VCE General & Further Maths Question Thread!

[Thorium]

I had a go with question 17a, i have attached the solution.

Here is the solution for 2d-e, sorry for late reply.

[Einstein]

thanks! how about this?

[99.96 plz]

Can someone help me with part b.

Thanks.

HINT: SOH CAH TOA

[Billion]

Questions:

[LiquidPaperz]

Im having one problem with matrices, and if you could clarify it that would be great. In the book they say the inverse is as stated in the attachment (the diagonal is switched and the remaining 2 elements are multiplied by -1), but then a few pages later it goes on about finding/determining the inverse using the 1/det(A) etc, would we just switch the diagonals like before and go on from their?.. could you tell me whats happening here?

Also, when a question asks, find the inverse of this/ or show A^-1A=I etc, which way do we use when determining the inverse?

Thanks

[keltingmeith]

It might seem weird at first, but they've used that method in the first question. The determinant of the matrix they've given is 2*5 - 3*3 = 1, which gives us:



(forgive the bad notation, AN doesn't seem to handle [ and ] that well)

So, you don't really have two different methods, it's actually the one mentioned in the second picture. So, always use the method in the second picture if it's a 2x2. If you have a higher order matrix, find the inverse using your CAS.

[Zealous]

Questions:

Because I'm not sure what CAS you use, I'll just use the annuities formula instead of TVM solver or Finance Solver. Just substituting values in and solving for the unknown is sufficient for all of these questions - make sure you write down all the information out so you know what information you have, and what information you need to find.

(have a look at your textbook for what each pronumeral represents, and this formula is pretty long!)

9c First we need to find out the value of the balance after the next 15 years if we are investing money each month. So . Basically, our growth factor (r) is which turns the percentage (7.2%) into a decimal, and also takes into account that we are dealing in months (hence why we multiply by 12). Our n value is because we have 15 years worth of 12 months, so we end up with 180 compounding periods.



So after 15 years, there will be $387038 available for retirement. Now we have to workout how much money we can take out of the $387038 each month, given we are going to take it out for 20 years and that the balance is compounding monthly at 8% p.a.





. So $3237 can be taken out every month in retirement each month because of the investment. Last step is to multiply that by twelve, because the question wants you to find the annual salary, which will be $3237x12=$38848.The annual salary in retirement will be $38848. (hopefully that's correct, it's been like ages since I did business maths!)

____________________________

I don't have time to go through all the questions, but I'll leave some advice here. If you can get good at using TVM solver or Finance Solver on your CAS, these questions will be much much easier. I used the method above of using the formula to check my answers during the exam because I had extra time, and I have shown that method as I'm not too sure on what calculator you use. For the rest of the questions you've sent, first write down all the information you've been given, then find the unknown using the formula or your CAS software. The hardest step is just taking in the information and picking out what is key to solving the question. You won't get many questions with multiple steps like the one above. Hopefully this helps! if you still need help with those last questions, post back here and I'll try get back to you.

[LiquidPaperz]

It might seem weird at first, but they've used that method in the first question. The determinant of the matrix they've given is 2*5 - 3*3 = 1, which gives us:



(forgive the bad notation, AN doesn't seem to handle [ and ] that well)

So, you don't really have two different methods, it's actually the one mentioned in the second picture. So, always use the method in the second picture if it's a 2x2. If you have a higher order matrix, find the inverse using your CAS.

Alright, that clears it up, so would you suggest always using the second option (only option) instead of the diagonal is switched and the remaining 2 elements are multiplied by -1, because the detminant will be different in cases?

[keltingmeith]

I think you misunderstand - the determinant method includes the switching.

For any matrix A,

For a 2x2 matrix , this can be simplified to

[LiquidPaperz]

Any help on 5b and 7a would be awesome! Thanks

answer:
5b: x=5w-250
7a: c = 0.2n + 175

[keltingmeith]

5b.

When x increases, so does w, so . But, when x = 0, w = 50, so there's some pesky constant in there, giving us . Subbing in the next point, we get So, we get . Now, there's one small issue with this relationship - whenever we write a relationship, we like to put it in the form of "what we see = what we control", but we've got this around the other way (which I did just because it was easier to do). So, solving for x, we get

7a.

This time they tell us the formula, so this works very much in our favour! C = an + b. Subbing in the four values they gave us, we get . Now, we just need to solve these simultaneous equations to find a and b. You can do this by CAS, but if you want to do it by hand, here's how I would:

Solve both equations for b:


Now, let both equations equal each other and solve for a.



Now, sub this into either of the equations to find b.



So, the answer is (I'm thinking the 0.2 is a mistake on the book's part, because I did double check this on a calculator)

[LiquidPaperz]

Thanks Euler!!, i sent a message to you off how i got 0.2 and my method of working it out, my method is wrong as im subbing cost for n, but it still yielded the correct answer thats why i was abit iffy with how to do it.

I also had these two questions, how do you do them? Thanks

[keltingmeith]

7. Firstly, let's give them each a pronumeral to make things easier. The best way to do it is first initial = pronumeral.

Next, interpret the words to be maths, one step at a time, and write it all down as you go along.
"The sum of Anne's mark and David's mark is 42". So, a + d = 42
"Sheila has twice as many marks as David". So, s = 2d
"The sum of Anne's an Sheila's marks is 52". So, a + s = 52

You're not expected to do this by hand at methods level, so I'd assume the same for further, but here's a way to anyway:


So, Anne got 32 marks, David got 10 marks and Sheila got 20 marks.

8 is on the way, but dinner be calling. (maybe someone will beat me to it, hahah )

EDIT:

8. So, we know that the mixture costs $6 per kilogram, and we need 60 kilograms, so all up we have 360 = ?a + ?b - where ? is the costs of the actual herbs a and b. So, this gives us 5a + 8b = 360. We also know that the mixture of a and b will give us 60 kg, so a + b = 60. We now have our simultaneous equations and are ready to go:



So, you need 40kg of herb A and 20kg of herb B.

[LiquidPaperz]

thanks

[Jono_CP]

Hi could I have some assistance please with transition matrices, thanks.