O-Level Additional Math

[beautifulalps]

Hello Teacher, pls help us.

(-2)^5x(-3)4(-5)+(-6)^2-(-7)( - 8 )

this answer must be 8. But i could not solve that answer. There is something wrong. :stupid:

[iFruit]

beautifulalps:

Hello Teacher, pls help us.

(-2)^5x(-3)4(-5)+(-6)^2-(-7)( - 8 )

this answer must be 8. But i could not solve that answer. There is something wrong. :stupid:

It should perhaps be

(-2)^5 + (-3)4(-5)+(-6)^2 -(-7)( - 8 )

[Guan Hui]

iFruit:

beautifulalps:

Hello Teacher, pls help us.

(-2)^5x(-3)4(-5)+(-6)^2-(-7)( - 8 )

this answer must be 8. But i could not solve that answer. There is something wrong. :stupid:

It should perhaps be

(-2)^5 + (-3)4(-5)+(-6)^2 -(-7)( - 8 )

beautifulalps
for your question ans shd be -1900 if i am not wrong
-32*60+36-56=-1900
maybe you copy it wrongly?

I think ifruit is correct
-32+60+36-56=8
which give you the ans you want=D

[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.

[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.