Hi siansterrr,

I agree with Mikethm's advice for "O" level Add Maths students who are taking the exam in two weeks time.

The patterns of the questions set in the "O" level Add Maths Exam are the same years after years. Hence, students are always told to practise the past actual "O" level exam questions in the ten years series at least 3 times before they go to sit for their exams.

For those very hardworking students who have already done it, read each question again in the ten years series and ask yourself what will be the steps required to work out the answer for each question. Once, you can do this effortlessly, you can be assured of a A1 or A2, provided you do not make careless calculation mistakes. 

However, for this year, there might be some surprises as there are new topics that do not have past actual "O" exam questions on them.

Students can go to those old ten years to practise on some of these new topics.

Students can also practise on the Specimen papers provided by MOE for the new 2008 syllabus.

In addition, students can practise on the various 2008 School Prelim Exam questions. 

Students can also practise on the Shing Lee Addtional Workbook 4 especially on those new topics in the 2008 syllabus.

Hope this will be of help to those students who will be taking their "O" Add Maths Exam in two weeks time. 

Thank you for your kind attention.

Regards,

ahm97sic

Hi bonkysleuth,

Alternatively, we can use the cover up method to solve this partial fraction question as the factors in the denominators are linear.

4x^2 - 11x + 9 / (2x^2 -x -3)(x+5)

= 4x^2 - 11x + 9 / (2x-3)(x+1)(x+5) = A/(2x-3) + B/(x+1) + C/(x+5)

[The cover up is done on the part in red]

Cover 2x - 3, substitute  x = 3/2 into 4x^2 - 11x + 9 / (x+1)(x+5) to get A

Cover x + 1, substitute x = -1 into 4x^2 - 11x + 9 / (2x-3)(x+5) to get B

Cover x + 5, substitute x = -5 into 4x^2 - 11x + 9 / (2x-3)(x+1) to get C

Thank you for your kind attention.

Regards,

ahm97sic

Hi tr@nsp0rt_F3V3R,

There are differences and similarities between the 2 methods.

The cover up method is just to let the students know that there is another way to solve partial fraction questions when the factors in the denominators are linear.

This does not mean that the cover up method is better than the substitution method or vice versa. 

(It is just like there are many ways (long division, multiply and equate, inverted L, inspection and factorise, calculator (using MOE approved calculator Casio FX 95 MS or Sharp EL 509WS) method) to solve the cubic equation eg 2x^3 + 3x^2 - 11x - 6 = 0)

Cover up Method                                       Substitution Method

Question                                                   Question

(12x - 6) / [(x+2)(x-4)]                                (12x - 6) / [(x+2)(x-4)]

= A/(x+2) + B/(x-4)                                    = A/(x+2) + B/(x-4)  

Step 1                                                      Step 1

Cover  up (x+2),                                        Multiply throughout by the denominator

substitute x = -2 into (12x - 6) / (x - 4)         [(x+2)(x-4)]

= (12(-2) - 6) / (-2 -4) = 5                           12x - 6 = A(x-4) + B(x+2)

So, A = 5

Step 2                                                       Step 2 (a)

Cover  up (x-4),                                          Substitute  x = -2 into

substitute x = 4 into (12x - 6) / (x +2)            12x - 6 = A(x-4) + B(x+2)

= (12(4) - 6) / (4+2) = 7                               12(-2) - 6 = A(-2-4) + B(-2+2)

So, B = 7                                                     A = 5

                                                                   Step 2 (b)

                                                                   Substitute  x = 4 into

                                                                   12x - 6 = A(x-4) + B(x+2)

                                                                    12(4) - 6 = A(4-4) + B(4+2)

                                                                     B = 7

Thank you for your kind attention.

Regards,

ahm97sic                                      

                                                                  

 

 

Partial Fraction - Cover up Method

The cover up method is not taught in the Shing Lee Additional Mathematics and Pan Pacific Additional Mathematics textbooks.

The cover method can only be used when the factors in the denominators are linear.

Example

If (12x - 6) / [(x+2)(x-4)] = A/(x+2) + B/(x-4), find the value of A and of B.

Step 1 : To find the value of A

Cover  up (x+2), substitute x = -2 into (12x - 6) / (x - 4) = (12(-2) - 6) / (-2 -4) = 5

So, A = 5

Step 2 : To find the value of B

Cover  up (x-4), substitute x = 4 into (12x - 6) / (x +2) = (12(4) - 6) / (4+2) = 7

So, B = 7

Hence, (12x - 6) / [(x+2)(x-4)] = A/(x+2) + B/(x-4)

           (12x - 6) / [(x+2)(x-4)] = 5/(x+2) + 7/(x-4)

Thank you for your kind attention.

