2012 Year 9 &10 Mathematics Marathon

[Triage]

Who here would like to do a Spiral exam?

me

[Fawun]

Who here would like to do a Spiral exam?

sup

[Demento1]

There are still infinite solutions for x

Let's make it between 0 and 360 degrees then?

Water after 5 hours
=800x5
=4000L

let a be height/depth
Volume of diving pool
=6x4xa
=24a m^3
=24000a L

equate: 24000a = 4000
a= 1/6 m

Nice work.

[kazemagic]

Here's another one:
Peter stands due south of a pole. Sam stands 10m due east of Peter. The angle of elevations of Peter and Sam to the top of the pole is 25(degrees) and 15(degrees) respectively. Find the height of the Pole.

[kev-kun]

Here's another one:
Peter stands due south of a pole. Sam stands 10m due east of Peter. The angle of elevations of Peter and Sam to the top of the pole is 25(degrees) and 15(degrees) respectively. Find the height of the Pole.

3.65 metres?

[kazemagic]

3.65 metres?

o.O I got 3.27 for that one. How did you do it?

[Demento1]

o.O I got 3.27 for that one. How did you do it?

Sorry that I didn't see this Q earlier. After about 3/4 of a page of working, I had 3.27 metres. I treated the length of P to the pole as 7.02 (2 d.p.).

[kev-kun]

o.O I got 3.27 for that one. How did you do it?

Lol probably because I used dp's too early == yeah did it again got the same

[kat-]

I feel like an idiot, can't get my head around this one. drew a 3D diagram and everything

[Demento1]

I feel like an idiot, can't get my head around this one. drew a 3D diagram and everything

Nah, don't worry too much about it. Never get thrown off by a question simply because it seems new to you. Make an effort to interpret it. If it doesn't hit you, take a break, have fun and relax and get back to the question once your mind is refreshed. Often, the human mind takes longer to comprehend things at times so it's perfectly normal not to get it the first time around.

When you do problem solving, think this: 'I have all this given information and thus I will record it but what do I need?'

[Carrotsticks]

Show that the sum of the two roots of any quadratic ax^2 +bx+c is -b/a.

[Demento1]

Show that the sum of the two roots of any quadratic ax^2 +bx+c is -b/a.

My attempt to type it all out on LaTeX. It would be quite tedious typing up the quadratic equation but I managed.



Add the 2 roots together.

[kat-]

damn beat me to it

[maths_genius]

An isosceles triangle has a height that is half the length of its base. If the area of the triangle is 36m^2, what is the perimeter?

[Fawun]

An isosceles triangle has a height that is half the length of its base. If the area of the triangle is 36m^2, what is the perimeter?

is the perimeter somewhere around 29m? because that's what I got. I'll post up my working out once I know if I got my answer right or not.

[maths_genius]

is the perimeter somewhere around 29m? because that's what I got. I'll post up my working out once I know if I got my answer right or not.

Yep

[Demento1]

is the perimeter somewhere around 29m? because that's what I got. I'll post up my working out once I know if I got my answer right or not.

You are correct. Was this your working out?

Let x = height of triangle, hence 2x = base of triangle

By triangle formula:







Reject - 6.

Now by pythagorean method on a right angle triangle, let y = hypotenuse:







Therefore, perimeter =

[maths_genius]

You are correct. Was this your working out?

Let x = height of triangle, hence 2x = base of triangle

By triangle formula:







Reject - 6.

Now by pythagorean method on a right angle triangle, let y = hypotenuse:







Therefore, perimeter =

Correct This one is a really hard question - actually from an hsc paper (Question 10)

Untitled.jpg

[twinklegal19]

Correct This one is a really hard question - actually from an hsc paper (Question 10)

Untitled.jpg

I think this is sort of a proof for the "acute angle between two lines" formula in 3U, nice question

hint:

[Demento1]

Correct This one is a really hard question - actually from an hsc paper (Question 10)

Untitled.jpg

For i)

OQ = OP (radii of circle)

Therefore, triangle OPQ is isosceles.



(angle subtended at the centre is twice the angle subtended at the circumference by the same arc)

[enoilgam]

Here is one I was doing the other day with a student - it isnt the hardest question but its definitely an interesting one (it had me stumped for a bit).

"In my money box, I have only $1 and $2 coins. I have 240 coins in total worth $318. How many $2 coins do I have ?"

[twinklegal19]

Here is one I was doing the other day with a student - it isnt the hardest question but its definitely an interesting one (it had me stumped for a bit).

"In my money box, I have only $1 and $2 coins. I have 240 coins in total worth $318. How many $2 coins do I have ?"

Ah, I remember those questions. I was so stumped when I came across them in the primary school maths olympiads and the selective test

However once I learnt the beauty of algebra and solving simultaneously, it made everything so much clearer haha

[Demento1]

Here is one I was doing the other day with a student - it isnt the hardest question but its definitely an interesting one (it had me stumped for a bit).

"In my money box, I have only $1 and $2 coins. I have 240 coins in total worth $318. How many $2 coins do I have ?"

Does somebody capable want to do do this question? I have an answer for it but I will let others answer it instead of me for a while.

[Demento1]

The circle paper (almost forgot about it)

For ii)

Now,

Apply sine rule:





I'm not quite sure if this is correct or whether I can continue to simplify. Worth a shot answering.

[twinklegal19]

The circle paper (almost forgot about it)

For ii)

Now,

Apply sine rule:





I'm not quite sure if this is correct or whether I can continue to simplify. Worth a shot answering.

phew, at least you didn't simplify it into 2!

if you want to know,



although this is a 3U shortcut, I highly doubt that it is actually needed

maybe try a slightly different approach?