Bazza's 3/4 Question Thread

[pi]

It was just last year where the SACs didn't scale much, and not even the teachers know what happened. We had excellent exams scores (full markers, and at least 15 people losing less than 5 marks over both), but for some unkown reason the SACs didn't scale.

I'd still say a "strong cohort" is appropriate, there are only a few schools better (Scotch, MGS, Mac.Rob, etc.).

[WhoTookMyUsername]

Meh it doesn't really make that much of a difference what we classify it as at the end of the day.
But there's only like 5000 spesh students in the state so having 3 better schools already, as well as tons of very nice public schools like balwyn, and plenty of amazing kids at just about every school in the state.
I guess last year the exam 1 was sooooo easy so it would have warped statistics a little bit.

[WhoTookMyUsername]

This is a modified SAC question from MHS this year (last sac, while since we did it)

Let's say you have a "coffee" cup that's either single or double, where the "single" capacity is 10 ml, and the "double" cup capacity is 20 ml

For the "single" cup release of coffee, there's a mean of 8 and a standard deviation of 2 ml; what's the chance the cup overflows?
(simple calc question)
prob = 0.15

But what is the probability that a DOUBLE cup will overflow; given that a DOUBLE cup is made up of 2 single shots ?
What i did in the SAC was like Pr(2X>20) = PR(X>10)
But some kids said only the MEAN would change and not the standard deviation for the double cup; in which case what i did was wrong. C
Can anyone shed light what to do in this scenario?

Also
2) For probability questions (normal distribution) if t>0 (as for most questions) do we restrict the distribution to t>0?
I did this on heffernan 2012 for trial exam and it caused quite a few problems as the area when t<0 was significant; and affected results... (trial exam at school, no answers yet)

If we restrict time (which i think we should, as i believe a VCAA exam indicated we should)
And then are asked, what's the probability t>10
should we take that to mean Pr(t>10|t>0) ?
(as the area under the graph over the region we are considering doesn't = 1)
Or alternatively; in a well written question will this area always be insignificant?

thanks!

[charmanderp]

SD(aX+b) = aSD(X), right? So it should change also.

[WhoTookMyUsername]

Yeah, but i think saying Pr(2X>20) = Pr(X>10) may account for that? not sure that's why i'm asking lol




This is a modified SAC question from MHS this year (last sac, while since we did it)

Let's say you have a "coffee" cup that's either single or double, where the "single" capacity is 10 ml, and the "double" cup capacity is 20 ml

For the "single" cup release of coffee, there's a mean of 8 and a standard deviation of 2 ml; what's the chance the cup overflows?
(simple calc question)
prob = 0.15

But what is the probability that a DOUBLE cup will overflow; given that a DOUBLE cup is made up of 2 single shots ?
What i did in the SAC was like Pr(2X>20) = PR(X>10)
But some kids said only the MEAN would change and not the standard deviation for the double cup; in which case what i did was wrong. C
Can anyone shed light what to do in this scenario?

Also
2) For probability questions (normal distribution) if t>0 (as for most questions) do we restrict the distribution to t>0?
I did this on heffernan 2012 for trial exam and it caused quite a few problems as the area when t<0 was significant; and affected results... (trial exam at school, no answers yet)

If we restrict time (which i think we should, as i believe a VCAA exam indicated we should)
And then are asked, what's the probability t>10
should we take that to mean Pr(t>10|t>0) ?
(as the area under the graph over the region we are considering doesn't = 1)
Or alternatively; in a well written question will this area always be insignificant?

thanks!

[brightsky]

1) the fact that the areas Pr(X>10) and Pr(2X>20) are equal does not mean the standard deviations are equal as well.

correct answer: method 1: normcdf(20,infty,16,4) = 0.1587; method 2: normcdf(10,infty,8,2) = 0.1587.

2) you'd need to show me the question.

[WhoTookMyUsername]

ahk thanks

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/mmcas1-sampfin-w.pdf
One of the dot points is to be able to show (tech free) (Q5)
"general solutions of equations
such as cos(x) + cos(3x) =  1/2
x ∈ R and the specification of
exact solutions or numerical
solutions, as appropriate, within a
restricted domain"

how on earth can you do this without double angle formula ?

thanks!

[pi]

ahk thanks

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/mmcas1-sampfin-w.pdf
One of the dot points is to be able to show (tech free) (Q5)
"general solutions of equations
such as cos(x) + cos(3x) =  1/2
x ∈ R and the specification of
exact solutions or numerical
solutions, as appropriate, within a
restricted domain"

how on earth can you do this without double angle formula ?

thanks!

I doubt that could be done tech free anyway, looks dodgy to me.

