efforts have paid off. Congrats!

Isn't it obvious?



This post has been edited by Critical_Fallacy: Jan 29 2015, 05:14 PM