brightsky's Maths Thread

[Mao]

lol i'm not complaining cos i didn't think it was on the study design...i'm complaining because the question was worded so ambiguously, i.e. since when did approximate the area using the triangles, mean approximate the area using left hand triangles and right hand triangles and find the average of the two?

Perhaps you missed the most important part of the study design. Let me quote:

Outcome 1

On completion of each unit the student should be able to define and explain key concepts as specified
in the content from the areas of study, and apply a range of related mathematical routines and
procedures.

To achieve this outcome the student will draw on knowledge and related skills outlined in all the
areas of study.

Key knowledge
This knowledge includes

• The thought patterns of the examiners, especially on topics where the examiners cannot express themselves clearly in words.

<snip>

Key skills
These skills include the ability to

• Read the mind of the examiners.

<snip>

How did you even miss that?

[Phy124]

lol i'm not complaining cos i didn't think it was on the study design...i'm complaining because the question was worded so ambiguously, i.e. since when did approximate the area using the triangles, mean approximate the area using left hand triangles and right hand triangles and find the average of the two?

I'm not sure, this (as in as correctly written) was just the way I was taught, I assumed it was the norm   

How did you even miss that?

[brightsky]

for the following two questions, the answers i got are at odds with the answers provided, yet i can't find anything wrong with what i wrote. any help would be much appreciated.

(the two questions are page 16 q 2b and page 26 4cii respectively)

the latter reads:

"On how many days of the year is the number of hours of daylight at least 10 hours and 45 minutes."

[Mao]

2b. 0.682

4a. 14.5 hrs on Jan 22nd.

[brightsky]

2b. 0.682

4a. 14.5 hrs on Jan 22nd.

@2b. yeah that's what i got, answers say 0.318...meh
@4a, soz, 'twas a bit vague the way i put it...asking for 4c)ii), which is not in any of the pdf files i've attached (i've typed out the second question above)

[Mao]

@4a, soz, 'twas a bit vague the way i put it...asking for 4c)ii), which is not in any of the pdf files i've attached (i've typed out the second question above)

On the 144th and 266th day, time=10.75 hrs
In between those dates, time<10.75 hrs

Thus, in 366 days, 23 have 145->265 days = 121 days with time<10.75 hrs

Therefore 245 days have at least 10.75hrs of daylight.

[brightsky]

thanks mao!

another question: is the function g(x)=x^3 - 9x^2 + 15x + 13 increasing in the interval (-infty,1)U(5,infty) or (-infty, 1]U[5,infty)? i put the latter as my answer, but kilbaha seems to think otherwise.

[kamil9876]

What's the question really asking ?

Because first of all those sets are not intervals, secondly yet so the function is not increasing on that set. (Just because a function is increasing on the set and doesn't mean it's also increasing on   )

[brightsky]

What's the question really asking ?

Because first of all those sets are not intervals, secondly yet so the function is not increasing on that set. (Just because a function is increasing on the set and doesn't mean it's also increasing on   )

good point...so i guess it's more correct to say (-infty,1] AND [5,infty), or...?

anyway, my main query is, would a function like y=x^2 be increasing in the interval [0,infty) or (0,infty)? vcaa (i think) seems to think the former, while kilbaha thinks the latter.

[brightsky]

another question: is the area of the region bounded by the graphs y = abs(6x-11) and y=abs(x) closest to 0.576 or 0.612?

(either i'm delusional or kilbaha's worked solutions booklet is ridden with errors...)

EDIT:

also:

how would one go about finding the asymptotes of a function like f(x) = 3 - (x+2)/(x^2+4x+5)?

[nerdgasm]

For the question involving the absolute value graphs, I get

= 0.576, to 3 d.p.

[pi]

another question: is the area of the region bounded by the graphs y = abs(6x-11) and y=abs(x) closest to 0.576 or 0.612?

(either i'm delusional or kilbaha's worked solutions booklet is ridden with errors...)

I have 0.576

how would one go about finding the asymptotes of a function like f(x) = 3 - (x+2)/(x^2+4x+5)?

Do you mean the parts of the graph that approach y=3?

[brightsky]

good good...so i'm not completely nuts

[BlueSky_3]

For the asymptotes one just consider what happens to the y-values when x ---> + or - infinity. You will find that the graph approaches y=3. 

Oh and wow are you already doing trial exams? Nice.

[brightsky]

Do you mean the parts of the graph that approach y=3?

yep...how would one go about writing up a formal solution? this one does not appear to be as clear cut as most others; the answer isn't immediately obvious when you let x tend to +- infty...