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

appleibeats

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

The answer to that question in the book says:

y / y + 1

I understand your answer, but is the answer in the book right??
 

appleibeats

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

Does anyone know how to answer question 21 from 6A:

a) if x = 2 ^ 1/3 + 4 ^ 1/3, show that x^3 = 6(1+x)

b) if x = 1/2 + 1/2root 5, show that x^2 + x^-2 / x - x^-1 = 3

c) show that pq^-1 - p^-1q / p^2q^-2 - p^-2q^2 = pq/p^2 + q^2


Thanks for your help.
 

appleibeats

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

Does anyone know how to answer question 21 from 6A:

a) if x = 2 ^ 1/3 + 4 ^ 1/3, show that x^3 = 6(1+x)

b) if x = 1/2 + 1/2root 5, show that x^2 + x^-2 / x - x^-1 = 3

c) show that pq^-1 - p^-1q / p^2q^-2 - p^-2q^2 = pq/p^2 + q^2


Thanks for your help.
 

Ambility

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

The answer to that question in the book says:

y / y + 1

I understand your answer, but is the answer in the book right??
Oh crap, I didn't simplify fully :( that's awkward. I'll begin where I left off.

 

WrittenLoveLetters

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

it's a terrible book. Use Cambridge instead. Make Maths in focus extinct from your lives pls :)

ty
I do MIF for class work - even my teacher says its shit, so she gives us hardcore past papers, work from selective schools and uses Cambridge.
 

appleibeats

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

Thanks Ambility for answer that question.
Also wondering if you could help me with Q 5 from 6G:

The question is:

1/ (k^1/2 + (k + 1 ) ^1/2 (k^1/4 +( k +1 )^ 1/4 = ( k + 1) ^ 1/4 - k^1/4

I know its hard to read, best to look at the textbook. Also wondering how do you write your maths on BOS, so I don't have to write it like I do above.

Thanks.
 

Ambility

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

Thanks Ambility for answer that question.
Also wondering if you could help me with Q 5 from 6G:

The question is:

1/ (k^1/2 + (k + 1 ) ^1/2 (k^1/4 +( k +1 )^ 1/4 = ( k + 1) ^ 1/4 - k^1/4

I know its hard to read, best to look at the textbook. Also wondering how do you write your maths on BOS, so I don't have to write it like I do above.

Thanks.
Honestly, I've spent 40 minutes on this problem and I can't get at it. Either it's something simple that I've been overlooking, or it requires some method I haven't yet learnt.

To answer you question on writing maths, I use a thing called LaTeX. It allows you to type in a code between ["tex"] tags (without the quotes), and it will format it in mathematics. If you want to learn how to use it, I recommend looking at this guide and looking at how some people set their LaTeX out. If you click the "Reply with Quote" button on the bottom left of people's comments, you should be able to see their LaTeX.

Anyway, if anyone wants to work out his question, this is it:

 

SpiralFlex

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

^Not silly at all, we all overlook things.
 

yog

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

How would you rationalise the denominator of:

1/(cuberoot(2)-1)
 

appleibeats

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

Question 18 a and c from 6A:

Simplify:

a)

the denominator is meant to be 2^n+1 +2, can't get it to work for some reason.

answer is :

c)

answer is: -2^n3^n
 
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appleibeats

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

Also Question 20F from 6A:

if a = 2^ 1/2 + 2^-1/2 and b = 2^1/2 - 2 ^-1/2

find:

a^3 + b^3

answer is 7 root 2

Also 21a)

If x = 2^1/3 + 4^ 1/3, show that x^3 = 6(1 + x )
 

InteGrand

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

Question 18 a and c from 6A:

Simplify:

a)

the denominator is meant to be 2^n+1 +2, can't get it to work for some reason.

answer is :

c)

answer is: -2^n3^n
To write , the LaTeX code needs to be written like this: 2^{n+1} (put curly braces around the thing you want in the exponent).

Part a)

Based on what you say the answer is, I think you made a typo in the numerator, it should be instead (OR, the denominator should be . I'll assume the numerator is .

Then the numerator can be written as:

(as )

(using the index law )

(factorising).

The denominator can be written as:

(as , using the index law )

(factorising).

So the original fraction is (cancelling ).

Part c)

The idea is to rewrite the numerator in terms of and using index laws, and then hopefully we will be able to cancel something with the denominator (notice that 12 and 18 can both be written in terms of powers of 2 and 3).

The numerator can be written as:

(as and )

(using the index law )

(using the index law )

(factorising by taking out a common factor of )

(as ).

So the original fraction becomes .
 

Feynman

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

Also Question 20F from 6A:

if a = 2^ 1/2 + 2^-1/2 and b = 2^1/2 - 2 ^-1/2

find:

a^3 + b^3

answer is 7 root 2

Also 21a)

If x = 2^1/3 + 4^ 1/3, show that x^3 = 6(1 + x )
First question:

Find the values of a, b, a squared, b squared and ab from previous parts of the question. Take the positive square roots of a squared and b squared to find a and b (because the question gives us positive values for a and b).

Factor to make calculating easier (sum of two cubes):



Substitute the values:



which becomes



Multiply:







Second question:





























 

appleibeats

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

Question 18b and c from 6B:



a) ALREADY ACHIEVED

Simplify SD, S + D, S - D, S^2 - D^2

b) Rewrite the formulae for S and D as quadratic equations in . Hence express x in terms of S, and in terms of D, in the case where x > 1

c)
 
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Feynman

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

dead thread?
 

shexz

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

Hi, not sure how to go about question 16 from chapter 4J. The question is

the side of a triangle are n2 + n + 1 , 2n + 1 and n2 - 1, where n>1. Find the largest angle of the triangle.

( n2 being --> n squared )

Thanks.
use cosine rule
 

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