'Stupid' Exam Questions

[Escobar]

Thanks, also
for the section of a function that is strictly decreasing/increasing,
is this inclusive of stationary points?
eg
local min at x=1
local max at x=3
strictly increasing= [1,3] or (1,3)?

[Zealous]

Thanks, also
for the section of a function that is strictly decreasing/increasing,
is this inclusive of stationary points?
eg
local min at x=1
local max at x=3
strictly increasing= [1,3] or (1,3)?

If I remember correctly, strictly increasing includes the endpoints. So in your situation it would be [1,3]. That being said, questions on this are very uncommon.

[Yacoubb]

Thanks, also
for the section of a function that is strictly decreasing/increasing,
is this inclusive of stationary points?
eg
local min at x=1
local max at x=3
strictly increasing= [1,3] or (1,3)?

OMG I've been wanting to ask this question. I thought 'strictly' means that it is JUST decrease, thus not inclusive of stationary points, and that's why I've used circular brackets. But solutions seem to tell otherwise... I'm just taking it as a rule now and using square brackets.

Quick clarification:
- Endpoints
- Cusps
- Points of Discontinuity

^^ derivative cannot be found at these points. Any other conditions where we cannot find the derivative?

[speedy]

Can you look at your bound reference during reading time?

[Yacoubb]

Can you look at your bound reference during reading time?

Yep :-)

[Blondie21]

If we are told to find the derivative of something, but it is reallllly long, do we need to write the entire equation?
Such as q3 e) of the 2010 exam 2 paper?

[abeybaby]

OMG I've been wanting to ask this question. I thought 'strictly' means that it is JUST decrease, thus not inclusive of stationary points, and that's why I've used circular brackets. But solutions seem to tell otherwise... I'm just taking it as a rule now and using square brackets.

Quick clarification:
- Endpoints
- Cusps
- Points of Discontinuity

^^ derivative cannot be found at these points. Any other conditions where we cannot find the derivative?

always use the square brackets, whether the points are differentiable or not, and whether they are increasing or strictly increasing. This is a bit long, but explains it perfectly. http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf

and those are all the cases in which the derivative does not exist:)

[IndefatigableLover]

If we are told to find the derivative of something, but it is reallllly long, do we need to write the entire equation?
Such as q3 e) of the 2010 exam 2 paper?

In that example, unfortunately you would need to write it all out since that derivative would be worth one mark which if omitted, may leave assessed wondering where you pulled your final answer though (basically don't risk it).

[Yacoubb]

always use the square brackets, whether the points are differentiable or not, and whether they are increasing or strictly increasing. This is a bit long, but explains it perfectly. http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf

and those are all the cases in which the derivative does not exist:)

Ah okay, thank you!!

So, you know how VCAA surprised many people with the similar figures in the first Methods exam, are there any other topics that could be sprung up on us that assume knowledge from previous years? I ask this because I want to be ready for anything VCAA can throw at us. I pray it's a similar triangles question, because I've learnt how to do it haha!

[keltingmeith]

always use the square brackets, whether the points are differentiable or not, and whether they are increasing or strictly increasing. This is a bit long, but explains it perfectly. http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf

and those are all the cases in which the derivative does not exist:)

If anyone has trouble with this article (I know I did when my teachers threw it at me), I'm happy to give another explanation as to why we include the endpoints based on this definition.

Ah okay, thank you!!

So, you know how VCAA surprised many people with the similar figures in the first Methods exam, are there any other topics that could be sprung up on us that assume knowledge from previous years? I ask this because I want to be ready for anything VCAA can throw at us. I pray it's a similar triangles question, because I've learnt how to do it haha!

Basically, anything from year 10 geometry and below can throw you off. This is more applicable to specialist, but make sure you remember the Z rule (angles of elevation/depression), adding angles up to certain degrees for inside/outside shapes, etc. Circle theorems isn't necessary, though, unless you're doing specialist.

Summation notation is something VCAA have never done before (not that I remember, at least. Did see it on some trial exams, though), but they could spring on you for some questions and completely throw you off - particularly for approximations of the area under the curve using left-hand and right-hand rectangles.

OMG I've been wanting to ask this question. I thought 'strictly' means that it is JUST decrease, thus not inclusive of stationary points, and that's why I've used circular brackets. But solutions seem to tell otherwise... I'm just taking it as a rule now and using square brackets.

Quick clarification:
- Endpoints
- Cusps
- Points of Discontinuity

^^ derivative cannot be found at these points. Any other conditions where we cannot find the derivative?

A nice little trick is to draw the graph of the function and its derivative. Then, the function isn't differentiable at any discontinuities on either of these graphs, including end-points.

[speedy]

always use the square brackets, whether the points are differentiable or not, and whether they are increasing or strictly increasing. This is a bit long, but explains it perfectly. http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf

and those are all the cases in which the derivative does not exist:)

Whoa, I didn't know VCAA published things like this... Is it a one off? Or are there any other helpful guides they have posted? (for spesh, chem or phys too)

[keltingmeith]

Whoa, I didn't know VCAA published things like this... Is it a one off? Or are there any other helpful guides they have posted? (for spesh, chem or phys too)

To memory, it was a one-off because they added this into the study design last minute.

But, they do those bulletins once a month (or bimonthly, maybe), and if you're willing to read through all of them, you might find hints about things.

[speedy]

Ok so I'm a little confused now, what's the difference between strictly increasing and regular increasing?

always use the square brackets... whether they are increasing or strictly increasing.

If anyone has trouble with this article (I know I did when my teachers threw it at me), I'm happy to give another explanation as to why we include the endpoints based on this definition.

Could you explain it? aha

Edit:
Another thing, can they give you matrix transformation questions in another form - such that you just expand the matrix and directly sub the result as the new x and y? I've heard someone mention it. If so, what would this look like? (Idk if that makes sense)

Also, what working should you give for matrix transformation questions - when it is appropriate to define the new function/get rid of x' and y'?

[myanacondadont]

When given one of those questions that ask you to find the values of (insert variable) such that the two equations have infinite solutions, is there a quick way to do this?

I solve det = 0 yet you always get 2 solutions. Is there a quick way to solve which will result in infinite solutions and which no solutions without having to go back and sub the values in and then rearrange and graph? Usually if I have to sub back in and stuff it'll take me a while which I hate spending on MC.
Also; is it possible that both values you get are both solutions for infinite solutions? or both result in lines with no solutions? Thanks!

[keltingmeith]

Alright speedy, your explanation is coming! I'll probably have time tomorrow to write it all out full and proper and such.

When given one of those questions that ask you to find the values of (insert variable) such that the two equations have infinite solutions, is there a quick way to do this?

I solve det = 0 yet you always get 2 solutions. Is there a quick way to solve which will result in infinite solutions and which no solutions without having to go back and sub the values in and then rearrange and graph? Usually if I have to sub back in and stuff it'll take me a while which I hate spending on MC.
Also; is it possible that both values you get are both solutions for infinite solutions? or both result in lines with no solutions? Thanks!

Sorry to be the bringer of bad news, but that is the quick way. Of course, you don't have to actually graph it. Let's say you have,

mx + 6y = 1
6x + my = 3

Then, you'll find out that there's no solution for . Subbing those in, we get:

-6x + 6y = 1
6x - 6y = 3

Multiply the first my -1,

6x - 6y = -1
6x - 6y = 3

From this, you can see that the gradient (the coefficients of y and x) are the same for both lines - so, it's that constant on the end is what determines if they're parallel or the same line (parallel gives no solutions, same line gives infinite)

Also, this specific example is one where both solutions produce parallel lines - there is no value of m that will give infinite solutions.