2011 maths past paper questions

[fishbiscuit]

Hey!
I have some concerns with some of the questions in this paper. I have attached the questions and answers.

First one is question 9 d) i)
I dont get why they did it the way they did, and why they had to be extra and make the root of n a negative - how would i know to just do that? I just did it as it is and when i followed through with what i did i got -9? can i just absolute value or something..?

Second one is question 10 b) v)
Again, I don't understand what theyve done and how they just placed the 2r in the first 'working out' and then where they brought in the 2pi in the second 'working out'.

An explanation would be very much appreciated, thank you.

[RuiAce]

Hey!
I have some concerns with some of the questions in this paper. I have attached the questions and answers.

First one is question 9 d) i)
I dont get why they did it the way they did, and why they had to be extra and make the root of n a negative - how would i know to just do that? I just did it as it is and when i followed through with what i did i got -9? can i just absolute value or something..?

Second one is question 10 b) v)
Again, I don't understand what theyve done and how they just placed the 2r in the first 'working out' and then where they brought in the 2pi in the second 'working out'.

An explanation would be very much appreciated, thank you.

I don't see what the problem is with d) i). You can do it this way if you prefer and still reach the same final answer.
\begin{align*}\frac{1}{\sqrt{n}+\sqrt{n+1}}&= \frac{\sqrt{n}-\sqrt{n+1}}{\left( \sqrt{n}+\sqrt{n+1}\right)\left( \sqrt{n} - \sqrt{n+1} \right)}\\ &= \frac{\sqrt{n}-\sqrt{n+1}}{n - (n+1)}\\ &= \frac{\sqrt{n} - \sqrt{n+1}}{-1}\\ &= \sqrt{n+1} - \sqrt{n}. \end{align*}
Otherwise, I don't understand your question.

I will add the second one to the compilation later in the day in its entirety.

[fishbiscuit]

I don't see what the problem is with d) i). You can do it this way if you prefer and still reach the same final answer.
\begin{align*}\frac{1}{\sqrt{n}+\sqrt{n+1}}&= \frac{\sqrt{n}-\sqrt{n-1}}{\left( \sqrt{n}+\sqrt{n-1}\right)\left( \sqrt{n} - \sqrt{n-1} \right)}\\ &= \frac{\sqrt{n}-\sqrt{n+1}}{n - (n+1)}\\ &= \frac{\sqrt{n} - \sqrt{n-1}}{-1}\\ &= \sqrt{n-1} - \sqrt{n}. \end{align*}
Otherwise, I don't understand your question.

I will add the second one to the compilation later in the day in its entirety.

Oh. I think I just did my working out wrong because when rationalising the denominator i didnt change the sign inside the root, are you meant to...?

[RuiAce]

Edit: I did something idiotic. I'm very sorry - will fix that now

[fishbiscuit]

Also... i know this isnt mathematics but i just tried a projectiles question for ext 1 maths and im confused about the working out in a question (2017 13 c ii)

Where did they get sin2theta < 1 ...?
I just don't understand their working out in general, is it okay if i can have another explanation to it?