VCE Methods Question Thread!

[Damoz.G]

vcaa 06 1d extended response

Let h:R --> R, h(x) = 2|sin(x)|. Find the general solution, for x, of the equation h(x) = 1.

You could just enter it on your CAS, using Solve

[shadows]

When a question says find the rule of the inverse function, you don't need to write the domain right? Is that correct?


Second question.

How do I express a height of a cone in terms of r?

Thanks

[Damoz.G]

When a question says find the rule of the inverse function, you don't need to write the domain right? Is that correct?


Second question.

How do I express a height of a cone in terms of r?

Thanks

Yes, you need to write the Domain.

For your second question, is there any other information provided?

[shadows]

Really? I thought that if it said find the inverse function, then you state the domain.

If it just says rule, you don't need to state the domain? Someone  correct me on this?

Umm.

Yeah theres no info provided.

* OH and r is the radius of the cone..

[ahat]

Really? I thought that if it said find the inverse function, then you state the domain.

If it just says rule, you don't need to state the domain? Someone  correct me on this?

What I was going to say (and I'm sure on this).
"Find inverse" domain and inverse
"Find rule" inverse only because more often than not, next question will be domain.

[Alwin]

vcaa 06 1d extended response

Let h:R --> R, h(x) = 2|sin(x)|. Find the general solution, for x, of the equation h(x) = 1.

To solve by hand:



Using the general formula solutions

When a question says find the rule of the inverse function, you don't need to write the domain right? Is that correct?

A function is a rule and a domain

If a question asks for the inverse function, you must give the domain too, even if the question is only worth a couple marks and it doesn't look like you need it.

If a question asks for the rule of the inverse function, you only need to stated the rule. Domain is optional but personally I would include it as it might be useful in the next part (sketch the graph or solving it etc)

Hope it helps

[Damoz.G]

LOL! As always, love your signature, Alwin!

[~T]

How do I express a height of a cone in terms of r?

Thanks

Phy124 may have answered your question, but I'm not sure without context. The other option might be the usual question that comes up in an exam with a cone leaking water or whatever, so I'll run through that too.

You'll have the dimensions of the full cone I presume, say of radius 10cm and height 40cm. If we draw a line from the point of the cone to the centre of the circular end, and connect this with the sloped side, a triangle is formed. The hypotenuse of this triangle is the slope, the longer side is the height of the cone (40cm) and the shorter side is the radius of the cone (10cm).

If we look at this triangle, we could also draw a similar (pun intended) triangle from the same point of the cone, to wherever the water level may lie. We have the same angle formed at the bottom, and we have a right angle in both, so (as my humour foreshadowed) we literally have similar triangles.

In our smaller triangle, the longer side represents the height of the water, or depth, which we'll call h. The shorter side represents the radius of the water at the surface level, which we'll call r. Now, with similar triangles, the ratios between the side lengths must be equal. So we can say...



and thus

[shadows]

Umm.. when I have to show steps of a transformation..

Do a have to change the the subject of the equation, will I lost marks if I keep it the same

Example.... y= x^2


y=x^2 -4 

or do I have to change it into y2 or something?

[Alwin]

Umm.. when I have to show steps of a transformation..

Do a have to change the the subject of the equation, will I lost marks if I keep it the same

Example.... y= x^2


y=x^2 -4 

or do I have to change it into y2 or something?

The convention is to use the prime symbol (') to indicate image.

However, I have never heard of marks being deducted because a student did not include that notation in their answers.

Another popular one is to use subscript if there are multiple transformations, plus the primes make it look like you're diffing something

But again, I think it's find to use just normal 'y' and 'x' so long as you make it clear what you're doing.

for example, this is perfectly fine (iirc)
   translated down 4 units (or equivalent wording)   
because it demonstrates to the examiner that you understand what the question is asking and provided a correct solution

hope it helps

[shadows]

Thanks man:

Oh another question:

How to you approach these mulitple choices

What value of f(x) satisfies

-af(x)= 1/af(x)  (Lol i dunno if that even makes sense but I hope you get idea of the question

What I do is I defined f(x) and write out the equation.  Teacher told me that it will tell you if it's true or false.  But it just spits it out, not say either true or false.

I had to sub a value of a random value for x, say 30. Then it will say either true or false, But it takes time and I don't know how reliable this method is.

How do  you guys solve these questions as fast as possible?

[Alwin]

Thanks man:

Oh another question:

How to you approach these mulitple choices

What value of f(x) satisfies

-af(x)= 1/af(x)  (Lol i dunno if that even makes sense but I hope you get idea of the question

What I do is I defined f(x) and write out the equation.  Teacher told me that it will tell you if it's true or false.  But it just spits it out, not say either true or false.

I had to sub a value of a random value for x, say 30. Then it will say either true or false, But it takes time and I don't know how reliable this method is.

How do  you guys solve these questions as fast as possible?

For the casio, use the "judge" function. no need to sub in values.

If you're using the Ti watever its name was (I'm not good with names sorry! pi`/snow brown will testify so) here:
Re: Mathematical Methods Guides and Tips

scroll down until you see "The x-y Function Test". Similar principle, you just put in your function first no need to do the x-y things

Don't think I was very clear, but hopefully should get things started for you

[ahat]

Thanks man:

Oh another question:

How to you approach these mulitple choices

What value of f(x) satisfies

-af(x)= 1/af(x)  (Lol i dunno if that even makes sense but I hope you get idea of the question

What I do is I defined f(x) and write out the equation.  Teacher told me that it will tell you if it's true or false.  But it just spits it out, not say either true or false.

I had to sub a value of a random value for x, say 30. Then it will say either true or false, But it takes time and I don't know how reliable this method is.

How do  you guys solve these questions as fast as possible?

Hey Shadows, using the CAS, I've figured out a method that is pretty fast but still require the subbing. CAS steps:

Menu 1,1 > Define f(x) = 1 + 2x (for example)
Type: -af(x) = 1/af(x) | x = 1
The vertical br can be found on the grey ones, its next to ctrl, on blacks I think it's in the pi sub menu
Result:  -af(x) = 1/af(x) | x = 1 False
Then, Very quickly and easily
Press up until you highlight your definition for f(x) > ctrl + c
Go down to an empty line, ctrl + v
Redefine f(x)
Go up and highlight -af(x) = 1/af(x) | x = 1 >  ctrl + c
Go down to an empty line, ctrl + v
Result True/False
Do these for all of the options until you get true. This should take you 1:30 mins tops.

[Stevensmay]

ahat,
Instead of copying and pasting the answers you can also just press enter when it is highlighted. Be warned that this is effectively copy and paste, so anything you had already copied will be overwritten.

[shadows]

Hopefully it's ok if I ask here. I have asked some people and I have gotten estimations ranging from 35 to 45 o.o

Exams 1. 37-39/40 (For some reason, I am yet to get 40) D:               

Exam 2: high 60s to low70s/80 

(I actually haven't done VCAA. But I have done a few Neap, MAV (early papers 2006/2007) and Insight and on average I've been getting these results, but from what I've heard their pretty similar to VCAA)

Sacs no idea after moderation
Low A to Low A+

Study score range estimation? 
Best case scenario: Exam 1: 39         Exam 2: 73     SACS LOW A+

Most likely scenratio Exam 1: 37        Exam 2: 70              SACS: MID A

Worse likely case (hopefully I don't get any worse, but you know it does happens sometimes)

Exam 1: 30                    Exam 2: 55         SACS: B+

Theres like 3 weeks left and I'm not sure if I can still improve. Main problem is silly mistakes. I swear... they are the death of me....