H2 math

last SG · 2009-03-19T19:16:48+00:00

Hi, I have a Q Express the general term of the series 2/(3)(5) - 3/(5)(7) + 4/(7)(9) - 5/(9)(11) + ... in partial fractions (can) and deduce its sum...

wee_ws SG

Hi,

1 / {(3 -x)(x - 1)} > 1

Multiply both sides by (3 - x)^2 . (x - 1)^2, we obtain

(3 - x)(x - 1) > (3 - x)^2 . (x - 1)^2

=> (3 - x)^2 . (x - 1)^2 - (3 - x)(x - 1) < 0, so your sign is incorrect.

For the other question, let a = |x|. Solve a < 2 / (a - 1) first.

Thanks!

Cheers,
Wen Shih

Destined2REIGN SG

Hi,

1 / {(3 -x)(x - 1)} > 1

Multiply both sides by (3 - x)^2 . (x - 1)^2, we obtain

(3 - x)(x - 1) > (3 - x)^2 . (x - 1)^2

=> (3 - x)^2 . (x - 1)^2 - (3 - x)(x - 1) < 0, so your sign is incorrect.

For the other question, let a = |x|. Solve a < 2 / (a - 1) first.

Thanks!

Cheers,
Wen Shih

Thanks. Updated Q A) Made a typo in the sign. Paiseh.

wee_ws SG

Hi,

Do not expand. Factorise instead, i.e.

(3 - x)^2 . (x - 1)^2 - (3 - x)(x - 1) < 0

=> (3 - x)(x - 1) [(3 - x)(x - 1) - 1] < 0

Thanks!

Cheers,
Wen Shih

blueftw SG

need a little asap help on my concepts.

when a question asks to calculate unbiased estimate, which test statistic to use?

wee_ws SG

Hi,

None at all. Formula for unbiased estimate for variance can be found in the formulae list. Thanks!

Cheers,
Wen Shih

wee_ws SG

Hi,

No worry, what matters most is that you see the light of concepts :)

You may like to take a look at the statistics summary I have done up on my website:

http://www.freewebs.com/weews/statisticssummary.htm

Thanks!

Cheers,
Wen Shih

Destined2REIGN SG

Sry ar... hijack back.

Find eqn of the following ellipses?
Intercepts at (0,+-2), (+-3, 0). Sketched the ellipse already but still dun know how to continue from there....

wee_ws SG

Hi,

Recall that an ellipse with centre at the origin has the general form (x^2)/(a^2) + (y^2)/(b^2) = 1.

Given the two points, can you find a and b?

Thanks!

Cheers,
Wen Shih

eagle SG

To add on, if you cannot remember the formula, just look at your friendly graphic calculator :D

Destined2REIGN SG

Hi,

Recall that an ellipse with centre at the origin has the general form (x^2)/(a^2) + (y^2)/(b^2) = 1.

Given the two points, can you find a and b?

Thanks!

Cheers,
Wen Shih

Thanks! is the answer: a=3 b = 2?

Got another qn:

A ractangular hyperbola has asymptopes whose intersection point is the same as the intersection point of the curve in the earlier question and passes through (1,1). Find the equation of the hyperbola.

Earlier Qn: Hyperbola intersects at x axis at x=-1 and x= 1 and y = 0.5

And asymptotes x=-2 and y=-x+2. So which intersection point is the qn referring to?

wee_ws SG

Hi,

Here is a question that I developed for my students as a form of practice:

The hyperbola H has two oblique asymptotes which intersect at the origin. The points A (2, 0) and B (-4, -sqrt(3)) lie on H. Find the equations of the two oblique asymptotes of H. [3 marks]

H undergoes a scaling of 2 units parallel to the y-axis. Sketch the resulting graph of H, indicating clearly its oblique asymptotes and the coordinates of the points corresponding to A and B. [3 marks]

Do give it a try it. Thanks!

Cheers,
Wen Shih

wee_ws SG

Earlier Qn: Hyperbola intersects at x axis at x=-1 and x= 1 and y = 0.5

And asymptotes x=-2 and y=-x+2. So which intersection point is the qn referring to?

Hi,

With the values you found for a and b, do the given points satisfy your expression? In Polya's problem-solving approach, that is the last step i.e. look back at the completed solution.

Starting point: a rectangular hyperbola has what general form?

Point of consideration: could the intersection point be the location where the asymptotes x = -2 and y = 2 - x meet?

Thanks!

Cheers,
Wen Shih

Destined2REIGN SG

Point of consideration: could the intersection point be the location where the asymptotes x = -2 and y = 2 - x meet?

If this is the case, is it safe to say the asymptotes of the hyperbola of this qn pass through (1,1) not the hyperbola itself?

Destined2REIGN SG

Double

wee_ws SG

Hi,

I feel that it's better to clarify with your teacher, rather than speculating :) Thanks!

Cheers,
Wen Shih

Destined2REIGN SG

Hi,

I feel that it's better to clarify with your teacher, rather than speculating :) Thanks!

Cheers,
Wen Shih

Just got it clarified. There was a missing sentence in the question. Thanks for yr help. =)

eagle SG

Mr Wee, can I check with you if mathematical induction on divisibility is in syllabus...

The SEAB syllabus list did not specifically mention what type of mathematical induction is tested...

Rudin SG

Hi Mr Wee,

I have difficulties with this question.

Let a and b be positive integers such that ab + 1 divides a² + b². Show that (a² + b²)/(ab + 1) is a perfect square.

Thanks for your help!

wee_ws SG

Mr Wee, can I check with you if mathematical induction on divisibility is in syllabus...

The SEAB syllabus list did not specifically mention what type of mathematical induction is tested...

Hi,

No divisibility test is assessed.

Specifically, the syllabus assesses:

1. MI to prove simple results and statements involving sequence or series,
2. MI to prove the formula for the general term of a sequence defined by a recurrence relation,
3. How to make conjecture and prove it by MI.

Thanks!

Cheers,
Wen Shih

wee_ws SG

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