Mathematics Question Thread

[RuiAce]

For this (iii):

(Image removed from quote.)

Can I just sub in y into the equation given or do I need to "show" how the equation is found by 'going the other way' if you get what I mean? If so, how would this be done?

Thanks!

Yeah if you subbed it in you would be assuming the result. You have to show it.

[jamonwindeyer]

For this (iii):

(Image removed from quote.)

Can I just sub in y into the equation given or do I need to "show" how the equation is found by 'going the other way' if you get what I mean? If so, how would this be done?

Thanks!

Will just say that, while Rui's method is definitely more mathematically correct, in general you can definitely just substitute, especially for a 1 marker. NESA's solutions do it

[kiiaaa]

hi guys

would you be able to please explain to me what is ' small angles and limits' and where/what types of questions should i beware of them?
i was away that day in class and every time i look at the notes i copied off my friend they make little sense =/
thank you

[RuiAce]

hi guys

would you be able to please explain to me what is ' small angles and limits' and where/what types of questions should i beware of them?
i was away that day in class and every time i look at the notes i copied off my friend they make little sense =/
thank you

[pokemonlv10]

Hey, for this question i just assigned a value and tested all the answers, but would like to know the proper method of doing this?

[kiiaaa]

oooh thats much more clearer than what i had down lool
what type of question would they ask such in? would it be in MC by any chance?

[RuiAce]

Hey, for this question i just assigned a value and tested all the answers, but would like to know the proper method of doing this?

[RuiAce]

oooh thats much more clearer than what i had down lool
what type of question would they ask such in? would it be in MC by any chance?

They seem to appear extremely often in 3U multiple choice questions. Usually it involves you to manipulate your way around it through the limit \[\lim_{x\to 0}\frac{\sin (ax)}{ax} = 1 .\]
It's a 2U concept but seems to appear more often in 3U exams than 2U exams for some reason.

[MisterNeo]

Hey, for this question i just assigned a value and tested all the answers, but would like to know the proper method of doing this?

[3.14159265359]

hey! I wanted to ask about part iv of this 2006 hsc paper q6b. when I completed this question I did the equation less than 200 (i.e. P<200) and solved but in the answers they had solved P=200 and I was confused as to why they did that since the question says "when the population falls below 200". with my working out, is the way I answered the question wrong? please clarify. thanks!

[_____]

Will just say that, while Rui's method is definitely more mathematically correct, in general you can definitely just substitute, especially for a 1 marker. NESA's solutions do it

Thanks for pointing that out, I'll just do that unless it's 3+ marks or a relatively easy manipulation

[roygbivmagic]

Hi, please can you explain how to do this question?
Find the exact length of the tangent from (4,-5) to the circle x^2 + 4x + y^2 - 2y - 11 = 0.
(Answer = square root of 56)

[wulverine]

Hi, could anyone explain 15c part (ii) from the 2013 paper? The solutions make no sense to me...
(i) Sketch the graph y = I 2x − 3 I
(ii) Using the graph from part (i), or otherwise, find all values of m for which
the equation I 2x − 3 I = mx + 1 has exactly one solution.

Also, question 9 from 2014 mc. These pop up every year and are the only ones I get wrong in mc

[kiiaaa]

hi guys!
i was wodnering if you could please help me tackle this question from the 2014 hsc paper. i dont know why i just found it confusing and i legit dont know what to do
thank you very much

[RuiAce]

Hi, please can you explain how to do this question?
Find the exact length of the tangent from (4,-5) to the circle x^2 + 4x + y^2 - 2y - 11 = 0.
(Answer = square root of 56)

Yeah. Technically not a 2U question, because the fact that \(\angle ABC = 90^\circ \) relies on circle geometry.. But I've seen the Cambridge textbook throw it at 2U students anyway.