VCE Methods Question Thread!

[keltingmeith]

Can someone help me with part (f) please??
Thanks in advance 

This one turned out quite the doozy! Here's some tips to help you along:

1. You don't actually need to find what a is - remember, they haven't asked you to find the unknowns, only when the population is "least". Try doing the question without thinking about a (don't remove it, per se, but just pretend it's any other number and pay it no mind)
2. The population will be "least" at the global minimum.
3. Does this graph look familiar to a function you've seen previously? If yes, how could you find the global minimum of that function?
4. We know that n is equal for t=30 and t=65 - this means that, even if we don't know what the number of the population is, we do know that n(30)=n(65)

Hopefully that's enough to steer you in the right direction.

[odeaa]

A restaurant buys lobsters from a local seafood supplier who is not always reliable with the weight. It is found that the weights of the lobster follow a normal distribution with mean kg and standard deviation kg. It is known that 25% of the lobsters have weights which differ from b at most kg.
Find the probability that a randomly chosen lobster has a weight that exceeds by at most kg, giving your answer correct to four decimal places.

[bulbasaur]

This one turned out quite the doozy! Here's some tips to help you along:

1. You don't actually need to find what a is - remember, they haven't asked you to find the unknowns, only when the population is "least". Try doing the question without thinking about a (don't remove it, per se, but just pretend it's any other number and pay it no mind)
2. The population will be "least" at the global minimum.
3. Does this graph look familiar to a function you've seen previously? If yes, how could you find the global minimum of that function?
4. We know that n is equal for t=30 and t=65 - this means that, even if we don't know what the number of the population is, we do know that n(30)=n(65)

Hopefully that's enough to steer you in the right direction.

Thanks so much!! 

 I just realised how silly the question is   

AHHAHA all the variables must've thrown me off

[Floatzel98]

I have a couple questions I need some help with.

Question 1

Suppose that the probability of a squash player winning a point is 0.7 if she has won the preceding point and 0.4 if she has lost the preceding point. Suppose X_{n} = 1 if the player wins the nth point and X_{n} = 0 if the player loses the nth point

1) The probability that the player wins the three points in a row after losing the first point, and then loses the next point is:
A - 0.1960
B - 0.0412
C - 0.0192
D - 0.0588
E - 0.1029

Question 2

Suppose that the probability of snow on Mount Buller is dependent on whether or not it has snowed on the previous day. If it has not snowed the day before the probability of snow is 0.8. If it has not snowed on the previous day then the probability  of snow is 0.1. If it has snowed on Thursday, what is the probability that it will not snow on the following Saturday?

Thanks

[knightrider]

How would you do this question attached?

[knightrider]

How would you do this question attached?

[knightrider]

How would you do this question attached?

How would you do this question attached?

Can anyone help with these?

Thanks 

[bills]

Just a quick question, if an exam asks you to solve for x, and you use the calculator, do you need to write something to indicate that? For instance, would you need to write something like:

[cosine]

How would you do this question attached?

Pretty hard to differentiate a mod of cos function, so let's just say that instead of having the modulus, we will put a negative sign in front of the function as modulus ensures that all values are positive, and if we put a negative sign infront then we ensure that all negative values will now become positive:





Now sub in x=k into it and see what it gives, but note that k is in between and so sine of any of the angles it is defined for are positive, and so on the graph of |cos(2x)|, the rate of change of any value between the domain we are given will always be negative, and so our rate of change must be a negative value:

[cosine]

Just a quick question, if an exam asks you to solve for x, and you use the calculator, do you need to write something to indicate that? For instance, would you need to write something like:

Absolutely not!

If you really want to be careful and not fall in the trap, like I did with my methods teacher where he would not give me the mark because i "skipped a step", despite that the whole SAC was a calculator based and tested our knowledge of rounding off and not actually integrating, you can do this: (sorry for the rant xD)

[StupidProdigy]

How would you do this question attached?

A little tip, always take notice of questions which give you two sets of values or bits of info because they often require simultaneous equations to be solved!
So the mean is calculated by n*p and variance is n*p*q or the more useful n*p*(1-p)
np=20
np(1-p)=14
Solve simultaneously for p

[dankfrank420]

Just a quick question, if an exam asks you to solve for x, and you use the calculator, do you need to write something to indicate that? For instance, would you need to write something like:

Do not do that. You WILL lose marks.

To skip steps in working, I just use arrows when I solve on CAS.

In your case, I'd write:

2^x = 4
--> x = 2

In other cases you could write:

Let f(x) = 2000
--> x = 12

Easy and simple.

[bills]

Thanks cosine and dankfrank. Another quick question, which of these answers are correct, or are they both considered correct? Example (theoretical question):

Find values of x which satisfies the equation


1.
2.

[keltingmeith]

Thanks cosine and dankfrank. Another quick question, which of these answers are correct, or are they both considered correct? Example (theoretical question):

Find values of x which satisfies the equation


1.
2.

The first one is correct for technical reasons - basically, the first is read "the set of x such that x is greater than or equal to 3", which very specifically defines what we care about. The second is read "the set of x greater than or equal to 3", which seems fine at first, but what if instead of 3, we were concerned with some number y? Then, the second would read "the set of x greater than or equal to y", and all of a sudden it's not clear whether our variable is x or y.

So, even though the second seems alright, we keep up with the more specific one for consistency reasons.

[knightrider]

Pretty hard to differentiate a mod of cos function, so let's just say that instead of having the modulus, we will put a negative sign in front of the function as modulus ensures that all values are positive, and if we put a negative sign infront then we ensure that all negative values will now become positive:





Now sub in x=k into it and see what it gives, but note that k is in between and so sine of any of the angles it is defined for are positive, and so on the graph of |cos(2x)|, the rate of change of any value between the domain we are given will always be negative, and so our rate of change must be a negative value:

Thanks so much cosine 

the answer says though?Is this wrong?