3U Maths Question Thread

[RuiAce]

Ok, thank you both! That's good to know about the x and y, I do it sometimes but I was never sure if it was required!

If I were marking I'd be lenient and say whatever, but technically speaking yes it is required.

TLDR of the above:
Jake's method: plot points and be lazy <3
My method: build it up

[jakesilove]

If I were marking I'd be lenient and say whatever, but technically speaking yes it is required.

TLDR of the above:
Jake's method: plot points and be lazy <3
My method: build it up

Gotta say, x and y will never lose you marks. And hey, I could have done it the mathsy way, I just reckon my method is faster xx

[znaser]

Not sure how to tackle part 2

[jakesilove]

Not sure how to tackle part 2

You sort of need to logic this one out. Between the two turning points, the gradient will be of a constant sign (ie positive or negative). Thus, by finding the y values at the two turning points, you can very easily sketch the graph. I imagine both turning points will be above or below the axis, meaning that the only intercept will be as one side goes to infinity! Basically, draw a rough sketch of the graph to prove that there is only one zero

[nimasha.w]

hi! i don't fully understand how you simplify things like these and those similar :-)

[znaser]

You sort of need to logic this one out. Between the two turning points, the gradient will be of a constant sign (ie positive or negative). Thus, by finding the y values at the two turning points, you can very easily sketch the graph. I imagine both turning points will be above or below the axis, meaning that the only intercept will be as one side goes to infinity! Basically, draw a rough sketch of the graph to prove that there is only one zero

Thanks. But I'm still not sure on how to show that for specifically A<3root3/2

[kevin217]

How do we get this calculation?

[Cindy2k16]

Could someone explain the answer to HSC Maths ext 1 2013 Q14 b) iii)? I have the Excel past papers book and I dont really understand what they're doing in the answers. [if anyone has the book, I'm confused starting from 'So (1+x² + 2x)²ⁿ = etc]

[jamonwindeyer]

hi! i don't fully understand how you simplify things like these and those similar :-)

Hey! These, your best bet is to start by putting everything over a common denominator (in this case, (k+2)!). Pick the biggest denominator, and then figure out what is missing from the others to obtain that! EG -



What you do from there is up to you, but the common first step for simplifying factorial expressions is to put everything over one denominator. The answer almost always comes out that way

[jamonwindeyer]

How do we get this calculation?

Like, where do the numbers come from? Remember that \(\cot\) is just the reciprocal of \(\tan\) if you mean the formula itself I'd have to peek the question

[jamonwindeyer]

Could someone explain the answer to HSC Maths ext 1 2013 Q14 b) iii)? I have the Excel past papers book and I dont really understand what they're doing in the answers. [if anyone has the book, I'm confused starting from 'So (1+x² + 2x)²ⁿ = etc]

That has definitely been answered before, and I'm hoping Rui can work his magic and dig up the answer because I can't find it. Otherwise I'll give you an explanation this evening (just doing a quick pass through of questions at the moment, and yours is a doozy)

[kevin217]

Like, where do the numbers come from? Remember that \(\cot\) is just the reciprocal of \(\tan\) if you mean the formula itself I'd have to peek the question

Sorry, I meant like when I input the numbers into my calculator, I'm getting a different answer. So I'm guessing when I'm typing in is wrong

[jakesilove]

Sorry, I meant like when I input the numbers into my calculator, I'm getting a different answer. So I'm guessing when I'm typing in is wrong

Is your calculator in degree mode?

[jamonwindeyer]

Thanks. But I'm still not sure on how to show that for specifically A<3root3/2

Substitute in the values of the turning points:




The point of interest is that top one; we will only have two zeroes if THAT function value falls below or on the x axis. Otherwise, it turns back around to soon and we are stuck with a single zero, as required. Therefore, we need:



That was actually a little trickier than it appeared on first glance does it make sense why I've done what I've done?

[kevin217]

I'm inputting 2000^2 x (tan(13)^2 - tan(15)^2)   Is this correct?