# Thread: Cambridge Prelim MX1 Textbook Marathon/Q&A

1. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

My answer:

Greatest displacement at amplitude where v = 0

When v = 0

( x - 2) (x + 4) = 0

so x = 2 or x = -4

Now acceleration = -3 -3x

when x = -4 ( greatest displacement )

acceleration = 9 m /s^2

But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2

Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??
The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.  Reply With Quote

2. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by Nailgun what do you mean lel?
When your identity is numerical, i.e there are no variables, you should be aiming to prove it without shifting anything.

When your identity has variables, you can shift things around, maybe prove it using calculus.

Or you could be me and do it by inspection.  Reply With Quote

3. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by InteGrand The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.
So displacement can be either positive or negative?
Whereas distance is positive or 0 only.  Reply With Quote

4. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats So displacement can be either positive or negative?
Whereas distance is positive or 0 only.
Distance is a scalar (magnitude only) whereas displacement is a vector (magnitude and direction)

Therefore yes  Reply With Quote

5. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

My answer:

Greatest displacement at amplitude where v = 0

When v = 0

( x - 2) (x + 4) = 0

so x = 2 or x = -4

Now acceleration = -3 -3x

when x = -4 ( greatest displacement )

acceleration = 9 m /s^2

But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2

Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??
Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.  Reply With Quote

6. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by davidgoes4wce Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.
It's from the Grammar Trial 2015  Reply With Quote

7. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats It's from the Grammar Trial 2015
Uhh

Sorry for nitpicking but can you please leave this thread for the textbook questions  Reply With Quote

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

.  Reply With Quote

9. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread  Reply With Quote

10. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats Have you learnt Implicit Differentiation?  Reply With Quote

11. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by si2136 Have you learnt Implicit Differentiation?
Yes, but the questions from the chapter about sums and products. So I think they want us to use that.  Reply With Quote

12. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats Yes, but the questions from the chapter about sums and products. So I think they want us to use that.
equate both sides, you have a quartic equation

α is a tangent, thus, a double root.

The four roots are α,α,β,1 where β is some other root.

Use the product and sum of roots formulae to determine the values of the roots.  Reply With Quote

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

Is there a way to do this question without "equating coefficients"?
http://pasteboard.co/C1Wjawh.png  Reply With Quote

14. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by Blitz_N7 Is there a way to do this question without "equating coefficients"?
http://pasteboard.co/C1Wjawh.png
Yes, there is also a combinatorial proof that can be given. (Note that cj is just n choose j, from the Binomial Theorem.)  Reply With Quote

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

Thank you Integrand!  Reply With Quote

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

polynomial.png
induction.png

Hey guys, need help with these questions on polynomials and induction  Reply With Quote

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

Say roots are a and a2

.: sum of roots: a + a2 = -m ==> m = -a(a+1)

product of roots: a x a2 = a3 = n

.: m3 = a3(-a3 - 3a2 - 3a -1)

= n(-n +3m -1)

= n(3m - n -1)  Reply With Quote

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

Screen Shot 2016-05-03 at 7.58.06 pm.png

Not sure how to answer part b

Do i get the cartisan form?  Reply With Quote

19. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats Screen Shot 2016-05-03 at 7.58.06 pm.png

Not sure how to answer part b

Do i get the cartisan form?  Reply With Quote

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

For part c) Do i differentiate this equation in part b) in respects to T ? If so how do you find the derivate of x(T) squared ??  Reply With Quote

21. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats how do you find the derivate of x(T) squared ??  Reply With Quote

22. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by InteGrand Found T to be 4, now how do I find max theta. Do I sub t = 4 into displacements of x and y and differentiate parametrically. I tried and got -cos(x)/sin(x) x for theta

Answer says 30 degrees  Reply With Quote

23. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Originally Posted by appleibeats Found T to be 4, now how do I find max theta. Do I sub t = 4 into displacements of x and y and differentiate parametrically. I tried and got -cos(x)/sin(x) x for theta

Answer says 30 degrees  Reply With Quote

24. ## Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread  Reply With Quote

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

Is it right for part b) to plug The new velocity and angle into part a max height and then equate it with part a) ?  Reply With Quote

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