Mathematics Question Thread

[jamonwindeyer]

I know that nobody really cares, but I just felt the need to share this exponential growth question which could've gotten 4-6 marks in the HSC... as opposed to in ACTL

(Image removed from quote.)

Any thoughts Jamon?

I think they'd have to step you through that one for it to be included in the HSC

[katnisschung]

Ruiace thanks for your reply
but im having trouble grasping the second part of your answer.
would u mind elaborating on s=5/2 [2(a+5d) +4d]
why is it +4d when the formula is sn=n/2 [2a+(n-1)d]
i dont understand 

[RuiAce]

Ruiace thanks for your reply
but im having trouble grasping the second part of your answer.
would u mind elaborating on s=5/2 [2(a+5d) +4d]
why is it +4d when the formula is sn=n/2 [2a+(n-1)d]
i dont understand 

T₆, T₇, T₈, T₉, T₁₀

There are 5 terms

So n=5

So n-1=4

So (n-1)d=4d

[katnisschung]

thanks Ruiace got it ! 

[RuiAce]

thanks Ruiace got it !

Excellent

[teapancakes08]

When proving that:

(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx

Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)

Or do you have to show the whole working out from A to B?

[Dolphax]

When proving that:

(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx

Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)

Or do you have to show the whole working out from A to B?

I was taught that (and pretty sure that for the HSC):

"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.

... however this seems to go against RuiAce's guide Verbs and Maths.

[jamonwindeyer]

I was taught that (and pretty sure that for the HSC):

"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.

... however this seems to go against RuiAce's guide Verbs and Maths.

Yeah, they don't make that distinction at the HSC level, prove and show are for all purposes identical

When proving that:

(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx

Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)

Or do you have to show the whole working out from A to B?

Hey pancakes! In this case, I would say that's a tad few steps to skip. If you are doing it anyway, you might as well write it down! Especially in proof questions, where the marker needs to verify that you didn't just fudge steps based on a guess/intuition,  it's best to show all but the most trivial steps in this case, try and show how you got to that next result; you've skipped virtually all of the hard work

[RuiAce]

I was taught that (and pretty sure that for the HSC):

"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.

... however this seems to go against RuiAce's guide Verbs and Maths.

[katnisschung]

The sum of 12 terms of an arithmetic series is 186 and the 20th term is 83 find the sum of 40 term....I tried

[RuiAce]

The sum of 12 terms of an arithmetic series is 186 and the 20th term is 83 find the sum of 40 term....I tried

Is that supposed to mean the sum of the first 12 and the first 40 terms?

[katnisschung]

Is that supposed to mean the sum of the first 12 and the first 40 terms?

thats the issue i had RuiAce so i just assumed it was the first 12

[RuiAce]

thats the issue i had RuiAce so i just assumed it was the first 12

Well doing a check with WolframAlpha this gives you
a=-12
d=5

Which gives S₄₀ = 3420

Is that meant to be the answer? (Where confusion arises supplying the answer helps.)

[katnisschung]

Well doing a check with WolframAlpha this gives you
a=-12
d=5

Which gives S₄₀ = 3420

Is that meant to be the answer? (Where confusion arises supplying the answer helps.)

yes that is the correct answer

[RuiAce]