O-Level Additional Math

[iFruit]

elkniwt:

Hi,


May I ask why this is not acceptable? This is from my niece test and she was only given 1 out of the 3 marks though she got it right.

Prove cos 3x - cos x = - 4 (sin^2 x )cos x

Her working :
LHS = cos 3 x - cos x
= -2 sin 2x cos x
= -2 (2 sin x cos x) cos x
= -4 (sin^2 x) cos x

[note sin^2 x = sin (square) x i.e. (sin x)^2 ]

Teacher said she did not write out the full factor formula so minus off 2 marks. So in the exam, cannot skip step is it? Anyone can help ??

Regards.

I think the correct working should be something like below..

LHS = cos 3 x - cos x
= -2 (sin2x sinx)
= -2 (2sinx cosx sinx)
= -4 sin²x cosx

HTH.

[elkniwt]

Hi iFruit,


Sorry, it is my typo, her actual working is like yours. I have typed the sin x as cos x, I have edited her actual working in bold. Please see.

Her working :
LHS = cos 3 x - cos x
= -2 sin 2x sin x
= -2 (2 sin x cos x) sin x
= -4 (sin²x) cos x

But she is given 1 mark out of 3 in her class test. This is the teacher's answer:

LHS = cos 3 x - cos x
= -2 {sin 1/2(3x+x) sin 1/2(3x - x) }
= -2 sin 2x sin x
= -2 (2sin x cos x ) sin x
= -4 sin x sin x cos x
= -4 sin²x cosx

The reason why teacher minus off the 2 marks in highlighted in bold. (cos she did not write out the formula. Please advise. Thank you. )

[p/s : How did you do the superscript for the square ? I copy your sin²x into my post to make it clearer. Thank You]

Regards.

[ADoc]

elkniwt:

Hi iFruit,


Sorry, it is my typo, her actual working is like yours. I have typed the sin x as cos x, I have edited her actual working in bold. Please see.

Her working :
LHS = cos 3 x - cos x
= -2 sin 2x sin x
= -2 (2 sin x cos x) sin x
= -4 (sin²x) cos x

But she is given 1 mark out of 3 in her class test. This is the teacher's answer:

LHS = cos 3 x - cos x
= -2 {sin 1/2(3x+x) sin 1/2(3x - x) }
= -2 sin 2x sin x
= -2 (2sin x cos x ) sin x
= -4 sin x sin x cos x
= -4 sin²x cosx

The reason why teacher minus off the 2 marks in highlighted in bold. (cos she did not write out the formula. Please advise. Thank you. )

[p/s : How did you do the superscript for the square ? I copy your sin²x into my post to make it clearer. Thank You]

Regards.

Hi there. Incidents such as above have always been contentious. In the strictest of sense, it can be considered as \"omission of essential workings\", since there are alternative (less intuitive) solutions, i.e. expanding cos(3x) instead; hence loss of marks.

As a guide, \"essential workings\" can be construed as workings that reflect the student's thought process, including the use or manipulation of formulae. For example, seasoned students will be able to see that 1-sin²x-cos²x = 0, but to ensure full marks, it will be \"essential\" to show that 1- (sin²x+cos²x) = 1-(1) = 0

My advice to my students is to spend that extra 5 seconds writing the working even though it may be a seemingly \"trivial\" mental arithmetic. This will eliminate any possible loss of marks (& avoid wasting precious exam time, perhaps at rationalising what is essential).

Hope this helps.

[iFruit]

elkniwt:

Hi iFruit,


Sorry, it is my typo, her actual working is like yours. I have typed the sin x as cos x, I have edited her actual working in bold. Please see.

Her working :
LHS = cos 3 x - cos x
= -2 sin 2x sin x
= -2 (2 sin x cos x) sin x
= -4 (sin²x) cos x

But she is given 1 mark out of 3 in her class test. This is the teacher's answer:

LHS = cos 3 x - cos x
= -2 {sin 1/2(3x+x) sin 1/2(3x - x) }
= -2 sin 2x sin x
= -2 (2sin x cos x ) sin x
= -4 sin x sin x cos x
= -4 sin²x cosx

The reason why teacher minus off the 2 marks in highlighted in bold. (cos she did not write out the formula. Please advise. Thank you. )

[p/s : How did you do the superscript for the square ? I copy your sin²x into my post to make it clearer. Thank You]

Regards.

Hi elkniwt,

1) Deducting 2 marks does seem harsh but I suppose ADoc's remarks are aptly put.

2) You can use \"& # 178;\" (without spaces & quotes) for superscript 2. It's part of iso-8859-1 character set.

HTH.

[atutor2001]

elkniwt:

.....
Teacher said she did not write out the full factor formula so minus off 2 marks. So in the exam, cannot skip step is it? Anyone can help ??

Regards.

Hi elkniwt

Imo it is lucky to have a teacher like that - forcing the kid to provide \"proper presentation\". I remembered questioning my kids why they are putting in such detail working steps. Much later, I realised that that is \"the requirement\" if one wants to do well for math in sec. Many students find last year's O level E math very easy. However, not many get A - I think it is because of their \"presentation\".

[SKT]

Answer obtained from a Trigo question as such:

sin x = 1/2 or sin x = 1
x = 30°, 150° or x = 90° --(1)
x = 30°, 90°, 150° --(2)

Should we stop at (1) or (2)?

TIA.

[ADoc]

SKT:

Answer obtained from a Trigo question as such:

sin x = 1/2 or sin x = 1
x = 30°, 150° or x = 90° --(1)
x = 30°, 90°, 150° --(2)

Should we stop at (1) or (2)?

TIA.

Hi there! Stopping at either is acceptable. However, in terms of mathematical presentation of coherence & convention, we usually write, x = 30°, 90° or 150° as a concluding statement.

Hope this helps. Cheers!

[elkniwt]

Hello,


Thanks to ADoc, iFruit and atutor2001 for your comments and advices !!
:thankyou:

Sorry I sound so exaperated in my posting. I just felt sorry to see her so upset and her eyes reddening when she told me. She got 11 out of 20 for the test, if not for this qn and another qn, she could have gotten 17. This other qn also as frustrating cos she got 0 out of 4 though she proved it correct. Teacher says she did not understand how my niece arrived at the answer. Though after explaining to the teacher, she could understand, she still did not give her the marks.

Appreciate this forum as there are many here to help and give advices.

Thanks!

[skyjuice]

Any one has a tuition centre to recommend for Sec 2 Math? Right now DS is borderline pass case but need a quick jump to at least 70 to be offered a Double Science class next yr.


We put up in Bukit Merah area but don’t mind travelling a bit if the teacher is gd. I just checked Learning Lab and its fees are $900+ a term. Is this the going rate for Sec Math classes?

[YLH88]

skyjuice:

Any one has a tuition centre to recommend for Sec 2 Math? Right now DS is borderline pass case but need a quick jump to at least 70 to be offered a Double Science class next yr.


We put up in Bukit Merah area but don't mind travelling a bit if the teacher is gd. I just checked Learning Lab and its fees are $900+ a term. Is this the going rate for Sec Math classes?

You may want to check out with maths hub at

http://www.mathshub.com.sg/