O-Level Additional Math

[Guan Hui]

leesf:

suiyuan:

Hi Teacher Guan Hui


Please help.

1)Mrs Lee has 2 daughters,Alice and Judy.The highest common factor and lowest common multiple of their ages are 3 and 168 respectively.If Alice is 3 years older than her sister, find her age.

2)The HCF and LCM of 270 and A are 18 and 5940 respectively. What is the value of A?

Thank you

Answer given for 2nd question in this thread was 396. My child got this question for his homework & I showed him the working but his teacher marked it wrong. Anyone can help? TIA

Hello... I guess the teacher is wrong>.>

[OK Lor]

Hi Sir,


:welcome: :celebrate:

[Guan Hui]

wassup

de email notification sort of stop and was having quite alot of things on hand so was unactive for the last few months.

[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.