Suggested Answers (and Discussion) of the Further Maths Exam!

[EdwinJS]

Please explain to me why the last question graphs and relations was B - 7.5 

I have come to understand that it could really be any answer if justified... because we aren't told what k is?

If you got B please tell me why, my answer was C and is explained in the picture attached. 

[Rayzorrz]

With Q24 Core, if you accept E, you overpay on the annuity giving you a negative value for your FV.
If you accept C, you work out the PV to be $180,000 and substituting the values into the solver they should be able to match with the stats (positive FV).

[EdwinJS]

With Q24 Core, if you accept E, you overpay on the annuity giving you a negative value for your FV.
If you accept C, you work out the PV to be $180,000 and substituting the values into the solver they should be able to match with the stats (positive FV).

For Q24 of Core this is what I did (I got E!)

We aren't told what the current value is so the value at 5 years is used as the PV

Financial Solver -
N: 5(years) * 12(months) = 60
I: 5.2%
PV: 130,784.83 (at 5th year)
Pmt: = $-3460.14911597 (money away is always negative)
FV: 66,992.27 (at 10th year)
PpY: 12
CpY: 12

Makes sense to me, I think E was correct from the start. No doubts.

[decentxion]

Please explain to me why the last question graphs and relations was B - 7.5 

I have come to understand that it could really be any answer if justified... because we aren't told what k is?

If you got B please tell me why, my answer was C and is explained in the picture attached. 

The problem with the question is an inherent error in the wording. There isn't enough information on the walking pattern of Megan to assume that she walks at the same pace, or a reason why she stopped at 600m for a break. Without this info, we can't just assume that k=100, because what if Megan just walks a tad faster or slower? That can change the a-value.

[Rayzorrz]

Please explain to me why the last question graphs and relations was B - 7.5 

I have come to understand that it could really be any answer if justified... because we aren't told what k is?

If you got B please tell me why, my answer was C and is explained in the picture attached. 

You can work out the value of 'k' by substituting in the coordinates (10,800) as you know after 10 minutes she has reached the shop (800m from house). Thus 'k' works out to be 80 so your new equation is 'distance'=80*t. Let distance=600 as you know it is a continuous piece-wise/hybrid function. t=(600)/80=7.5.

[DontDrinkAndDerive]

I think Core Q2 is B - if Age (which is an increasing numerical value) groups don't have an order, then nothing does!

Core Q24 is definitely C. In this case PV should be negative and FV should be positive.

I don't teach Graphs and Relations, but I'd love an explanation of question 8 as well. It seems to me that any of the options are possible, since we don't know the value of k. Essentially k is telling us how quick she walks and a is telling us when she leaves for the last 200m of the walk. She can leave early and walk slow, or leave late and walk fast! We need more info, or at least that's how it seems to me. Unless there was an ammendment my school didn't find out about?

[deejay9]

For Q24 of Core this is what I did (I got E!)

We aren't told what the current value is so the value at 5 years is used as the PV

Financial Solver -
N: 5(years) * 12(months) = 60
I: 5.2%
PV: 130,784.83 (at 5th year)
Pmt: = $-3460.14911597 (money away is always negative)
FV: 66,992.27 (at 10th year)
PpY: 12
CpY: 12

Makes sense to me, I think E was correct from the start. No doubts.

Pmt is positive for annuities, since money is being received from the bank. Check out my working on the last page for this question, the answer is C

[Rayzorrz]

For Q24 of Core this is what I did (I got E!)

We aren't told what the current value is so the value at 5 years is used as the PV

Financial Solver -
N: 5(years) * 12(months) = 60
I: 5.2%
PV: 130,784.83 (at 5th year)
Pmt: = $-3460.14911597 (money away is always negative)
FV: 66,992.27 (at 10th year)
PpY: 12
CpY: 12

Makes sense to me, I think E was correct from the start. No doubts.

I think PV should be positive as you receive money. If PV is negative you are paying the receiver money.

[decentxion]

You can work out the value of 'k' by substituting in the coordinates (10,800) as you know after 10 minutes she has reached the shop (800m from house). Thus 'k' works out to be 80 so your new equation is 'distance'=80*t. Let distance=600 as you know it is a continuous piece-wise/hybrid function. t=(600)/80=7.5.

You make a good point. How annoying of a question, glad I haven't had to experience VCAA exam wording in a few years!

[EdwinJS]

I think PV should be positive as you receive money. If PV is negative you are paying the receiver money.

But I said PV is positive

[Rayzorrz]

But I said PV is positive

Apologies, was referring to PMT. PMT is positive if you receive money, negative if you give money.

[EdwinJS]

Apologies, was referring to PMT. PMT is positive if you receive money, negative if you give money.

Yes, totally agree with that but we were taught that when the initial PV is not known, make PV and FV negative, which I didn't show on the previous reply but if that was done then this would be the answer obtained:

Financial Solver -
N: 5(years) * 12(months) = 60
I: 5.2%
PV: -130,784.83 (at 5th year)
Pmt: = $3460.14911597
FV: -66,992.27 (at 10th year)
PpY: 12
CpY: 12

[Syndicate]

For matrices question 8, I believe the correct answer is A (my apologies if this has already been discussed).

Teams C and B have an equal amount of wins (2 each), however team C is ranked one. This is because team C has won the match against team B. If team A wins the match against team B, then team A and team C will have an equal amount of win, however, since team A had already won a match against team C, they will be ranked one in the tournament.

E can't be the correct answer. If team C loses a match against team D, then team D and team B will have the most wins (from this it can be inferred that E is not the correct solution).

[Rayzorrz]

Yes, totally agree with that but we were taught that when the initial PV is not known, make PV and FV negative, which I didn't show on the previous reply but if that was done then this would be the answer obtained:

Financial Solver -
N: 5(years) * 12(months) = 60
I: 5.2%
PV: -130,784.83 (at 5th year)
Pmt: = $3460.14911597 (money away is always negative)
FV: -66,992.27 (at 10th year)
PpY: 12
CpY: 12

Ah. I've always known that if you are still owed money, FV should be positive. If you now owe money, FV should be negative. In this case your original amount still owed (PV) is negative so you are stilled owed $130,784.83 but if you have FV as negative, you now owe $66,992.27 since you have overpaid.

Edit: if you use Cambridge's Further Maths revised textbook, they follow the same method.

[cosecant]

can someone please explain to me why 13 was C? Seasonality are predictable patterns that occur within a year or less.  However, for the time series plot shown it was across 4 years and when you divide it into each year, there is no obvious pattern.