VCE Methods Question Thread!

[pi]

There was a question in a VCAA exam in which you had to find the nature of the stationary points. The nature of one of them was 'local max.,' in the solutions, if i only wrote 'maximum,' would it be correct?

No, you need to mention "local"

[FlorianK]

There was a question in a VCAA exam in which you had to find the nature of the stationary points. The nature of one of them was 'local max.,' in the solutions, if i only wrote 'maximum,' would it be correct?

No!

Maximum =/= Local Maximum

Nature of stationary points means:
local maximum
Local mimimum
stationary point of inflection

[sin0001]

is a maximum turning point always labelled as a 'local max.', and never as only a 'max.'?

[pi]

is a maximum turning point always labelled as a 'local max.', and never as only a 'max.'?

Well for y=-x^2, (0,0) is the max and local max.

[sin0001]

Also, do graphs such as y=x^(1/3) have a stationary point at the vertical line thingy at (0,0), because stat. points are defined as points of zero gradient, but the vertical line has an undefined gradient?

[pi]

Also, do graphs such as y=x^(1/3) have a stationary point at the vertical line thingy at (0,0), because stat. points are defined as points of zero gradient, but the vertical line has an undefined gradient?

If it's defined as grad=0, how would undefined also be stationary then You answered your own q there haha

[soccerboi]

Suppose that in a particular year the percentage increase in the value of stocks listed on the Australian Stock
Exchange was a normally distributed random variable with a mean of 5% and standard deviation of 10%.
The proportion of stocks that would have decreased in value, in that particular year, is closest to
A. 0.31
B. 0.5
C. 0.69
D. 0.05
E. 0.1

How do you get option A as the answer?

Also, when solving something like b²-4 < 0, how do you determine which way the inequality sign goes?
Thanks

[FlorianK]

Also, do graphs such as y=x^(1/3) have a stationary point at the vertical line thingy at (0,0), because stat. points are defined as points of zero gradient, but the vertical line has an undefined gradient?

When the tangent to a point is a horizontal line then it's a stat point.
Here the tangent would be, if the gradient would be defined, a vertical line.
However the gradient is not defined because:
d/dx(x^(1/3)=1/(3*x^2/3) --> if x=0 then you divide by 0 which is just wrong.

[b^3]

Suppose that in a particular year the percentage increase in the value of stocks listed on the Australian Stock
Exchange was a normally distributed random variable with a mean of 5% and standard deviation of 10%.
The proportion of stocks that would have decreased in value, in that particular year, is closest to
A. 0.31
B. 0.5
C. 0.69
D. 0.05
E. 0.1

How do you get option A as the answer?

Note that it is the percentage increase that is the normally distributed random variable, so we can make that X.
i.e.
(as this corresponds to 5%)


Then (on the ti-nspire) use normCdf [Menu] [5] [5] [2] (on mine anyway)
normCdf(-inf,0,0.05,.01) (don't write this calculator syntax on the exam, but this is MC anyway)
=0.3085=0.31 i.e. A

Also, when solving something like b²-4 < 0, how do you determine which way the inequality sign goes?
Thanks

You're values will be at the x-intercepts, so find them first.


Then the best way to go about it is to draw it out visually (just a little sketch).
So we draw out y=x²-4, and look when it is below 0, that will be for
So that leaves us with

[BubbleWrapMan]

If you want an algebraic method:





and or and (they have to be opposite signs to be negative)

and or and

or

[soccerboi]

Suppose that in a particular year the percentage increase in the value of stocks listed on the Australian Stock
Exchange was a normally distributed random variable with a mean of 5% and standard deviation of 10%.
The proportion of stocks that would have decreased in value, in that particular year, is closest to
A. 0.31
B. 0.5
C. 0.69
D. 0.05
E. 0.1

How do you get option A as the answer?

Note that it is the percentage increase that is the normally distributed random variable, so we can make that X.
i.e.
(as this corresponds to 5%)


Then (on the ti-nspire) use normCdf [Menu] [5] [5] [2] (on mine anyway)
normCdf(-inf,0,0.05,.01) (don't write this calculator syntax on the exam, but this is MC anyway)
=0.3085=0.31 i.e. A

May i ask why its -infinity to 0?

[b^3]

X is the percentage increase in value of the stocks, we want to know when they decrease. They will decrease when x<0,  as your 'percentage increase' would now be negative.

[Phy124]

If you want an algebraic method:





and or and (they have to be opposite signs to be negative)

and or and

or

I used to just take the square roots of both sides and ignore the negative result of the square rooted number.

e.g.









But I'm not necessarily going to advise this in case the person forgets the method and stuffs up completely.

[BubbleWrapMan]

^ That method is useful for quadratics of that form, though if you have a more complicated quadratic you'll have to either factorise it (to use the method I used) or complete the square (to use the method you used). So it depends on the situation. I like the square root/modulus one though, it's easier to keep track of what you're doing (I forgot about that method until now, lol). If you get something like you'd be better off factorising, though if you get something like , completing the square isn't overly difficult, so yeah, knowing both is useful. In exam 1 last year the factor method would have come in handy for most.

[soccerboi]

How do i find the variance of X, given the mean of X is 1.60625. Express your answer correct to four decimal places. (Info attached below)
Answer should be 0.8750

Thanks