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

bookss12 · Dec 21, 2016

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

Hi ! could someone lease help with these questions:

9
10c
11a

thanks heaps!

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iso1234 · Dec 21, 2016

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

Does anyone have the answer (and preferably the logic) to 7B Q15? Thanks

envlam · Dec 22, 2016

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

@books: Here is q9. Try to attempt the other questions again. http://imgur.com/KNGlrhH

@iso: https://imgur.com/a/4kQbG

aroon · Jan 2, 2017

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

Raiza_98 said:
Hi I was just wondering where would the best and most useful content be within the book?? Like the 1st excercises are too much a waste of time, which chapters cover the most worth-wile course content??

Do the series and sequences (you don't really need a teacher to understand it), try the calculus (chapter 7) and the trig in chapter 4

vickyera · Jan 8, 2017

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

Has anyone done 8I Q7
a) (p+q+x)(pq+px+qx)-pqx=(p+q)(p+x)(q+x) and the rest b,c,d
do they want me to expand everything or is there an easier way?
thankyou

davidgoes4wce · Feb 6, 2017

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

EX 9A Q 12, I've seen the first stage in writing the answer as :

$\sqrt{x^2+y^2}+y=2$

Part of the reason I've seen is that 'P must above the x-axis' $\implies |y|=y$

I'm not sure why they add the 'y' to it still? It has got me thinking for the last couple of hours. Is there a better way to understand this visually?

InteGrand · Feb 6, 2017

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

davidgoes4wce said:
EX 9A Q 12, I've seen the first stage in writing the answer as :

$\sqrt{x^2+y^2}+y=2$

Part of the reason I've seen is that 'P must above the x-axis' $\implies |y|=y$

I'm not sure why they add the 'y' to it still? It has got me thinking for the last couple of hours. Is there a better way to understand this visually?

What is the question (don't have a copy of the textbook nearby)?

boredofstudiesuser1 · Feb 6, 2017

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

InteGrand said:
What is the question (don't have a copy of the textbook nearby)?

I think it might be this one:

Find the locus of a point P(x, y) which lies above the x-axis so that the sum of its distances to the origin and the x-axis is 2.

InteGrand · Feb 6, 2017

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

boredofstudiesuser1 said:
I think it might be this one:

Find the locus of a point P(x, y) which lies above the x-axis so that the sum of its distances to the origin and the x-axis is 2.

$\noindent In that case, the distance of $P(x,y)$ to the origin is $\sqrt{x^{2} + y^{2}}$ and the distance to the $x$-axis is $y$ (since $P$ is to lie above the $x$-axis). We want \emph{the sum} of these to be $2$, so $\sqrt{x^{2} + y^{2}}+y = 2$.$

a_t · Apr 20, 2017

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

Need help with question 3(allparts) of 10E please

Drongoski · Apr 20, 2017

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

a_t said:
Need help with question 3(allparts) of 10E please

Should try to include the actual question. Not everyone willing to help you has the book. I have the older 3U Yr 11 - the Chapters and exercise numberings may have changed.

Pakka · Apr 22, 2017

Help with Question 11 Exercise 2J
For those without the book: Determine how the curve y = x^3 - x must be transformed in order to obtain the graph of y = x^3 - 3x. {hint: only stretchings are involved}
Full worked solutions would appreciated.
Cheers

InteGrand · Apr 23, 2017

Pakka said:
Help with Question 11 Exercise 2J
For those without the book: Determine how the curve y = x^3 - x must be transformed in order to obtain the graph of y = x^3 - 3x. {hint: only stretchings are involved}
Full worked solutions would appreciated.
Cheers

$\noindent Stretch the original graph vertically by a factor of $b$ and horizontally by a factor of $a^{-1}$, i.e. the graph becomes $y = b\left((ax)^{3} -ax \right) = ba^{3}x^{3} -ba x$. Comparing this to $x^{3} -3x$, we want $ba^{3} = 1$ and $ba = 3$. Dividing these equations shows $a^{2} = \frac{1}{3}\Rightarrow a = \frac{1}{\sqrt{3}}$. Then $ba = 3 \Rightarrow b = \frac{3}{a} = 3\sqrt{3}$. (We can check that these satisfy those two equations.) So the answer is to stretch the original graph vertically by a factor of $b = 3\sqrt{3}$ and horizontally by a factor of $a^{-1} = \sqrt{3}$.$

Pakka · Apr 23, 2017

Thank you

Thatstudentm9 · May 6, 2017

guys I'm in need of some help with [

]simplify
a)1+tan^2(90degrees- θ )
prove
b)cot θ cos θ/cot θ +cos θ=cos θ /1+sin θ

Drongoski · May 6, 2017

Drongoski · May 6, 2017

Thatstudentm9 said:
guys I'm in need of some help with [

]simplify
a)1+tan^2(90degrees- θ )
prove
b)cot θ cos θ/(cot θ +cos θ)=cos θ /(1+sin θ)

Should be amended as shown; otherwise it shows you don't know your algebra or you are being careless and/or sloppy.

z3bra · May 13, 2017

Can someone please help me with Question 12.

Mahan1 · May 19, 2017

z3bra said:
Can someone please help me with Question 12.

$\textrm{Base case} , n=1, \textrm{then} \ \varnothing \ \textrm{and the whole set are the only subsets and the statement follows.}$

$\textrm{Suppose it is true for} \ n=k: \ \textrm{the set A with k elements has } 2^{k} \ \textrm{subsets}$

$\textrm{where } A = \{a_{1},a_{2},\dots, a_{k} \}$

$\textrm{add one element, } a_{k+1} \ \textrm{to A}$

$\textrm{let's call the new set B } = A \cup \{a_{k+1} \} \{a_{1}, \dots, a_{k+1} \}$

$\textrm{We note that all the subsets of B either contain } a_{k+1} \ \textrm{or not}$

$\textrm{number of subsets do not contain }a_{k+1} \ \ texture{is equal to the number of subsets of A} = 2^{k}$

$\textrm{number of subsets containing }a_{k+1} \ \textrm{if we add }a_{k+1} \ \textrm{to each subset of A} \ \textrm{we obtain}$

$\textrm{all the subsets containing } a_{k+1} \ \textrm{which is equal to } 2^{k}$

$\textrm{since the subsets of B either contain }a_{k+1} \textrm{or not then the total number of subsets of B is }$

$2^{k} + 2^{k} = 2^{k+1}$

a_t · Jun 12, 2017

Need help with this please. Q2A of Ex 7B
For each function below, simplify f(x + h) − f(x) / h , then take lim h→0 to find the derivative.

(a) f(x) = 5x + 1

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