VCE Methods Question Thread!

[achre]

How do you stop the CAS from doing change of base when transposing exponential functions, like on MC Q8 VCAA 2006? You don't need to tell me it's trivially easy to do it by hand, but just for my own knowledge, is there a way to make the CAS not include an ln term in the solution? Also the jargon it spits out giving more than one solution ('blah blah blah' and sqrt(y-b) > 0 or 'blah blah blah' and sqrt(y-b) < 0).

[Flor]

Hope that helps.

You guys are awesome! Thanks a bunch. I would shower you guys with +1s if I could.

[gibbsy06]

How can you introduce simeltaneous equations with more than 2 unknowns that are different to the standard x, y, z variables on the CASIO Classpad? My CAS doesn't seem to like it..

[Alwin]

Hey again! Could someone help me with question 2dii and e section 2? (link below) I know how to find the expected value but I'm kind of confused about how to do it with this particular question. Could someone just explain it to me? http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010mmcas2-w.pdf

Ooooo this question I like this one. I'll give you a proper explanation of the VCAA method compared to the "standard" long boring method!

From VCAA

[img width]http://i.imgur.com/OR8Ward.png[/img]

I assume from your reply that you understand ahat's method yeah, coz it's the table method in the top half of the VCAA solns.

Now, the matrix method is pretty cool, because it works on the principle for n repeats:





So, for this question you would calculate:

How do you stop the CAS from doing change of base when transposing exponential functions, like on MC Q8 VCAA 2006? You don't need to tell me it's trivially easy to do it by hand, but just for my own knowledge, is there a way to make the CAS not include an ln term in the solution? Also the jargon it spits out giving more than one solution ('blah blah blah' and sqrt(y-b) > 0 or 'blah blah blah' and sqrt(y-b) < 0).

Unfortunately, most CASs I know work in the standard base . So, rather than having to program in the numerical solutions for EVERY log or exponential of base watever, the cas uses change of base to calculate it in base .

I could try to explain more, but idk what question you're talking about, checked the VCAA methods CAS and non-CAS 2006 exam 2 papers. I don't see how you get a "b" in either question... sorry!

How can you introduce simeltaneous equations with more than 2 unknowns that are different to the standard x, y, z variables on the CASIO Classpad? My CAS doesn't seem to like it..

Unlike the TI-Nspire which only has one keyboard, the Classpad has two (ikr, way to overcomplicate it).
If you use the "abc" tab which is between "mth" and "cat", it does NOT treat it as a variable, rather a word or a function.
You have to use "VAR" tab, which is found next to the "EXE" on the soft keyboard. Eg on the "mth" tab, it is next tot he "TRIG", "CALC", "OPTN" tabs.

If you use these "VAR" characters, it should work. If not, try clear_a_z

[achre]

Unfortunately, most CASs I know work in the standard base . So, rather than having to program in the numerical solutions for EVERY log or exponential of base watever, the cas uses change of base to calculate it in base .

I could try to explain more, but idk what question you're talking about, checked the VCAA methods CAS and non-CAS 2006 exam 2 papers. I don't see how you get a "b" in either question... sorry!

Whoops, yeah, it was question 9. No worries, I just prefer to check with the CAS, but if that's not possible, oh well.

[Alwin]

Whoops, yeah, it was question 9. No worries, I just prefer to check with the CAS, but if that's not possible, oh well.

Okay, since you said you didn't want the whole " it's trivially easy to do it by hand " stuff, I tried it on my classpad.

1. Traditionally solving for x gives ln, because the CAS converts any other base to ln (coz that's how they work)
2. "Simplify" or "Combine" or "Collect" do nothing
3. By hand method would probs be fastest, since I can't see a way to keep things in base a...

sorry I can't be of more help!

[gibbsy06]

Ignore the previous question. Forgot you could let it equal zero!

Can anyone be of assistance with regards to non-CAS transformation matrices questions that always seem to pop up on CAS free exams? Ways to recognise particular transformations?

[SocialRhubarb]

I use a Ti-nspire, and on that you can input , and that'll give you the value with a different base.

[Alwin]

Ignore the previous question. Forgot you could let it equal zero!

Can anyone be of assistance with regards to non-CAS transformation matrices questions that always seem to pop up on CAS free exams? Ways to recognise particular transformations?

This should all be in your textbook, but here's a quick run down of the common ones:

	Means a translation of +a units parallel to the x-axis     and  translation of +b units parallel to the y-axis
	Means a dilation by factor |A| from the y-axis     and dilation by factor |B| from the x-axis
	Means the sign of x is changed, x'=x     in other words, reflected in the y-axis
	Means the sign of y is changed, y'=y     in other words, reflected in the x-axis
	Means inverting the equation, x'=y and y'=x     in other words, finding the inverse

You can go crazy with these matrices if you want, be remember BODMAS. The transformation matrices closest to happen first

For example:


Means:

• Translation of -3 units parallel to the x-axis
  and  translation of +2 units parallel to the y-axis
• Dilation by factor 3 from the y-axis
  and dilation by factor 1/2 from the x-axis
• Translation of 1 units parallel to the x-axis
  and  translation of -5 units parallel to the y-axis
• Reflection in the y-axis

OR, you could multiply out the matrices to give:


Meaning:

• Dilation by factor 3 from the y-axis
  and dilation by factor 1/2 from the x-axis
• Reflection in the y-axis
• Translation of +10 units parallel to the x-axis
  and  translation of -4 units parallel to the y-axis

Will a VCAA question be that hard? lol probs not, I just made it up on the spot but it recognising matrices by sight and knowing how to interpret and manipulate them can be useful

Hope it helps + makes sense + didn't majorly screw up anywhere

[ahat]

I assume from your reply that you understand ahat's method yeah, coz it's the table method in the top half of the VCAA solns.

Now, the matrix method is pretty cool, because it works on the principle for n repeats:





So, for this question you would calculate:

Btw, do you know this because you are a genius or did I miss something in class? 

[zvezda]

Hey,
With strictly increasing/decreasingg questions, are cusps included??
Cheers

[Alwin]

Hey,
With strictly increasing/decreasingg questions, are cusps included??
Cheers

Yup, turning points cusps (shoot I was thinking of something else, but same thing applies) are included, indicated by brackets or signs.

There are quite a few formal proofs about this (you can look them up if you want on google )but they all are along the lines that at the stationary point the curve hasn't changed concavity so it is still strictly increasing/decreasing.

oops

Just a side note, if it was talking about where or something similar you should already know not to include stationary points

PS: @ahat, nah this method ain't covered in class. Our teacher mentioned it as a 'shortcut' but couldn't explain it (ironically he is now my umep maths teacher) but I did a bit of researching and found a proof of sorts etc etc. Normal drawing up of tables works perfectly well too, so if you don't like matrices dw about it

[abcdqd]

Alwin you didn't even answer the question.

Cusps are not included as they are not differentiable (strictly increasing/decreasing does not include undifferentiable points such as end points and cusps).

yes it does..

[abcdqd]

Well on that VCAA document about increasing/decreasing that's what they said iirc


I may be wrong so if that's the case, sorry

Nah, if you check example 2, it says the function is strictly increasing over the whole interval, despite there being a cusp at x=2. Same thing with example 3, it says [0,1/sqrt3], which is inclusive of the cusp. http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf just wanted to clarify that's all

[abcdqd]

Ohh

So what do they mean when they say under example 1, "flat areas are not allowed"?

If a hybrid function had a part like y=5 (a horizontal line), the function would not be strictly increasing over that interval.