VCE Methods Question Thread!

[camrenis]

Hi, I'm having trouble solving question 1c on the Insight 2015 paper 1.

"The average value of the function f:(-(3/2), infinity) ->R, f(x)=1/(3+2x) over the interval [1, k] is (ln(3)/10). Find the value of k.

The solutions give the answer 6, but they don't really show the algebra. They just leave it at "setting __ = to ln(3)/10 yields k=6". I understand how to do these types of problems, but the algebra that I'm doing gives really ridiculous, impossible to solve by hand stuff. E.g. I got up to (k-1)*(ln(3)) = 10 (ln((2k+3)^(1/2)/5^(1/2))) in the working, which is clearly not doable. Any help?

Don't bring the 1/2 inside the log, just collect the like terms, for example you can have ln(3)=ln((2k+3)/5) and then solve for k, or likewise 1/10=1/(2(k-1)).  Both cases you have k=6.  Technically you could bring the 1/2 inside the log, but it just makes the working longer.

[Alter]

Don't bring the 1/2 inside the log, just collect the like terms, for example you can have ln(3)=ln((2k+3)/5) and then solve for k, or likewise 1/10=1/(2(k-1)).  Both cases you have k=6.  Technically you could bring the 1/2 inside the log, but it just makes the working longer.

Thanks. Got it now

[Mc47]

39/40 on my last two exam 1's

So frustrating

[Floatzel98]

EDIT: Don't worry. Been solved haha Can't read questions properly

[grannysmith]

Anyone know what the 45 SS cutoff was for 2012? 18.5 marks could be lost for exam 2, so I'd assume around 7 marks (on exam 2) could be lost for 45?

[schooliskool]

Anyone know what the 45 SS cutoff was for 2012? 18.5 marks could be lost for exam 2, so I'd assume around 7 marks (on exam 2) could be lost for 45?

Sorry off-topic but what do you mean '18.5 marks could be lost for exam 2'

[popsicles]

When a question asks to give the values of x for which y is continous, do we include end points? (The endpoints are included in the actual domain)

[sparkyblossom]

Hi, this is regarding Question 5b from MAV 2015 exam 1.

How do you get from 3^5/12*6^1/3 to 3^3/4*2^1/3?

In the solutions, they just went directly from the first step to the final answer without any explanation.

Thanks!

[cosine]

When a question asks to give the values of x for which y is continous, do we include end points? (The endpoints are included in the actual domain)

yes because end points are also considered as continuous points.

[zsteve]

@Cosine: My previous post was deleted by the system for some reason. I don't think endpoints can be continuous, as a one-sided limit will be undefined, hence the limit of the function approaching that endpoint will also be undefined. This is a requirement for continuity at a point - that the limit of the function approaching that point must be equal to the value of the function at that point. Hence the limit is undefined means that it can't be continuous, by the definition of continuity.

If a question asks for 'find the total length of time', can I give my answer like 8/3 hours? Or does it have to be DMS? What about, 'find the time after midnight'? Can I say 8/3 hours after midnight? Or do I have to do DMS

[schooliskool]

@Cosine: My previous post was deleted by the system for some reason. I don't think endpoints can be continuous, as a one-sided limit will be undefined, hence the limit of the function approaching that endpoint will also be undefined. This is a requirement for continuity at a point - that the limit of the function approaching that point must be equal to the value of the function at that point. Hence the limit is undefined means that it can't be continuous, by the definition of continuity.

If a question asks for 'find the total length of time', can I give my answer like 8/3 hours? Or does it have to be DMS? What about, 'find the time after midnight'? Can I say 8/3 hours after midnight? Or do I have to do DMS

I would change it to 2 hours 40 mins because nobody really uses fractions when it comes to time, and it only takes 3 seconds to figure out. Examiners are weird so I would just leave it in the most logical term just incase.

[Escobar]

Hi, this is regarding Question 5b from MAV 2015 exam 1.

How do you get from 3^5/12*6^1/3 to 3^3/4*2^1/3?

In the solutions, they just went directly from the first step to the final answer without any explanation.

Thanks!

they use the fact that 6^(1/3)=(3*2)^(1/3)=3^(1/3)*2^(1/3)
then they distributed it

If a question asks for 'find the total length of time', can I give my answer like 8/3 hours? Or does it have to be DMS? What about, 'find the time after midnight'? Can I say 8/3 hours after midnight? Or do I have to do DMS

you can leave it as a fraction if it asks how many hours
but if it says "find the time after midnight", it sounds like it wants an actual time eg 2:40am

[cosine]

@Cosine: My previous post was deleted by the system for some reason. I don't think endpoints can be continuous, as a one-sided limit will be undefined, hence the limit of the function approaching that endpoint will also be undefined. This is a requirement for continuity at a point - that the limit of the function approaching that point must be equal to the value of the function at that point. Hence the limit is undefined means that it can't be continuous, by the definition of continuity.

If a question asks for 'find the total length of time', can I give my answer like 8/3 hours? Or does it have to be DMS? What about, 'find the time after midnight'? Can I say 8/3 hours after midnight? Or do I have to do DMS

you know this was my exact thought when i was doing it too, but ages ago I remember kinslayer saying that endpoints are actually immune to that rule, I used to wonder why the point was continuous because the right hand limit does not even exist, so how could the limits from both sides equal? Exactly, but for VCE they say end points are included in continuity.

[Escobar]

i think that endpoints are continuous if the limit approaches it from one direction

[cosine]

i think that endpoints are continuous if the limit approaches it from one direction

yeah exactly, although this does defy the rules, saying that the limit from both sides must equal each other, but yeah i guess its an exception for endpoints that rule... (however, if an endpoint is NOT defined for f(x), then it is not continuous)