Cambridge Prelim MX1 Textbook Marathon/Q&A (2 Viewers)

InteGrand

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

I understand your answer and working. But could you explain how you get your second set of points:



because the equation is both symmetric. I know it has something to do with the circle being centred at (0,0) but am not entirely sure.

Thanks
 
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appleibeats

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

Without doing any calculations, my guess is that it's a square.
Thanks for that previous question. I understand now how y and x are interchangeable.

Could you please expand on how to get a square in this question.

Thanks.
 

appleibeats

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

Desperately need help with Question 26 from 8H.

if the equations mx^2 + 2x + 1 = 0 and x^2 + 2x + m = 0 have a common root, find the possible values of m and the value of the common root in each case.

The answer in the book is:

When m = 1, x = -1, and when m = -3 , x = 1

Thank you for helping me answer this question!
 

calebwhitaker199

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

Could somebody please post a picture of the cover of the 2015 year 11 extension 1 cambridge textbook ??
 

lollipopstupid

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

6N 18. [A rather difficult proof] CAMBRIDGE
 

appleibeats

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

Need help with question 12 from 10B

the function y = ax^3 + bx^2 + cx + d has a relative maximum at the point (-2,27) and a relative minimum at the point (1,0). Find the values of a,b,c,d.

Thank you for your help.
 

leehuan

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

We have several simultaneous equations here:

From the fact that the points (-2,27) and (1,0) pass through the graph of y=ax^3+bx^2+cx+d
27 = a(-2)^3 + b(-2)^2 + c(-2) + d ---------eqn 1
0 = a(1)^3 + b(1)^2 + c(1) + d ----------eqn 2

dy/dx = 3ax^2 + 2bx + c
Since (-2,27) and (1,0) are relative minima and maxima respectively, we know that when x=-2 and x=1 we have stationary points.
At a stationary point, dy/dx = 0
So we also have:
0 = 3a(-2)^2 + 2b(-2) + c ----------eqn 3
0 = 3a(1)^2 + 2b(1) + c -----------eqn 4

My advice is to do eqn 1 - eqn 2 first. Then you have another equation in terms of a, b, and c. Call that eqn 5.

Then solve eqn 3, 4 and 5 to get a, b and c. Which you can sub in to 2 to get d.
 

appleibeats

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

Thanks for that help.

Do you also know how to solve Q 13 part b from 10B.

b)

Show that y = x^a(1-x)^b has a turning point whose x coordinate divides the interval between the points (0,0) and (1,0) in the ration a:b


It is obviously related to part a) which I have done but am unsure how to go about this question.

Thank you for your help.
 

InteGrand

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

Thanks for that help.

Do you also know how to solve Q 13 part b from 10B.

b)

Show that y = x^a(1-x)^b has a turning point whose x coordinate divides the interval between the points (0,0) and (1,0) in the ration a:b


It is obviously related to part a) which I have done but am unsure how to go about this question.

Thank you for your help.
















 
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appleibeats

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

Need help with 10C.

Question 8:

y = |x| +3

a) find dy/dx when x < 0 and when x > 0

I know what the curve look like, and that when < 0 it has a negative gradient and when x > 0 it is positive gradient.

But how do you show that working out with the absolute value. Isn't any number ( positive or negative) inside the absolute value become positive??

Also Q10)

Part a) can do : differentiate f(x) = ( x - 2) ^ 1/5

Part b) show that there are no stationary points, but that a critical value occurs at x = 2 .

I thought stationary points is when the derivate is 0. But that is wrong as that would mean 2 is a stationary point but it isn't. It is instead a critical point. Please help clarify the meanings.

Thanks for helping and explaining.

Cheers.
 

InteGrand

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

Need help with 10C.

Question 8:

y = |x| +3

a) find dy/dx when x < 0 and when x > 0

I know what the curve look like, and that when < 0 it has a negative gradient and when x > 0 it is positive gradient.

But how do you show that working out with the absolute value. Isn't any number ( positive or negative) inside the absolute value become positive??

Also Q10)

Part a) can do : differentiate f(x) = ( x - 2) ^ 1/5

Part b) show that there are no stationary points, but that a critical value occurs at x = 2 .

I thought stationary points is when the derivate is 0. But that is wrong as that would mean 2 is a stationary point but it isn't. It is instead a critical point. Please help clarify the meanings.

Thanks for helping and explaining.

Cheers.




Graphically, the function's slope tends to plus or minus infinity as you approach x = 2: http://www.wolframalpha.com/input/?i=plot+(x-2)^(1/5)
 
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appleibeats

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

Thanks for your help. Really appreciate it. It now makes more sense.

Also do you know how to do question 10b from 10D.

If y = (2x - 1)^ 4, prove that d/dx(y dy/dx) = y d^2y/dx^2 + (dy/dx)^2.

What is most troubling me is how to find d/dx of y dy/dx which equals i believe 8y(2x -1)^6 ... what do you do with the y at the front??

Thanks for your help in advance.

Cheers
 

InteGrand

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

Thanks for your help. Really appreciate it. It now makes more sense.

Also do you know how to do question 10b from 10D.

If y = (2x - 1)^ 4, prove that d/dx(y dy/dx) = y d^2y/dx^2 + (dy/dx)^2.

What is most troubling me is how to find d/dx of y dy/dx which equals i believe 8y(2x -1)^6 ... what do you do with the y at the front??

Thanks for your help in advance.

Cheers




 

appleibeats

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

could you explain how you used the product rule? I don't quite seem to get that. Thanks.
 

appleibeats

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

Disregard my last question, I figured it out. But could you explain what you mean by 'both functions of x' in your working out. Thank you.
 

appleibeats

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

Also, do you know how to answer question 13 from 10D. Thank you.
 

appleibeats

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

Sorry, the question is:

Find positive integers a and b such that

x^2y'' + 2xy' = 12y, where y = x^a + x^-b.

Thank you.
 

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