[brightsky]

ahk thanks

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/mmcas1-sampfin-w.pdf
One of the dot points is to be able to show (tech free) (Q5)
"general solutions of equations
such as cos(x) + cos(3x) =  1/2
x ∈ R and the specification of
exact solutions or numerical
solutions, as appropriate, within a
restricted domain"

how on earth can you do this without double angle formula ?

thanks!

I doubt that could be done tech free anyway, looks dodgy to me.

seconded. you know something's amiss when the cas can't even give an exact general solution.

[WhoTookMyUsername]

silly vcaa 

[Jenny_2108]

ahk thanks

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/mmcas1-sampfin-w.pdf
One of the dot points is to be able to show (tech free) (Q5)
"general solutions of equations
such as cos(x) + cos(3x) =  1/2
x ∈ R and the specification of
exact solutions or numerical
solutions, as appropriate, within a
restricted domain"

how on earth can you do this without double angle formula ?

thanks!

I don't understand why they write cos(x)+cos(3x)=1/2

Why can't we just solve like: sin(x)+cos(x)=0
                                            sin(x)=-cos(x) => tan(x)=-1 => x=-pi/4 + npi
Did I do wrong somewhere? Why is it question 3 marks? :O

[WhoTookMyUsername]

Probably my last question spurt before the exams

1) Is e.g. median X=2 or x=2 (notationally wise)
2) If we're asked to "find radius for which A is a max" and we only get 1 point, do we need to verify it's a local max?
3) Do we need to label more points than it asks for?
If e.g. it asks, label intercepts - do we need to label TP ?
4) for a question like d(x^3/sin(x))/dx that's worth 2 marks, how should you set out working so you can also gain method mark?
like i just go to the answer straight away not sure if that's OK
5) can we indicate areas on the exam by shading? and then saying /// (shaded area) = ?
6) Do we have to combine fractions? like is leaving an answer such as pi/12 + 31/5 acceptable?
7) If say we have a binomial dist 100 trials, what's prob success of having 10 or less, how would you set out your working if it's worth say 3 marks? (where do the two method marks come from, listing Pr(x=0) + Pr(X=1) etc.?
Will the domain of an inverse function on a graph will always equal the range of the original function over it's specified domain?
let's say h(x) is restricted domain to (2,9) but range (11, 20) will the domain of inverse h(x) that we have to sketch become (11,20) or stay as (2,9)?
9) Does area bound by 2 curves refer to the area ENCLOSED within those 2 curves? e.g. let's say you have x^2 - 5 and -x^2 + 10, and your asked to find the area inclosed by the curves over the domain [-3,3] (intercepts at -2.7 and 2.7) would the area be referring to the area enclosed by the two curves (that is between -2.7 and 2.7) or the whole area between the curves from -3 to 3?
10) Should we indicate an asymptote on the graph if the graph has a restricted range/domain?
i.e. let's say we're asked to sketch e^x over the domain (-5, 20), shoudl we have an asymptote at y = 0?
thanks very much! Sorry for some questions which i know are slightly tedious :\

[brightsky]

1) just say median is 2 or m = 2 if you've previously introduced m.
2) no.
3) do so if you're paranoid. better safe than sorry.
4) you could potentially write [d/dx(x^3)*sinx - x^3*d/dx(sinx)]/sin^2(x) first before writing the answer. that will defs get you the mark.
5) definitely. 'area' would probably do.
6) yes. 2007 examiner's report split fractions.
7) i use sum notation. avoid calc syntax at all costs. and it most likely would not be worth 3 marks since it's such a standard question.
8 ) dom of inverse = range of original. that's true for all inverse functions.
9) whole area. but vcaa will word it more clearly so there should be no ambiguity. they will tell you exactly what the bounds are. for example x = -3, x = 3, y = x^2 - 5 and y = -x^2 + 10 in which case you have to include the two small areas at the sides.
10) certainly not.

[WhoTookMyUsername]

For the question attached, with the rounding off at the end, not sure if i read it wrong but i thought it was implying -> find the answer, then round to whatever integer is closest.
Cos the question doesn't specifiy whether the measerurs round before they exclude / include
But the answers rounded up (attached)

Could someone please explain which is the more correct answer?
In general how can we tell which way to round with these sorts of questions?


Thanks!

[BubbleWrapMan]

Imagine a horizontal bar that's 177 cm off the ground. If someone were 176.46 cm, their head would not touch the bar, hence they are not accepted. If the bar were instead 176 cm off the ground, then a person who is 176.46 cm would just be able to touch the bar with their head, and they would be accepted. This implies that the minimum acceptable height is 177 cm rather than 176 cm. Slightly crude explanation but hopefully you get the idea.

There isn't really a general way to do these sorts of questions (other than be logical). The idea is that you can't arrive at the answer based on questions you've seen before, you need to re-think it each time for these sorts of questions (not that this sort of 'logical rounding' question is overly common).