questionable_i:

Can anyone help me? :thankyou: in advance.


Q1) A function f is defined by f(x)=|x^2-3x|. Find the values of x for which f(x)=x-3.

Q2) Find the x-coordinates of the points of intersection of the curve y=|16-x^2| and the line y=33.

Q3) Find the x-coordinates of all the points at which the graph of y=|x^2-9|-5 meets the x-axis.

For Q1, first we sub one equation into another.

|x^2 - 3x| = x - 3

For modulus, there is the positive and negative side.

For the positive (and removing the modulus),

x^2 - 3x = x - 3
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0

x = 3 or x = 1

For the negative,

x^2 - 3x = -(x - 3)
x^2 - 3x = -x + 3
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0

x = 3 or x = -1

So the values of x are: -1, 1 or 3


You can use the same approach for Q2 and Q3. For Q3, the equation of x-axis is y = 0.

KSP2013777:

Thank you, Kenneth Tutor.

Can you help me with another question, Please?
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Thank you.

The fraction is an improper fraction, since the degree of the numerator is 4 while the degree of the denominator is 3.

Perform long division first. You obtain x + (9 - 3x^2)/(x^3 + 3x)

Finally perform partial fraction decomposition on (9 - 3x^2)/(x^3 + 3x)

Final ans should be: x + 3/x - 6x/(x^2 + 3)

KSP2013777:

I need help with this question part (ii). Can somebody please help. Thank you

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Use the double angle formula: cos 2β = 2 cos^2 β - 1

Make cos β the subject.

Because of the square root, there will be two possible answers (one positive and one negative).


Since 2β and α are in the same quadrant, and sin α is negative and tan 2β is positive, both angles are in the fourth quadrant (between 270° and 360°).

Angle β should be between 135° and 180° (2nd quadrant). Thus we expect cos β to be negative.

Ans should be -√(7/8)

Newtandcucumber:

Hi, can anyone who is familiar with the Singaporean Chemistry O level, advise if the new Chemistry Higher GCSE, done here in the UK, is easier or harder than your o level. Please look at the Specimen Higher Paper only. The URL is below:


http://www.aqa.org.uk/subjects/science/ ... -resources

Generally, I find the specimen papers easier.

The format is different as well. In Singapore, Paper 1 is purely Multiple Choice Questions while Paper 2 is purely open ended.

The topics covered are generally similar, except:

Paper 1: Q3.2 Ball and Stick Model (Not taught in O Level)
Paper 2: Q10.2 & 10.3 Le Chatelier's Principle (Taught in Singapore in A Levels)


Should be okay to practice the Singapore papers!

questionable_i:

Can anyone help me with this question?

Evaluate 2^x/2^4=2^1/2^(2y-2)
Thank you in advance. I need the answer ASAP.

Applying a^m / a^n = a^(m - n),

2^x/2^4 = 2^1/2^(2y - 2)

2^(x - 4) = 2^(1 - (2y - 2))

2^(x - 4) = 2^(3 - 2y)

Comparing the indices on both sides,

x - 4 = 3 - 2y

x = 7 - 2y

I think this is probably a simultaneous equation question. You need another equation to solve for x and y.

KSP2013777:

Yes, thank you, Eddow. Got the answer now.


Can you help me with another one.
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My ans is e^(3/2), but ans key is 1/e^(1/2). Pls help. Tks

Hello. I think you might have made a mistake in the differentiation.

Anyways I suggest you try to simplify the expression (ln part) before differentiating. It will make the differentiation less tedious.


Solution: http://imgur.com/7viZpYS

nani:

What about those in Business Accountancy course, are there any tasks during the holidays?


Thanks

For NBS Accountancy & Business there is an attachment in the May - July holidays. http://www.nbs.ntu.edu.sg/Undergraduate/Bachelor_of_Accountancy/Pages/Programme_Structure.aspx

Should be the same for NUS.

Edit: It will occur only once out of the three/four years.

CarrotTree:

Does this also mean that the student's internship ( overseas or local ) also fall during their holiday break? so it quite difficult to plan for all in the family when there are those in secondary level

There are short and long internship. For some courses it may be optional.

The short ones occur during the long holiday break (Late May - July).

The long ones occur during Semester time and it can eat into the holiday. Typically it lasts for around 5-6 months.

Check your child's school's website for more information on when the internship will occur. Usually, the school will suggest a time period so you can plan in advance. Typically it occurs in Year 2/3.

For example, this is the information for attachment for NTU's EEE:http://www.eee.ntu.edu.sg/Programmes/CurrentStudents/undergraduate/undergraduatefull-time/Documents/Attachments.pdf

Look for the red column that states the condition students must fulfill before being eligible for internship.

Also look out for the time period.

nani:

Thanks for your input.


So the final year is as good as no vacation break. May I know for the non-academic in Dec is it compulsory? What are the consequences if we do not attend.

Reason asking as my family intend to be away for the whole month.

Non-academic activities typically are mainly related to Hall and CCA. These events are student organised.

In NUS & NTU, one reason why students participate in these activities is due to the points system for Hall (Hostel) allocation.


I guess your child is starting university in the upcoming academic year (Aug 2016). So if you miss some events due to holiday, it may affect your child's chances for Hall Admission in the next academic year (Aug 2017).

On the other hand, if your child is not interested in staying in Hall, it's perfectly fine to go on holiday.

Let me know if you need more information!

nani:

Hi


anyone can advice for nus/ntu vacations in june & dec, do they still have to go back for projects etc?

Appreciate an urgent reply. Thanks

June holiday is the long holiday. Typically it starts mid-late May and ends by early August.

December holiday is the short one. Typically it ends early January.


For academic projects, some projects may last an entire academic year. For example, my Final Year Project (Engineering major) started from July and ended May the next year. My December holidays was mostly spent in school.

Check with your school's office if there's any such projects. They should be able to help you.


For non-academic projects (e.g. CCA or hall-related), students can be quite active during the holidays.