VCE Methods Question Thread!

[rani_b]

Hey guys!

I was wondering if someone could explain the last question for Exam 1 NHT 2017 (Q8c.ii).  I understand how to get c=1, I'm just not sure how to get c>2.

https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017MM1-nht-w.pdf <-- link for exam

https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/mm1nht_examrep17.pdf  <-- link for exam report

Thank you in advance!!

[KiNSKi01]

Hey guys!

I was wondering if someone could explain the last question for Exam 1 NHT 2017 (Q8c.ii).  I understand how to get c=1, I'm just not sure how to get c>2.

https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017MM1-nht-w.pdf <-- link for exam

https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/mm1nht_examrep17.pdf  <-- link for exam report

Thank you in advance!!

Hey this is tricky to spot but you have to consider the domain of g(x) because this is what gives the solution of c>2.

When c=2, the graph of g(x) starts on the line y=x, (therefore there are two solutions for y=x as it also intercepts at (1,1) - this is what the examiners report is getting at

This means that for any value of c>2 there will only be one real solution because the domain of g(x) restricts it from intercepting its inverse twice

ngl would not have considered the c>2 under exam conditions

[tigerclouds]

Hi there, just a general question.
When asked to find the range of a composite function, how do you go about doing this? Should I always sketch it (which is difficult cause they have the weirdest equations) or is there a specific rule?
I know that the range of the interior has to be a subset of the domain of the exterior. So when the range of the interior is smaller, can you always make an inequality equation? And what do you do when the range of the interior is already a subset, do you just sub that in?
I hope that makes sense. I guess I just need a general rule
Your help is very much appreciated

[jkay__]

Hi there, just a general question.
When asked to find the range of a composite function, how do you go about doing this? Should I always sketch it (which is difficult cause they have the weirdest equations) or is there a specific rule?
I know that the range of the interior has to be a subset of the domain of the exterior. So when the range of the interior is smaller, can you always make an inequality equation? And what do you do when the range of the interior is already a subset, do you just sub that in?
I hope that makes sense. I guess I just need a general rule
Your help is very much appreciated

For composite functions, I always draw out 2 boxes, and have the "input" and "output" of each (attached picture). The domain of the inside function will be the overall domain, and range of outside will be the overall range. Restrict where needed when the inside range is greater than the outside domain (so change the domain + range of inside function and range of outside function if needed).

If the range of inside is already a subset, you don't need to change anything (if I recall correctly). Someone feel free to correct me if I am wrong however

[rani_b]

Hey, could someone help me out with this question (attached)? I've seen these types of questions on a few exams but I'm not sure how to do them efficiently.

Thank you!!!!

[KiNSKi01]

Is the answer A?

f'(x) multiplied by f'(y) (which is the same as the inverse) is equal to 1

therefore in this question you just divide 1 by -5 to get A

similar to MCQ 20 on 2018 NHT exam, check the exam report for that question 

[rani_b]

Is the answer A?

f'(x) multiplied by f'(y) (which is the same as the inverse) is equal to 1

therefore in this question you just divide 1 by -5 to get A

similar to MCQ 20 on 2018 NHT exam, check the exam report for that question 

Yep it's A! Thanks for the help 

NHT was actually the one i was thinking of, but couldn't remember. I'll have a look now!

[tigerclouds]

For composite functions, I always draw out 2 boxes, and have the "input" and "output" of each (attached picture). The domain of the inside function will be the overall domain, and range of outside will be the overall range. Restrict where needed when the inside range is greater than the outside domain (so change the domain + range of inside function and range of outside function if needed).

If the range of inside is already a subset, you don't need to change anything (if I recall correctly). Someone feel free to correct me if I am wrong however

Thank you for your help! I just wanna ask, how would you apply that to the attached question from the 2016 VCAA Exam 1. The range of the outside would be R since it's a log but the range of the composite is meant to be [0,∞).

[pat0029]

Hey does anyone know if the maths methods unit 3 and 4 book from Cambridge publications is the only one used throughout Victoria or any other maths textbooks used in other schools, if so what are they?

[Tau]

Hey does anyone know if the maths methods unit 3 and 4 book from Cambridge publications is the only one used throughout Victoria or any other maths textbooks used in other schools, if so what are they?

There’s also the Maths Quest series by Jacaranda.

[KiNSKi01]

hey people

Is it safe to assume that if a question does not say answer in terms of a (or any random variable) that it shouldn't be in the answer - hence indicating that there's enough information in the question to know what this variable already is

here's an example of what I'm referring to :
https://twmpublications.com/resources/free_exams/TWM%20Publications%20Free%20Mathematical%20Methods%20Trial%20Examination%201.pdf     - in the final question I was confused because I blanked and didn't realise you could already find a in terms of b. If I had noticed that the question didn't have something like find b in terms of a, I would have been more likely to realise there's something I haven't considered yet

hope that makes sense 

[Sine]

hey people

Is it safe to assume that if a question does not say answer in terms of a (or any random variable) that it shouldn't be in the answer - hence indicating that there's enough information in the question to know what this variable already is

here's an example of what I'm referring to :
https://twmpublications.com/resources/free_exams/TWM%20Publications%20Free%20Mathematical%20Methods%20Trial%20Examination%201.pdf     - in the final question I was confused because I blanked and didn't realise you could already find a in terms of b. If I had noticed that the question didn't have something like find b in terms of a, I would have been more likely to realise there's something I haven't considered yet

hope that makes sense 

Yeah I think it's a safe assumption for VCAA. They are usually quite specific on how they want their answer. If they do want it with variables they will often say it.

[studyingg]

how do you convey to examiners that you've used the invnorm function on the cas in order to solve a question without using calculator syntax?

[undefined]

how do you convey to examiners that you've used the invnorm function on the cas in order to solve a question without using calculator syntax?

i usually say pr(X>a)=area
therefore a=?

[studyingg]

i usually say pr(X>a)=area
therefore a=?

thanks, that sounds good