2012 Year 9 &10 Mathematics Marathon (3 Viewers)
- Thread starter TerenceM
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Re: 2012 Year 9 &10 Mathematics Marathon
Here is one of the last questions in my yearly, have fun!
Here is one of the last questions in my yearly, have fun!
Re: 2012 Year 9 &10 Mathematics Marathon
So, back from table tennis training. What I have gathered from this maths marathon thread: If ymcaec really is a year 10 student, then the person is quite impressive.
So, back from table tennis training. What I have gathered from this maths marathon thread: If ymcaec really is a year 10 student, then the person is quite impressive.
Re: 2012 Year 9 &10 Mathematics Marathon
Will do, gimme a few minutes. I'm quite a novice at LaTeXing and I take a long time to do that. The typing is going to consume most of my time.agreed
(please do my question *hint hint*)
Re: 2012 Year 9 &10 Mathematics Marathon
\\$\angle$ OBC = 30$^{\circ}$ (half of 60$^{\circ}$)\\\\sin 30$^{\circ} = \frac{OC}{OB}\\\frac{1}{2} = \frac{OC}{OB}\\ \therefore$ OB = $2r$ (given OC = r)\\\\ii. In $ \triangle $ ADB:\\$\angle$ ADB = 60$^{\circ}$ (angle in equilateral triangle) \\tan 60 = $\frac{AB}{AD}$\\tan 60 = $\frac{r+2r}{AD}\\$tan 60 = $\frac{3r}{AD}\\ \therefore AD = \frac{3r}{tan 60}\\ AD = r\sqrt{3})
hate these kinds of questions & latex -.-Here is one of the last questions in my yearly, have fun!
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Re: 2012 Year 9 &10 Mathematics Marathon
Then: We are given that
Edit: Haha, my typing speed is godly to ymcaec.
Obviously for c)i) All it requires is the use of sine rule:Here is one of the last questions in my yearly, have fun!
Then: We are given that
Edit: Haha, my typing speed is godly to ymcaec.
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Re: 2012 Year 9 &10 Mathematics Marathon
Just like any other question involving 3D shapes :/
That question hurts my brain.Here is one of the last questions in my yearly, have fun!
Just like any other question involving 3D shapes :/
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Re: 2012 Year 9 &10 Mathematics Marathon
For c)iii) You had to simply express the volume of the sphere over the cone. This was extremely painful to type. I probably typed it wrong somewhere.
^2 ~* ~ 3r}{3}} )
Eventually, you'll get:
For c)iii) You had to simply express the volume of the sphere over the cone. This was extremely painful to type. I probably typed it wrong somewhere.
Eventually, you'll get:
Re: 2012 Year 9 &10 Mathematics Marathon
I know that feel, it was already annoying to write all of that in exam conditions let alone latexing lol..For c)iii) You had to simply express the volume of the sphere over the cone. This was extremely painful to type. I probably typed it wrong somewhere.
Eventually, you'll get:
Re: 2012 Year 9 &10 Mathematics Marathon
For c)iv) There is no way in hell i'm going to latex my working out. Although I can say that all you have to do is find the ratio of the volume of the cone inside the sphere. Then you'll get your answer and compare the ratios of the two. The one which is larger, means that more space is covered within that volume. I believe the sphere inside the cone occupies more space.
For c)iv) There is no way in hell i'm going to latex my working out. Although I can say that all you have to do is find the ratio of the volume of the cone inside the sphere. Then you'll get your answer and compare the ratios of the two. The one which is larger, means that more space is covered within that volume. I believe the sphere inside the cone occupies more space.
Re: 2012 Year 9 &10 Mathematics Marathon
What I have found, ~75% of the time I took to answer your Qs came from the latexing.
Re: 2012 Year 9 &10 Mathematics Marathon
Here are the actual solutions for part iv. if anyone wants a look
Correct! Sorry for the Latex torture lol
Here are the actual solutions for part iv. if anyone wants a look
Re: 2012 Year 9 &10 Mathematics Marathon
Thus you just see which one occupied more space. Good question by the way, it actually asked for people to utilise more then simply geometrical applications.
Edit: Here's a question I personally liked when I did it back in year 9. It can be quite easy if you think a little outside the box:
A point P lies inside a square ABCD of side 120. Let F be a point on CD so that PF is perpendicular to CD. P is equidistant from A, B, F. Find PA.
Yeah, basically
Edit: Here's a question I personally liked when I did it back in year 9. It can be quite easy if you think a little outside the box:
A point P lies inside a square ABCD of side 120. Let F be a point on CD so that PF is perpendicular to CD. P is equidistant from A, B, F. Find PA.
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