VCE Methods Question Thread!

[achre]

VCAA 2009 Part 1, question 5c. How do you find the numerator? I keep getting it as (1/3)/(1/3), which can't be right..

[shadows]

VCAA 2009 Part 1, question 5c. How do you find the numerator? I keep getting it as (1/3)/(1/3), which can't be right..

It is a conditional question. Pr(second ball draw is 1 given sum of numbers on 2 balls is 5)

= Pr (first ball is 4, second ball is 1)/ Pr(sum of 2 balls is 5)

= (1/12) / (4/12)

= 1/4

[Zealous]

can someone exlpain how to do q4e and 4f in detail in vcaa exam 2012?

4E:
We know the volume of the cone is given by:

So we sub in h=2metres to find out the volume of the cone when the height of liquid is 2 metres:
 

The liquid flows at 0.2m^3/minute so:

Time taken =


Even more steps:

Spoiler

Time:


The m^3 cancel out and you get:

4F:

By the time we reach 4F, we have two big pieces of information (from previous sections):
- The liquid height will first decrease to 2 metres after 12.2 minutes (or another way of putting it: the liquid level was above 2 metres for the first 12.2 minutes).
- The liquid height will reach 0 metres after 20 minutes.

Tasmania can only climb down when the depth of liquid is at 2 metres or less. So we need to find the time in which the water is above 0 metres and less than 2 metres (for when the liquid is draining out of the cone).

So we take the 20 minutes it takes to completely empty, and take away the 12.2 minutes in which the liquid was above the 2 metres mark, giving us the amount of time in which the liquid is between 0 and 2 metres.

Then we can add the 8pi/15 on top of that which is the amount of time it takes for the liquid to fill back up to 2 metres (after completely draining).

Hopefully that makes sense!

[Sanguinne]

thanks i understand, but umm why does the time taken = volume divided by 0.2

Time taken =

[shadows]

can someone exlpain how to do q4e and 4f in detail in vcaa exam 2012?

Once the depth reaches 2 metres, h=2

Therefore V= 8pi/(75) metres cubed

Time in minutes is volume divided by rate of 0.2 ms cubed.

Which gives 8pi/(15) minutes



f: We know that it takes 20 minutes for height to reach zero (from when it is full)

It reaches 2 metres at 12.2 minutes

Therefore time taken for the height to go from 2 to 0 is (20-12.2) metres,

But then as soon as liquid reaches zero, poisonous liquid enters. It takes 8pi/15 minutes to get to 2 metres (found in previous question)

Therefore total time is (20-12.2) + 8pi/15

Round to once decimal place 9.5 mins

Haha beaten

[clıppy]

VCAA 2012 Tech

Q20MC
It says Pr(X>1), if we were trying to find the probability of that without going to the nth number, we could do 1-Pr(X=0), how come the answers say its 1-(Pr(X=0) + Pr(X=1))?

In general, if we're asked to find for example, an equation of volume in terms of h. Would we give units at the end of the equation?

[ahat]

Is it alright to label axis intercepts as degrees?

[lzxnl]

VCAA 2012 Tech

Q20MC
It says Pr(X>1), if we were trying to find the probability of that without going to the nth number, we could do 1-Pr(X=0), how come the answers say its 1-(Pr(X=0) + Pr(X=1))?

In general, if we're asked to find for example, an equation of volume in terms of h. Would we give units at the end of the equation?

Pr(X>1) does not include X=1

And for the formula, nah. VCAA isn't that strict. Besides, the units of volume will depend on the units of h.

Is it alright to label axis intercepts as degrees?

What do you mean? What's this for?

[Jaswinder]

also 2008 Exam 1, Question 10b, how do we find the domain of the graph? I wouldve have thought that its the range of inverse, which is R?

thanks

[Sanguinne]

VCAA 2012 Tech

Q20MC
It says Pr(X>1), if we were trying to find the probability of that without going to the nth number, we could do 1-Pr(X=0), how come the answers say its 1-(Pr(X=0) + Pr(X=1))?

In general, if we're asked to find for example, an equation of volume in terms of h. Would we give units at the end of the equation?

Pr (X>1) = P(X ≥2)

Pr(X ≥2) = 1 - (Pr(X=0) + Pr(X=1))

thats my try at explaiining it

beaten

[Zealous]

also 2008 Exam 1, Question 10b, how do we find the domain of the graph? I wouldve have thought that its the range of inverse, which is R?

thanks

Domain of inverse is (which is the range of f(x):



The domain of a composite function is the domain of the inside function. In this case the inside function is f-1(x), which has the domain (-1,infinity). That is why we only sketch from -1 onwards.

[clıppy]

If we have a function f(x) and g(x). If we make a composite function f(g(x)) the domain is g(x) right?
What happens if the new rule of f(g(x)) can't be defined for the original domain of g(x), what do we do then? Do we work from g(x)'s domain and try to find a maximal domain?

[Jaswinder]

but shouldn't the range of inside must be contained within domain of outside, both of which is R?

[papertowns]

Help please I've done part e&f just need help with g thanks!

[shadows]

Questions from 2013 Neap Exam 1

1. The mean and the standard deviation on Mrs Tuff’s last Year 12 Maths Methods test were
72 and 8 respectively. She thought these were too high. Mrs Tuff is going to transform the
scores so that the new mean is 65 with a standard deviation of 5.
If the random variable X represents the original scores and the random variable Y represents
the transformed scores, then Y = aX +b, where a and b are positive constants.
Find a and b

EDIT: a= 5/8        b=20
2. In a certain town the rate of deaths due to a particular disease has been found to closely fit the
mathematical model DN/dt = (1000)/(t+3)^2  where t is the time in months after the disease was first detected
and N is the number of deaths.
Calculate the total number of deaths predicted by the model, giving your answer to the nearest whole
number of deaths.

N=556

I tried to integrate it, but i got a neg number?