A maths - Differentiation

siansterrr SG

1) A curve is defined by y = [(x - a)/(b - x)]^1/2 where a < x < b and a and b are constants.Show that the gradient of the curve at x = (a + b)/2 is 2/(b - a).

I cant seems to get 2/(b - a) and i got 4/[2/(b - a)]^1/2 instead.any1 can help?

2) Find the equation of the equation of the tangent to the curve y = (4/x^2) + 1 at the point where x = a.This tangent meets the axes at P(b,0) and Q(0,b).Find the value of a and of b.

skythewood SG

for 2, differentiate your curve equation.
than sub in x=a to get the gradient for your tangent.
use Y =mX + C, where C is the constant and m is the gradient
to find C, let it mX +C = your curve.

sub in y= 0 or x =0 to get your intercept with axes.

Mikethm SG

y = [(x - a)/(b - x)]^1/2

y = [(x-a)^(1/2)]/[(b-x)^(1/2)]

dy/dx

= [ (1/2)(x-a)^(-1/2)(1)(b-x)^(1/2)-(1/2)(b-x)^(-1/2)(-1)(x-a)^(1/2)]/(b-x)

= 1/2(x-a)^(-1/2)(b-x)^(-1/2)[(b-x)+(x-a)]/(b-x)

=(b-a)/ [2(x-a)^0.5(b-x)^1.5)]

When x = (a+b)/2

dy/dx

= (b-a)/ {2[(b-a)/2]^0.5][(b-a)/2]^1.5}

=(b-a)/{2[(b-a)/2]^2

=(b-a)/0.5(b-a)^2

=2/(b-a)

Now that I had answered your question. I would like to tell you that you are wasting precious time if you are preparing for the O levels A Maths papers. Because such messy mechanical aspect will never come out in the O level. If any of my students dare to waste their time on such stupid questions in this final 2 weeks, I will refuse to answer them and whack them with 100 simple questions. Maybe you forgot O stand for Ordinary? But go ahead and practice more of such questions if you like, a couple of my students are in danger of ending up with B3s and if more people are like you, then their chance of an A2 would be very much increased. :)

The O level is a test of consistency and understanding (simple logic). Not a game of who can do more stunts. Never had I seen in 30 years such a machanically complex question in the O level and never had I seen question requiring more than common sense and logic. You show me any questions in the past 30 years and I will show you a simple answer. And don't be stupid and think that your year must be harder... 1st this is the first year of a new syllabus and they don't rock the boat in such a situation. 2nd they are going about content reduction, not content increase you know?

Ahm97sic SG

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