Regards,

ahm97sic

Hi Eagle,

You are welcome to include these questions in the examworld.

Thank you for your kind attention.

Regards,

ahm97sic

Hi Xiaobai,

It is logn (9/4) = logn 9 - logn 4.  This rule is found in all the textbooks, guides and 

                                                 ten years series

But, logn 9 / logn 4 is not equal to logn 9 - logn 4.

logn 9 / logn 4 = log10 9 / log10 4 = loge 9 / loge 4    This rule is not found in the

                                                                               usual textbooks, guides and

                                                                               ten years series. However,

                                                                               many students and teachers

                                                                               have already known about it.

[The number or letter in red is in subscript ie the base of the log].

Thank you for your kind attention.

Regards,

ahm97sic

Hi Wishboy,

Well done, your answer is perfectly correct.

The concept used in the second question is

a^loga y = y.

So, 2^[log2 (z + x)] = z + x, 3^ (log3 4) = 4, e^ (ln x^2) = x^2, 10^ (lg 7) = 7 and so on

[The number or letter in red is in subscript ie the base of the log].

Thank you for your kind attention.

Regards,

ahm97sic

 

 

Hi Secretkiller and Skythewood,

The concept used in question 1 is

logn 9 / logn 4 = ratio of the logarithms of any same base ie

logn 9 / logn 4 = log10 9 / log10 4 = loge 9 / loge 4 = log2 9 / log2 4 and so on.

[The number or letter in red is in subscript ie the base of the log].

Thank you for your kind attention.

Regards,

ahm97sic

 

There are two logarithm concepts that are not in the usual textbooks, guides or ten years series. However, these two concepts are already known to students and teachers.

Question

(1)     Evaluate logn 9 / logn 4

(2)     Given that zy = 2^[log2 (z + x)], show that z = x / [y-1]

[The number or letter in red is in subscript ie the base of the log].

These two questions are not dificult as these two questions are just used to illustrate the two logarithm concepts where some students might not be aware.

Thank you for your kind attention.

Regards,

ahm97sic

Hi Secretkiller and Donkhead333,

Oops, I just realized that I have forgotten to type equal zero for the question ie

Question

Given that log3[log2(log5 a)] = log5[log3(log2 b)] = log5[log2(log3 c)] = 0,

Find the value of a + b + c. 

[The number in red is in subscript ie the base of the log].

Please accept my apologies.

The answer of a + b + c = 42.

Thank you for your kind attention,

Regards,

ahm97sic

Hi Donkhead333,

The first part is on the correct path to the answer but the second part has gone off the path. Keep trying and you are sure to get the answer. Don't think it to be difficult, the answer is actually quite simple once you discover the trick or the fun part of the question.

This question appears to be complicated and difficult but actually it is quite simple once you found the answer ie the fun part of the question.

Thank you for your kind attention.

Regards,

ahm97sic

Hi Wishboy,

Thank you for the reply.

I hope that we can just type mathematical symbols in the forum without going through the entire process.

Perhaps they can get the IT moderators to do some programming to allow mathematical symbols and drawings to be done in the forum. It will be best if we can just cut and paste from Microsoft Word or Excel.

Thank you for your kind attention.

Regards,

ahm97sic

Hi Wishboy,

Congratulation, your answer is perfectly correct !

Thank you for your kind attention.

Regards,

ahm97sic

PS : Dear Wishboy, I have noticed that you can type mathematical symbols in the forum and you use a better method than the other forumers. They used to type the mathematical symbols in Microsoft Word or Excel and then print screen and save it as a picture file and then upload it to a website that processes this image before the image file can be inserted into the forum.

Can you kindly share your method of typing mathematical symbols in the forum with us ? Thanks.

Hi Wishboy, there is another fun question on logarithm on the thread "A Logarithm Question" in the forum, perhaps you will like to try it too. The question looks difficult and completed but actually it is not complicated or difficult once you discover the trick or the fun part of the question. Just like the above question that you discover the fun part of the question tan-1 (2) = x and tan x = 2 and tan (x + y).

This question is fun. Perhaps you will like to solve it.

Question

Without using a calculator,

evaluate tan ( tan-1 2 + tan-1 8)

(The number in red is in superscript)

Thank you for your kind attention.

