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Year 13 Maths Help Thread

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Original post by jamestg
Thanks! The bit I put in bold, is that just a principle we have to know then?


You have to know that - it comes from the infinite series of e^x being equal to

1+x+x^2/(2!)+x^3/(3!)+x^4/(4!) + ...
Note that if you take the derivative term by term the first term disappears and the rest 'shift' so that you end up with the same sequence (e^x) again
(edited 7 years ago)
Original post by jamestg
Thanks! The bit I put in bold, is that just a principle we have to know then?


Yes, that's one of the definitions of e^x.
Original post by Zacken
Yes, that's one of the definitions of e^x.


If only we did the exponentials chapter before differentiation...
Reply 603
Avatar for Palette
Palette
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Is this a good question to leave up to Year 13 students?

Can we use matrices to see how many solutions the following simultaneous equations have?

x−2y+3z=1x-2y+3z=1
2x+3y−z=42x+3y-z=4
4x−y+5z=64x-y+5z=6.

[Question adapted from MAT 1997].
Original post by Palette
Is this a good question to leave up to Year 13 students?

Can we use matrices to see how many solutions the following simultaneous equations have?

x−2y+3z=1x-2y+3z=1
2x+3y−z=42x+3y-z=4
4x−y+5z=64x-y+5z=6.

[Question adapted from MAT 1997].


For those who study 3x3 matrices it is, and that's in one of the later FP modules, so not sure how many that would be. Quite a straight forward one in which case by the looks of it.

Spoiler

(edited 7 years ago)
Original post by Palette
Is this a good question to leave up to Year 13 students?

Can we use matrices to see how many solutions the following simultaneous equations have?

x−2y+3z=1x-2y+3z=1
2x+3y−z=42x+3y-z=4
4x−y+5z=64x-y+5z=6.

[Question adapted from MAT 1997].

It's fine for yr13 because it can be done with awkward algebra (the way i'd do it, remember to consider any cases with denominators (which there will be) equaling 0 differently though)
You can use matrices.
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Palette
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Ok, the Bernouilli polynomial one is ready to cook, though I wish Siklos had used the identity sign instead of the equals sign in
Unparseable latex formula:

\frac{\mathrb{d}B_n}{\mathrb{d}x}=nB_{n-1}(x)

. I will type it up for marking soon. The key to the last part is 'adding zero creatively'.
(edited 7 years ago)
Original post by Palette
Is this a good question to leave up to Year 13 students?

Can we use matrices to see how many solutions the following simultaneous equations have?

x−2y+3z=1x-2y+3z=1
2x+3y−z=42x+3y-z=4
4x−y+5z=64x-y+5z=6.

[Question adapted from MAT 1997].


Surely the answer to your question is just a simple yes.
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Original post by B_9710
Surely the answer to your question is just a simple yes.


I should have then added the multiple choice similar to the one in the actual MAT question:

a) One solution b) two solutions c) three solutions d) no solutions e) infinitely many solutions.

Or I could have phrased it as 'find the number of solutions to the simultaneous equations using matrices'
(edited 7 years ago)
http://files.physicsandmathstutor.com/download/Maths/A-level/S2/Solutionbank-Heinemann/S2%20Chapter%202.pdf
s2 question 9c exercise 2c
Why is the (pX>n)>0.99 not the probability its greater or equal to as if they have a number of boats equal to the amount demanded is that not sufficient to meet all demands so why is it just greater than n as i thought it cud equal n too if n are demanded?
Original post by youreanutter
http://files.physicsandmathstutor.com/download/Maths/A-level/S2/Solutionbank-Heinemann/S2%20Chapter%202.pdf
s2 question 9c exercise 2c
Why is the (pX>n)>0.99 not the probability its greater or equal to as if they have a number of boats equal to the amount demanded is that not sufficient to meet all demands so why is it just greater than n as i thought it cud equal n too if n are demanded?


dodgy link
Reply 611
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Palette
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Let f(x+1)−f(x)=(n+1)xnf(x+1)-f(x)=(n+1)x^n and F′(x)=f(x)F'(x)=f(x). Is F(x+1)−F(x)=xn+1+cF(x+1)-F(x)=x^{n+1}+c?
Original post by Palette
Let f(x+1)−f(x)=(n+1)xnf(x+1)-f(x)=(n+1)x^n and F′(x)=f(x)F'(x)=f(x). Is F(x+1)−F(x)=xn+1+cF(x+1)-F(x)=x^{n+1}+c?


Yes
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Original post by ValerieKR
Yes


I'm worried that the presence of the 'c' completely derails my proof by induction for the Bernouilli polynomials STEP question which is really annoying although I think I may get around that by using another property. :frown:
Original post by Palette
I'm worried that the presence of the 'c' completely derails my proof by induction for the Bernouilli polynomials STEP question which is really annoying although I think I may get around that by using another property. :frown:


you're on the right lines
Q) "The diagram shows a particle of mass 0.5 kg resting on a rough plane inclined at 30 (degrees) to the horizontal. The coefficient of friction between the particle and the plane is 0.4. A of force of magnitude PN, acting directly up the plane, is just sufficient to prevent the particle sliding down the plane. Find the value of P."
Original post by Coolsul98
Q) "The diagram shows a particle of mass 0.5 kg resting on a rough plane inclined at 30 (degrees) to the horizontal. The coefficient of friction between the particle and the plane is 0.4. A of force of magnitude PN, acting directly up the plane, is just sufficient to prevent the particle sliding down the plane. Find the value of P."


Do you know how to resolve forces?
Original post by B_9710
Do you know how to resolve forces?


Yeah did that for Fgrav and added it to the Coefficient of friction but my answer is way off. P=0.768 in the mark scheme. Im not sure how they arrived to that answer
http://www.physicsandmathstutor.com/a-level-maths-papers/s2-solutionbank/question 9c exercise 2cWhy is the (pX>n)>0.99 not the probability its greater or equal to as if they have a number of boats equal to the amount demanded is that not sufficient to meet all demands so why is it just greater than n as i thought it cud equal n too if n are demanded
(edited 7 years ago)
http://files.physicsandmathstutor.com/download/Maths/A-level/S2/Solutionbank-Heinemann/S2%20Chapter%202.pdf
s2 question 9c exercise 2c
Why is the (pX>n)>0.99 not the probability its greater or equal to as if they have a number of boats equal to the amount demanded is that not sufficient to meet all demands so why is it just greater than n as i thought it cud equal n too if n are demanded
If first link dont work its chapter 2 s2 http://www.physicsandmathstutor.com/a-level-maths-papers/s2-solutionbank/
(edited 7 years ago)

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