Maths Methods 3/4 Help Thread 2011

[homosapiens]

From the VCAA 2010 exam 2

Victoria hears that another company, Shoddy Ltd, is producing similar statues (also classified as Superior or
Regular), but its statues are entirely made by machines, on a construction line. The quality of any one of Shoddy’s
statues is independent of the quality of any of the others on its construction line. The probability that any one
of Shoddy’s statues is Regular is 0.8.
Shoddy Ltd wants to ensure that the probability that it produces at least two Superior statues in a day’s production
run is at least 0.9.
e. Calculate the minimum number of statues that Shoddy would need to produce in a day to achieve this aim

When i put it all into my calculator i keep getting 12 when the answer is 18. Im doing 1 - ((PrX=0)+(PrX=1))
Any suggestions

1 - (Pr(X=0) + Pr(X=1) ≥ 0.9
0.1 ≥ Pr(X=0) + Pr(X=1)
Then solve on CAS,
solve((0.8 ) ^ n+x*(0.8 ) ^ (x-1) = 0.1,x)
x = -3.82982, 17.9479
Can't be negative, so it's 17.9479 and just to check:
binomCdf(x,0.2,2,x)|x=18
Pr(X=18) = 0.900921

[DavidSheena]

State the interval over which x^(1/2) is increasing.

Would it be (0,infinity) or [0, infinity)? Could someone please explain when and when to include the endpoints or turning points when a function is increasing?

[tony3272]

From my knowledge it's (0,infinity). For an increasing function it's gradient dependent. For a strictly increasing function you include endpoints and turning points as it's function value dependent.

[Cappuccinos]

Hey guys... I can't seem to get my head around the part ii  of this question?
It's from Insight 2011, Exam 2

i)  Derivative of
=     

ii) HENCE find the anti derivative of
The working out says:
 =
=  

How did they get that? I get that if something is to the power of -1 you get a log, but wheres did they get that from? I tried simplifying    on the Calc and it didn't simplify any further :S

[tony3272]

The rule that they're applying is: .

So since the numerator is the derivative of the denominator, as you have previously worked out in part i), this rule works.

[Cappuccinos]

The rule that they're applying is: .

So since the numerator is the derivative of the denominator, as you have previously worked out in part i), this rule works.

Wha...? Where has that rule been all my life?! Hahahaha
Anyway thanks!

[pi]

I don't think that would ever be a methods exam question btw, more of a spesh question tbh.

[luken93]

I don't think that would ever be a methods exam question btw, more of a spesh question tbh.

Yeah that's what I thought when I saw it, albeit a tiny bit relevant it was quite tough to think of it in the context of the question...it's basically u-substitution (spesh)

[tony3272]

Yeah that rule isn't used very often in methods. That's why a lot of people only know it as

[nacho]

harro,
question;
what is adequate when explaining questions like
'Explain why A  = 5, B = 3/2 and n = 2pi

and you have the graph of the equation:
d = Asin(nx) + B
which shows Amplitude is 10, vert translation is 10, and repeated after 2pi.
Do you just say
"Max height minus min height divided by 2 = 10, therefore amplitude = 10" ?

[knightstarr17]

After Most Exams I go over my mistakes and actually re do the questions I got wrong. I guess I will just go over all the mistakes from all the papers. Also should I push to finish quicker so I will have a longer period of time to go over my exam to fix up the little mistakes? What is the recommended time to finish the exam? Thank you for you help

Yeah it's best to leave ~10 minutes at the end to check, how long do you usually take to finish a paper? If not after you finish every question, just reread the question quickly and skim through making sure you've answered what it asked with units etc, so you're checking as you go and aren't as pressed at the end and have the question fresh in your mind as well as what you've done. If you've got time at the end go through and check again with a fresh mind, you might see things you didn't pick up the first time.

I finish with 10-15 mins to spare but I rarely use that time to check, because I'm so anxious to correct the paper, but thank you what you have said is very helpful and I will do as you say

[dc302]

Finishing as fast as possible is best, given that you're not compromising your work. Finishing faster than in half the allocated time is probably not recommended though

[dc302]

harro,
question;
what is adequate when explaining questions like
'Explain why A  = 5, B = 3/2 and n = 2pi

and you have the graph of the equation:
d = Asin(nx) + B
which shows Amplitude is 10, vert translation is 10, and repeated after 2pi.
Do you just say
"Max height minus min height divided by 2 = 10, therefore amplitude = 10" ?

I think it's a well known rule/definition that for any y = Asin(nx), you have amplitude = 2A and period = 2pi/n. So you can just state those and it should be fine.

Also, if your graph repeats after 2pi, n = 1, not 2pi. Just clearing that up!

[b^3]

harro,
question;
what is adequate when explaining questions like
'Explain why A  = 5, B = 3/2 and n = 2pi

and you have the graph of the equation:
d = Asin(nx) + B
which shows Amplitude is 10, vert translation is 10, and repeated after 2pi.
Do you just say
"Max height minus min height divided by 2 = 10, therefore amplitude = 10" ?

I think it's a well known rule/definition that for any y = Asin(nx), you have amplitude = 2A and period = 2pi/n. So you can just state those and it should be fine.

Also, if your graph repeats after 2pi, n = 1, not 2pi. Just clearing that up!

Amplitude = 2A? The difference between the maximum and minimum will be 2A but the amplitude is still A is it not?

[dc302]

harro,
question;
what is adequate when explaining questions like
'Explain why A  = 5, B = 3/2 and n = 2pi

and you have the graph of the equation:
d = Asin(nx) + B
which shows Amplitude is 10, vert translation is 10, and repeated after 2pi.
Do you just say
"Max height minus min height divided by 2 = 10, therefore amplitude = 10" ?

I think it's a well known rule/definition that for any y = Asin(nx), you have amplitude = 2A and period = 2pi/n. So you can just state those and it should be fine.

Also, if your graph repeats after 2pi, n = 1, not 2pi. Just clearing that up!

Amplitude = 2A? The difference between the maximum and minimum will be 2A but the amplitude is still A is it not?

Ah, it may be different for methods, but peak amplitude is A, and peak to peak amplitude is 2A. I can't remember which one VCAA uses. You're probably right though.