VCE General & Further Maths Question Thread!

[keltingmeith]

I would interpret an interior angle to be the angle contained inside the hexagon at the point A, or the point B. For a regular hexagon, the interior angle is actually 120 degrees, as the sum of all interior angles is 720 degrees, and 720/6=120.

[SarahLoria]

Hey guys, I have a question I am having some difficulties with in Business Maths. If anyone could help that would be great!

Question:
Joel invests $55,000 into an annuity at 7.8% interest compounding annually. After the interest has been added each year he plans to withdraw $6000 from this account to travel.

a) Using this formula A=PR^n - (Q(R^n-1))/R-1 (Reducing balance - annuities formula)
    State the Q and R values.

b) How many trips would Joel be able to take before the balance in the account falls below $39,000?

c) How many trips can Joel make from this investment?

[clidedescope]

Hey guys. A question in my textbook about business mathematics has been bugging me and causing me quite a bit of stress. I've tried solving it the way the textbook says, but I keep on getting the wrong answer according to the book, so I figure it's either the example it used being wrong (I followed it exactly), or the answer itself. Two teachers have given me two different solutions too. Any insight would be great, because the SAC is getting closer and I am beginning to worry.

[plato]

Question:
Joel invests $55,000 into an annuity at 7.8% interest compounding annually. After the interest has been added each year he plans to withdraw $6000 from this account to travel.

a) Using this formula A=PR^n - (Q(R^n-1))/R-1 (Reducing balance - annuities formula)
    State the Q and R values.

b) How many trips would Joel be able to take before the balance in the account falls below $39,000?

c) How many trips can Joel make from this investment?

Where did you get this question?

A couple of VCAA examiners reports have said that this annuities formula has not been in the syllabus for more than eight years. Forget the first part of the question and use TVM solver for any compound interest or annuity question.

Read the reports from VCAA as they can help you with other difficulties in business maths.

[plato]

Hey guys. A question in my textbook about business mathematics has been bugging me and causing me quite a bit of stress. I've tried solving it the way the textbook says, but I keep on getting the wrong answer according to the book, so I figure it's either the example it used being wrong (I followed it exactly), or the answer itself. Two teachers have given me two different solutions too. Any insight would be great, because the SAC is getting closer and I am beginning to worry.

(Image removed from quote.)

It may happen in real life but I don't think there has been a further question like this. From what I can see, exam questions have all calculated and paid interest at the same time.

The $1241.37 balance on 19 May is an example of the reason you could get different answers. Is the interest for this day based on this balance or on the $445.82 balance that was there on this same day one second before the salary was deposited?

I don't think VCAA would risk having something this complicated on an exam.

[Jono_CP]

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[LiquidPaperz]

for q8, answers A, but how did they get w is greater than or equal to 5b that doesnt make sense to me in this context.

i thought it would be 5w is greater than or equal to b??

thanks

[kinslayer]

For each loaf of brown bread made, you have at least five loaves of white bread made.

So take the number of loaves of brown bread (b), multiply it by five (5b). The number of loaves (w) is greater than equal to this number, so w >= 5b.

5w >= b would mean that for each loaf of white bread made, you have at most five loaves of brown bread.

[LiquidPaperz]

i know what you did but i dont get how that makes sense?

why do you multiply it by 5?

5w >= b would mean that at least 5 white loafs would be made for each brown?

[kinslayer]

i know what you did but i dont get how that makes sense?

why do you multiply it by 5?

5w >= b would mean that at least 5 white loafs would be made for each brown?

Look at it this way. In your example, 5w >= b, if you set w = 1, what are the possible values for b?

b, the number of brown loaves, can be equal to 5w = 5, or it can be smaller, so 4, 3, 2, 1, or 0. If w = 2, then b is less than or equal to 10.

So you can see that for each white loaf made there can be at most five brown loaves.

Now if w >= 5b, set b = 1. Then w >= 5. If b = 2, w >= 10. So for each brown loaf made, you must have at least five white loaves.

[LiquidPaperz]

ok that clears it up but with  w >= 5b if we sub 1 we get w>= 5 however it says atleast so wouldnt it need to be w <= 5 or am i thinking of it wrong?

[kinslayer]

ok that clears it up but with  w >= 5b if we sub 1 we get w>= 5 however it says atleast so wouldnt it need to be w <= 5 or am i thinking of it wrong?

>= means "at least". w >= 5b means w is at least five times b.

For every loaf of brown bread you must have at least five loaves of whit ebread.

[LiquidPaperz]

alright i get everything, i just dont get why you times the other letter by what your supposed (in my mind) to times the first letter by. if i have at least 5 loafs white bread for 1 brown wouldnt it be 5w >= b i just dont get why its 5b cause thats 5 brown?

[plato]

There is an explanation for a similar problem on last year's VCAA Examination Report.

Look at their explanation of the solution to 4b in Graphs and relations at
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2013/FM2_examrep13.pdf

[kinslayer]

alright i get everything, i just dont get why you times the other letter by what your supposed (in my mind) to times the first letter by. if i have at least 5 loafs white bread for 1 brown wouldnt it be 5w >= b i just dont get why its 5b cause thats 5 brown?

It's not easy to get your head around the first time you see it. It might help to replace the inequality sign with an equals, and forget about 'w' and 'b'. Read out in words what each equation is telling you and it may be easier. Check out plato's link, it's the same idea.