VCE General & Further Maths Question Thread!

[Yacoubb]

Hello, I have a few questions:

1. Number Patterns
i) For the difference equation tn+1 = 2tn - 1, if t4=5, then t3=       (my answer was 5, just unsure whether it is 1)

t4 = 2t3 - 1
5 = 2t3 - 1
(5+1)/2 = t3
t3 = 3.

[lala1911]

Oh thanks, lol wow I just realised that I did 2-1 so it was 5 = 1-t3 wasnt paying attention.. forgot it was 2 x t3  not 2 + t3

thanks

[Cort]

Is there a reason why the answer's E instead of A? Is it because Adjacency matrixes count degrees? I thought it was only for edges.

[Damoz.G]

Is there a reason why the answer's E instead of A? Is it because Adjacency matrixes count degrees? I thought it was only for edges.

Loops count as 2, not 1. It's because you can go clockwise (which counts as one), and anti-clockwise (which also counts as one). But I remember my teacher last year saying something about Loops counting as 1. =/ Looking at the font, it I'm guessing its a past VCAA Exam question - what year is it from?

[Cort]

Loops count as 2, not 1. It's because you can go clockwise (which counts as one), and anti-clockwise (which also counts as one). But I remember my teacher last year saying something about Loops counting as 1. =/ Looking at the font, it I'm guessing its a past VCAA Exam question - what year is it from?

Great, now I feel mentally challenged. It's from Kilbaha 2011 exam 1.

[Damoz.G]

Great, now I feel mentally challenged. It's from Kilbaha 2011 exam 1.

Sorry. I'll try and find out more and get back to you. I'll ask my Further teacher from last year and see how it worked.

[yazza]

Can anyone take me through question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf

and can someone show me how shelley was right in question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007furmath1.pdf

[KevinooBz]

Can anyone take me through question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf

and can someone show me how shelley was right in question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007furmath1.pdf

Spoiler

You'll need to calculate the height of a triangle with the length 4m (the pole) given, and the base which is the midpoint of MN to T. So firstly, you have all the lengths of the triangle so you use the cosine rule to find the angle you want. In this case, you want angle NMT, so cos(NMT)=6^2 + 4^2 - 5^2 / 2 x 6 x 4. NMT = cos^-1(9/16) = 55.7711. Now you can work out the length of T to the midpoint of MN. sin(55.7711)= x/4. x= 4sin(55.7711)= 3.3072. Last step is finding the height, so you can use Pythagoras' theorem. sqrt(4^2 - (3.3072)^2)= 2.25 = 2.3
With the next question, hopefully you did the diagram correctly. The length of 1/2NP is given by cos(35) = x/4 -> x=4cos(35) -> 1/2NP = 4cos(35). NP is 2 times 1/2NP, so you get 2 x 4 x cos(35). If you need a diagram for both questions, I could make one later if you can't make sense of the numbers.

[lala1911]

A square pyramid has a volume of 25m^3 (with a height of 3m).
The square pyramid is filled with foam insulation to a depth of one metre.
What percentage of the original roof space is now filled with foam insulation? Write your answer correct to the nearest whole number.

Thank you
edit; height is actually 3m ._.

[Stick]

This is a similar figures question. The second pyramid is the entire pyramid minus the foamed volume. Once you see this it is a routine question. These are quite common to keep practicing them.

[lala1911]

Hi thank you, can you please guide me through it I've never seen one of these questions before o.O

[#J.Procrastinator]

A square pyramid has a volume of 25m^3 (with a height of 3m).
The square pyramid is filled with foam insulation to a depth of one metre.
What percentage of the original roof space is now filled with foam insulation? Write your answer correct to the nearest whole number.

Thank you
edit; height is actually 3m ._.

Firstly, find the length of one side of the base (Use 25m^3):

Volume of square base pyramid is 1/3 l^2 times its height: 1/3 x l^2 x 3 = 25
                                                                                              l^2 = 25
                                                                                              length = 5 metres

Now, use ratios to find the length of one side, where the foam reaches 1 metre:       Small : Large       Small : Large
                                                                                                                  length ratio:   x     :    5      =     2     :    3
                                                                                                                                                x/5        =        2/3
                                                                                                                                                    x = 2/3 x 5
                                                                                                                                                    x = 10/3 (leave this as a fraction for more accurate results)


Now find the volume of the smaller square base pyramid on top. Because the foam reaches 1 metre, the height of the top pyramid is 3-1= 2 metres. Use this to find its volume: V= 1/3 x (10/3)^2 x 2 = 7.4 metres^3 approx.

From the initial 25 m^3, take away the 7.4m^3 to get the volume of the bottom half of the pyramid (which is what you want- with the foam insulation):  25-7.4= 17.6 metres cubed


Finally, put this value over the original volume and multiply by 100 to get the volume that the roof space is filled with insulation. That is,

17.6/ 25 x 100= 70.4%

BUT WRITE ANSWER TO THE NEAREST WHOLE NUMBER. Hence, 70% ! Hope this is correct
                                                                                                                                                 
                                       

[Stick]

I'm on my iPad right now so this isn't going to work too well, but I'll try anyway.

So you have a pyramid of height 3m and this "smaller" pyramid of height 2m. That gives you a k value of 2/3. Cube that (for volume) and you'll get 8/27.

So 8/27 of the pyramid is not filled up with foam. That means that 19/27 of the pyramid has been filled with foam. (19/27)*100 = 70% to the nearest whole number.

Maybe you'll see this a bit better with a diagram too. I hope this helps, and I'm sorry that my help has been a bit limited.

[lala1911]

I appreciate your post, I just found out a solution on the VCAA website though, still thx.

[Cort]

quick question: Are Itute practice exams meant to be a kick in the face, similar to the Kilbaha ones?
Another one: Is it best to revisit some previously done exams, or best if you find/do other ones and struggle with them?