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

Blitz_N7

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

Thank you InteGrand!
 

Blitz_N7

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

Question 21b. Chapter 14 set B
21. The diameters of two circular pulleys are 6cm and 12cm and their centres are 10cm apart.
(a) Calculate the angle α in radians, correct to four decimal places.
(b) Hence find, in centimetres correct to one decimal place, the length of a taut belt that goes round the two pulleys.

My working out is this
http://i.imgur.com/BNZP1GT.jpg

However at the end the answer is supposed to be 49.2cm which is 2sqrt91 + 30.1 . Is the 8.511 not supposed to be there or is the answer from the textbook incorrect?
 

Ambility

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

Question 21b. Chapter 14 set B
21. The diameters of two circular pulleys are 6cm and 12cm and their centres are 10cm apart.
(a) Calculate the angle α in radians, correct to four decimal places.
(b) Hence find, in centimetres correct to one decimal place, the length of a taut belt that goes round the two pulleys.

My working out is this
http://i.imgur.com/BNZP1GT.jpg

However at the end the answer is supposed to be 49.2cm which is 2sqrt91 + 30.1 . Is the 8.511 not supposed to be there or is the answer from the textbook incorrect?
 

hedgehog_7

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

(Induction) P.g. 235 Question 4 (a) (i) For even n: n^3 + 2n is divisible by 12.
(B) (ii) n^2 + 2n is a multiple of 8.

In the final step of the induction process for 4(a) i end up with 6k^2 +12k +12 +12m. Am i allowed you just factorise it like this 12(k^2/2 + 2k +2 +2m) or have i done something wrong in the process?
 

InteGrand

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

(Induction) P.g. 235 Question 4 (a) (i) For even n: n^3 + 2n is divisible by 12.
(B) (ii) n^2 + 2n is a multiple of 8.

In the final step of the induction process for 4(a) i end up with 6k^2 +12k +12 +12m. Am i allowed you just factorise it like this 12(k^2/2 + 2k +2 +2m) or have i done something wrong in the process?
 

hedgehog_7

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

1) Prove n^2 > 10n + 7 using induction, n>=11
2) Prove 2^n > 3n^2 for n>=8
 

hedgehog_7

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

Silly question which is why im stuck. Why is (n+1)^2 > 10n + 2n +1? by using the inductive hypothesis.
 

Blitz_N7

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

Excercise 14H, Question 19.
In part d they ask to show that the area of the rectangle is maximised when tana=1/2. However when I find the nature of the stationary point it gives me a minimum. :/
 

InteGrand

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

Excercise 14H, Question 19.
In part d they ask to show that the area of the rectangle is maximised when tana=1/2. However when I find the nature of the stationary point it gives me a minimum. :/
 

Blitz_N7

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

A=(2tana+1)^2/2tana
dA/da=sec^2a(4tan^2a-1)/2tan^2a
d^2a/da^2=(sec^2a(4tan^4a−tan^2a+sec^2a))/tan^3(x)
 
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Blitz_N7

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

 

InteGrand

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

It must be a typo, they meant minimised. It is clear by drawing a quick sketch that the area can be made arbitrarily large by making the line near-vertical or near-horizontal. (This shows why it is a good idea to quickly sketch the situation, to help get a feel for the question, if nothing else.) :)
 

Blitz_N7

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

It must be a typo, they meant minimised. It is clear by drawing a quick sketch that the area can be made arbitrarily large by making the line near-vertical or near-horizontal. (This shows why it is a good idea to quickly sketch the situation, to help get a feel for the question, if nothing else.) :)
That's what I thought. Thank you InteGrand. Btw is it allowed to test nature of stationary points by using a table of values or is it always have to be done by finding second derivative?
 

InteGrand

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

That's what I thought. Thank you InteGrand. Btw is it allowed to test nature of stationary points by using a table of values or is it always have to be done by finding second derivative?
 

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

Pg 234, Q 1 (a)...

I saw the example, but I'm just soo confused.
 

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