VCE Specialist 3/4 Question Thread!

[Robert123]

Any ideas how to do question 21?

Thanks.

It's asking for the direction of travel, is the direction of the velocity. So to solve this problem, derive the position vector to get the velocity vector, sub in your value of time. Once done, divide by the magnitude of that vector and that will give you a unit vector in the direction of travel.
Does that help?

[keltingmeith]

Just going back with the previous question,


If you had something like


But if t > 0,

That means you would have to make the RHS  - 4y, right since you have modded the argument of the logarithm?

What I don't get is why:

If it's



You don't change it to -loge(2)? Is it something to do with transformations?

No - in your first case, if t<4, then your equation becomes .

In your second case, .

You keep using the word argument, and I think that's getting you confused with complex numbers. So, I'm going to call it an input.

If in your complex number you have a negative length, you make it positive and put the negative into the argument.
If in your logarithm you have a negative input, you cannot evaluate the logarithm - it's as simple as that.
If the input for the logarithm has a modulus sign, you simply make the input positive - that way, you can evaluate the logarithm. You do not take a negative out the front like you would a complex number, that is the equivalent of taking the reciprocal of your input - which seems pretty silly, doesn't it?

[M_BONG]

Also, if the body's acceleration is negative the whole way through

eg. a = v-4/2
does that imply that the velocity is always negative (ie. moving left as well?)

Does acceleration being negative means it's going left of O (negative direction)? I always just thought a negative acceleration meant it was decelerating... It can mean it's moving left as well?

[keltingmeith]

Also, if the body's acceleration is negative the whole way through

eg. a = v-4/2
does that imply that the velocity is always negative (ie. moving left as well?)

Does acceleration being negative means it's going left of O (negative direction)? I always just thought a negative acceleration meant it was decelerating... It can mean it's moving left as well?

Negative acceleration simply means it's accelerating in the opposite direction. You see, something can accelerate to a halt (deceleration), and then continue to accelerate in the "non-positive" direction. Of course, if you think about it this isn't too big a deal. I mean, "non-positive" simply refers to whichever direction you choose to call "positive", and this decision is completely arbitrary. I mean, a car can accelerate backwards if you put it in reverse, but we'd call moving forwards the positive because that just seems logical. Why not call its backwards motion the positive?

[M_BONG]

Negative acceleration simply means it's accelerating in the opposite direction. You see, something can accelerate to a halt (deceleration), and then continue to accelerate in the "non-positive" direction. Of course, if you think about it this isn't too big a deal. I mean, "non-positive" simply refers to whichever direction you choose to call "positive", and this decision is completely arbitrary. I mean, a car can accelerate backwards if you put it in reverse, but we'd call moving forwards the positive because that just seems logical. Why not call its backwards motion the positive?

So there is a difference between negative acceleration and deceleration? Isn't deceleration just the negative of the acceleration equation? Like when I slow down a car, I am not moving in the opposite direction... but I am slowly the motion. If the acceleration of the car is like 2t isn't the deceleration just -2t (assuming if it follows the same acceleration)

But then why does moving in the opposite direction also involve the negative of the acceleration equation (sorry do I make any sense here?)

[keltingmeith]

So there is a difference between negative acceleration and deceleration? Isn't deceleration just the negative of the acceleration equation?

Nope - they're exactly the same. However, deceleration implies that an object is just slowing down, when in reality it could continue to have this negative acceleration beyond when it has stopped, and keep moving in the opposite direction.

[lzxnl]

In common usage, deceleration refers to a reduction in speed.

[M_BONG]

When you can't do a question (but the answer for that part is required for subsequent parts), can you "make" or "guess" a random answer and hopefully get all the other method (consequential) marks for the subsequent questions?

Does VCAA specific marking guides on how strict that can occur, and how many marks (like everything but the answer mark or...?) do you normally get by doing this?

[brightsky]

My recommendation would be to let a be the answer to the earlier part, and then express all subsequent answers in terms of a. The Chief Examiner distributes a marking scheme to all assessors each year, but no one really knows the contents of the marking scheme apart from those who have served as assessors in previous years. However, I don't see any reason why the assessors would deduct a mark from subsequent parts, provided that what you have written is correct of course. For example, suppose you could not answer part a., and part b. and c. all depend on part a.. My guess would be that you will lose all the marks for part a., but none of the marks for part b. and c. provided that you've shown the correct working details, and the expression you have given as your final answer is correct.

[Valyria]

Are there any ways to express vector functions in terms of i, k & k components on the CX CAS?

[keltingmeith]

Are there any ways to express vector functions in terms of i, k & k components on the CX CAS?

To memory, the CAS uses vectors as a row matrix (1xn). If I'm wrong, it's a column matrix (nx1). In fact, row/column matrices are often referred to as "vectors", because when using them in matrix multiplication, they function as vectors.

Just to clarify - create a 3x1 matrix. First box is the i component, second box is the j component, third box is the k component. You can then differentiate/integrate the whole matrix to differentiate/integrate your vector function.

This is quite a lengthy process, though - wouldn't recommend it for multiple choice.

[psyxwar]

To memory, the CAS uses vectors as a row matrix (1xn). If I'm wrong, it's a column matrix (nx1). In fact, row/column matrices are often referred to as "vectors", because when using them in matrix multiplication, they function as vectors.

Just to clarify - create a 3x1 matrix. First box is the i component, second box is the j component, third box is the k component. You can then differentiate/integrate the whole matrix to differentiate/integrate your vector function.

This is quite a lengthy process, though - wouldn't recommend it for multiple choice.

Both column and row matrices can be used to represent vectors (on TI Nspire anyway)

[keltingmeith]

Both column and row matrices can be used to represent vectors (on TI Nspire anyway)

On my old dinosaur (it was grey, what what ) it didn't like me using both - it was one or the other, so.

[psyxwar]

ah idk then, on my one at least (TI Nspire CX CAS, with the color screen and everything ) both work

[Edward Elric]

Can someone please explain to me the answers for 4 c, d and e on the 2007 VCAA Spesh exam 2? Please? There are no worked solutions and I dont understand the method behind doing these type of Qs, thanks in advance.