Regards,

ahm97sic

Hi Secret Killer and Donkhead333,

This question looks complicated and difficult but actually it is not difficult or complicated once you discover the trick or the fun part of the question.

I do not know how to type mathemtical symbols eg log 5 a in the forum.

I have typed out the answer using Mathtype in Microsoft Word 2003. I can send you an email with the answer in the attached file. 

Thank you for your kind attention.

Regards,

ahm97sic

Hi Wishboy,

For question on money, if the answer is not exact, we should round off to 2 decimal places eg 18.35892 should rounded off to $18.36.

Another common mistake that students made on questions on money is if the answer is 21.2, some students will leave their answers as 21.2. However, this is not correct, the answer should be $21.20, otherwise marks will be deducted or worse in E. maths where the question is only 1 mark and "O" level examiner cannot give 1/2 mark, so the examiner will give the students zero mark in this case.

Thank you for your kind attention.

Regards,

ahm97sic

Hi tr@nsp0rt_F3V3R

I thought you had just completed your "O" level Prelim exam and you are preparing for the coming "O" level exam.

Never mind, getting 4 A1s in your secondary three year end exam is also very good results. Keep up the good work. Aim for straight As in your next year "O" level exam. Do lots of lots of ten years series questions and REMEMBER the patterns and the ways to solve/ answer these questions without careless mistakes in the actual "O" level exam.

Thank you for your kind attention.

Regards,

ahm97sic

 

Hi tr@nsp0rt_F3V3R,

Congratulations, you have done well in your maths and science.

Indeed, it is more important to practise actual "O" level exam questions instead of practising on school Prelim exam papers or questions in assessment books or questions in textbooks. There are many questions in the school exam papers, assessment books and textbooks that are not really similar to the actual "O" level exam questions.

When a student practises doing the ten year series, he or she will soon realise that there are patterns or fixed ways that the actual "O" level exam questions are being asked. These patterns appear years after years.

So, to excel in the "O" level exam, students are always advised by teachers to practise the whole ten years series at least 3 times before the "O" level exam. Many students got A1 or A2 using this method of study, provided the students can remember the patterns and the ways to solve these questions without careless mistakes. Careless mistakes in the actual "O" level exam can easily cost students a grade (or two grades) below eg from A1 to A2 or from A2 to B3 and so on.

Phua Choo Kang says "Don't play, play"  ,  so study hard now.

Wishing tr@nsp0rt_F3V3R getting straight As in his or her coming "O" level exam.

Thank you for your kind attention.

Regards,

ahm97sic

Question

Given that

Find the value of a + b + c

 

Hi xXBlack_RebelXx,

To ace in "O" and "A" level accounts, you must have the ten years series with the worked solutions. Next, go through the whole ten year series, you will be able to identify that final accounts ie trading, profit and loss statements and balance sheet, partnership accounts, balance day adjustments and so on are commonly tested. Take out some papers or best a notebook, write down all the items that can appear in the trading, profit and loss statement, balance sheet, partnership accounts, balance day adjustments and so on and memorise them. Make sure you do not miss out any items. Next,practise the ten years series at least 3 times before you go for your "O" or "A" level exam. This is what I do to get distinctions A1 and A in my "O" level and "A" level accounts.

Hope this will be of help to you for the study of accounts in your coming exam.

Thank you for your kind attention.

Regards,

ahm97sic

 

Hi Tamago,

Thanks for helping to type the mathematical symbols in the forum.

Thank you for your kind attention.

Regards,

ahm97sic

This question is fun. Perhaps you will like to solve it.

Question

Given that log3[log2(log5 a)] = log5[log3(log2 b)] = log5[log2(log3 c)],

Find the value of a + b + c. 

[The number in red is in subscript ie the base of the log].

Thank you for your kind attention.

Regards.

ahm97sic

Hi Wishboy,

I have sent the answer in an email with the attached file to your email account.

I like this question. It is fun. Please post more.

Thank you for your kind attention.

Regards,

ahm97sic

Hi Mikethm,

Thank you for the information.

Regards,

ahm97sic

 

 

Hi Wishboy,

I do not know how to type the mathematical symbols eg the log n 4 in the forum.

Do you have any email account that can receive attached file ? I have typed out the answer using Mathtype in Microsoft Word 2003. I can send you an email with the answer in the attached file.

Or I can send the attached file to the moderator Eagle and he will kindly type out the answer in the forum.

Thank you for your kind attention.

Regards,

ahm97sic