Futher Maths is a sick joke!

[astone788]

Below is an excerp from the 2009 VCAA further maths exam 2 that shows why VCE futher maths is a sick joke!  Source: http://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/exams.aspx

In 2009, the school entered a Rock Eisteddfod competition.
When rehearsals commenced in February, all students were asked whether they thought the school would make the state finals. The students’ responses, ‘yes’, ‘no’ or ‘undecided’ are shown in the initial state matrix S0.
         [160]
SO = |120|
         [220]
 
Each week some students are expected to change their responses. The changes in their responses from one week to the next are modelled by the transition matrix T shown below   
       
           Yes   No  Undecided
           [.85 .35 .60] Yes
T =      |.10 .40 .30| No
           [.05 .25 .10] Undecided

Evaluate the product S1 = T S0 , where S1 is the state matrix at the end of the first week
S1 = [310]
        |130|         Note: This answer is correct!
        [60  ]
In total, how many students are not expected to have changed their response at the end of the first week?
S1 = [310]                                               85% × 310 = 263.5
        |130|                                               40% × 130 = 52
        [60  ]                                               10% × 60   = 6
                    total students not expected to change  =  321.5
This answer is wrong? WTF?
According to VCAA 2009 futher exam 2 assesment report the answer is:
85% × 160 + 40% × 120 + 10% × 220 = 206 
So what they did was evaluate how many students that are not expected to have changed their response using the initial state matrix e.g.
         [160]                                                          85% × 160  = 136
SO = |120|                                                           40% × 120  = 48
         [220]                                                           10% × 220  = 22
                     Total students that are not expected to change = 136 + 48 + 22
                                                                                                 = 206

But the question clearly states "how many students are not expected to have changed their response at the end of the first week?"

Using T x S1 we should be able to evaluate the number of students that are not expected to have changed their response at the end of the first week given that "S1 is the state matrix at the end of the first week."

Little do we know, the question wants us to calculate how many students that are not expected to change their response using the initial state matrix (S0)

When I showed this to my teacher, even he was caught dumbfound!

Oh my goodness! Further maths is stressful as it is, the least VCAA could do is give us some consistency so I can study knowing that the equations I'm following are faithful. The ground beneath me is starting to shake because the foundation to which I've built my knowledge is corrupt. Whoever writes these exams I want to rip their hearts out of their ass, so I can show it to them, so they can see how cold and black it is before they die. I'm pissed! 

[Truck]

Whoever writes these exams I want to rip their hearts out of their ass, so I can show it to them, so they can see how cold and black it is before they die. I'm pissed! 

I don't know much about Further, but I just gotta say that was an excellent line, seriously well done.

[Yendall]

So:

→ S₀

  → T

We are told that T represents this description: Each week some students are expected to change their responses
'Each week' here tells that at the end of each week they may or may not change their responses.

You are now trying to find how many students are not expected to have changed their responses at the end of the first week.

So we use the formula: S₀ = T⁰ x S₀


S₀ = ⁰ x

=

Therefore, the amount of people who have not changed their preferences will be 85% of 160, 40% of 120 and 10% of 220, which ends up being 206.

I know you just stated that, but I think the end of the first week is the initial state. Because the students could not vote prior to the first week or at the start, it had to be at the end. I initially thought that S₁ would indicate the start of the second week, thus being the end of the first week. However, S₁ is the end of the second week. I'm fairly certain that's how it was supposed to be attempted. I could be wrong though.
The question itself however lacks clarity as we are not told whether the students are voting at the start or the end of the week, and i see how that would confuse everyone

[astone788]

I initially thought that S₁ would indicate... the end of the first week. However, S₁ is the end of the second week.

I agree. I talked to my teacher about it, and I got nothing out of him other than a dumbfound expression. I've completed hundreds of practice exams that are based on matrices and 99% of them imply that S1 = end of the first week. For example, this is a question that appeared on the 2011 VCAA Further maths exam2.

The matrix S0 displays the number of juvenile female ducks (J) and the number of adult female ducks (A) that are introduced to the wetlands at the start of the program.
S0 = [32] J
        [64] A

T is the breeding matrix
T = [0      2]
      [.25  .5]

Use matrices to calculate the number of juvenile and the number of adult female ducks expected in the colony at the end of year 3 of the breeding program.
S3 = T3 X S0
     = [104]
        [46  ]
Note: This answer is correct!
This confirms our initial conclusion that S1 indicates the end of the first week. Hence, S2 indicates the end of the 2nd week. Hence in this case, S3 indicates the end of the 3rd year.
As with any Rule, there are exceptions (for no reason other than "further maths is a sick joke") But for 99% of cases, S1 indicates the end of the first week. S2 indicates the end of the 2nd week. And so forth.
Damn VCAA. Anyway, I don't like to hold grudges. I gotta keep my cool 

[Yendall]

I initially thought that S₁ would indicate... the end of the first week. However, S₁ is the end of the second week.

99% of them imply that S1 = end of the first week.

You would think that for everything. I've done tones of questions where S₁ is typically after one *insert time period*. Which makes me think this question was an attempt by VCAA to ensure that hardly anyone got it correct. Damn VCAA!

[Tomanomanous]

I initially thought that S₁ would indicate... the end of the first week. However, S₁ is the end of the second week.

99% of them imply that S1 = end of the first week.

You would think that for everything. I've done tones of questions where S₁ is typically after one *insert time period*. Which makes me think this question was an attempt by VCAA to ensure that hardly anyone got it correct. Damn VCAA!

VCAArse*