Cambridge Prelim MX1 Textbook Marathon/Q&A (3 Viewers)

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Find the derivative of in the simplest form :

sin^-1 1/4 . ( 2x - 3)

Answer says 2/ (7 + 12x - 4x^2)^1/2

Not sure what to do with the 1/4
Do you multiply it with the numbers in the brackets??




 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I have tried the chain rule and I am not getting your result above.

I let u = (2x - 3) / 4 and did the usual du/dx and dy/du
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I have tried the chain rule and I am not getting your result above.

I let u = (2x - 3) / 4 and did the usual du/dx and dy/du
This'll work too, it's just a bit more algebraically tedious when simplifying it.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Still very confused. I still am not getting the result. Also where does the 1/4 go now?
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I don't know that formula. I tried searching for it in the cambridge 3u textbook and can't find it.
If I don't use the formula, is there another method to solving the question?
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I don't know that formula. I tried searching for it in the cambridge 3u textbook and can't find it.
If I don't use the formula, is there another method to solving the question?
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If I don't use the formula, is there another method to solving the question?
Yeah, definitely. You can do it with your original substitution too, it's just more tedious when simplifying it. Maybe you made an algebraic mistake when doing it, so you might want to post your working.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Finally worked it out.

Now stuck on the Show part of part c) in this question. Not sure how to do the branching of it.

Screen Shot 2016-01-10 at 7.24.26 pm.png
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-10 at 10.30.22 pm.png

Could you explain how do find the domain. part a)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

For part b), I get the answer they have in the question except for no absolute sign around the x in the denominator. Why is that? I used chain rule to differentiate the fn.
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread



The fact that x^2/|x| = |x| can be determined by simply realising that |x|^2=x^2

Extra fact: That function is actually f(x)=sec^-1(x)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-11 at 2.29.49 pm.png

Don't know how to do part b)

Answer is 1 - 1/2 (3)^1/2

I have A = integral from 0 to pi/6 sin^2 y du

Is that correct?

then I got integral from 0 to pi/6 1/2 (1 - cos2y) dy

I further continued on but got an incorrect answer.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-11 at 4.23.45 pm.png

Having trouble with part b

Using part a), I took the integral of both side and I got this

Integral of tan^-1 x dx = xtan^-1 x - Integral of x/(1 + x^2) dx

So I need to find the integral of x/(1 + x^2)

Is this the correct method??
 

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