Okay, here it is! The winner gets to post the next set of ten questions. If we have more than one winner, we'll have a lucky draw and then see who wins. Questions must be mathematical in nature (can be qualitative or quantitative), and they can be as easy as arithmetic to as hard as differential equations!? It's a good thing if they're hard (uni-level or something)...People like me will probably learn something new in Maths, and will make an effort to get that question right! :razz: To make things fair, let's make this look like a typical Maths examination. Harder questions requiring complex diagrams/graphs (:twisted:) or working can carry more points.

For instance... Find the area of a square with a perimeter of 36 cm. (2 points)

Perimeter = 4l
36 = 4l
l = 36/4 = 9 cm (1 point)

Area of a square = l^2 = 9^2 = 81 cm^2 (1 point; no points if cm^2 omitted)

Questions may be fill-in-the-blank, true/false, multiple-choice or direct in nature. Working must be shown for every question, unless it's as easy as 1+1 or the like. Proper use of parentheses/brackets is NECESSARY.The number of points per quiz can vary from as little as 10, to as much as 100 (or even more!). But more time should be given for longer quizzes containing difficult questions, maybe a week and a half or two weeks. The number of points per question are an indication of how much working should be shown. Note: This is NOT a weekly Brain Teasers quiz! But, of course, questions constructed by your cool encephalon which show how Maths can be used in real life, or questions you'll have to answer to solve a mystery on a spaceship, for instance, are encouraged! :razz: That means you CAN start with a story... and the questions can be part of your cool mathematical adventure!

Since this is my first Maths quiz, let's keep it sweet and simple.

Q1) What's the area of a triangle with base 6 cm, perpendicular height 8 cm and slant height 10 cm? (1 point)

Q2) What's LXIV - XXIII, in Roman numerals? (1 point)

Q3) A minor arc BC of a circle subtends an angle of 35 degrees at the centre of the circle. What is the size of the angle the same arc subtends on a point on the circumference of the circle? (1 point)

Q4) What is a reflex angle? (1 point)

Q5) In this popular online party game called iSketch, the first person to guess the word within a time limit gets 10 points. The second person gets 9 points. The third gets 8 points, and so on... The sixth person gets 5 points, and every following person gets 5 points. What is the probability that I get 5 points for correctly guessing a word out of time, if I'm the seventh person to guess? (1 point)

Q6) What does the line x = 3 look like in the x-y plane? a) Vertical b) Horizontal c) Diagonal d) x = 3 cannot be a line; it's just a point. (1 point)

Q7) Write the number that comes before 1.00 * 10^6, in WORDS. (1 point)

Q8) How many lines of symmetry does a parallelogram have (A normal parallelogram, NOT a square, rectangle or a rhombus)? (1 point)

Q9) What's 1 - 1 + 1 * 1 / 1 + 1 - 1 * 1 + 1 / 1? (2 points)

Q10) What's the time when 60 minutes after 11:00 pm have elapsed? (1 point)

Total points for this quiz: 11
Last date/time for submission of entries: 3:14 pm GMT, 5th January, 2009, Monday

I hope I've made all the rules clear. However, feel free to ask further questions regarding the quiz rules, or any questions you didn't understand (after the week's quiz is over... :twisted:, unless there's a grammatical/mathematical error, of course! :razz:)

EDIT: Only ONE entry may be submitted. If you realise you've typoed or given an incorrect answer later, your revised entry will NOT be accepted. So be careful... Maths teaches you how to be observant and careful!

If you make a quiz with uni-level questions, or the like... and many people aren't satisfied with it (because it's out of their current Maths expertise), you can have two alternatives for the same question. One can be a high-school level difficult question, and the other can be a uni-level question. Those who are capable of doing the uni-level question (like Sparrow, Saff, tortoise bro, bb, jenni?...) must attempt it; the others can attempt the high-school level question. Both questions must carry the same number of points, and be more or less of the same difficulty.

One question can have several sub-questions. But the sub-questions must not belong to completely different topics. A question cannot have a sub-question on both trigonometry, and then, say, compound interest. However, if the first sub-question is about finding the missing length of a triangle, the second sub-question can be about finding other missing lengths. The following sub-questions can be about finding the area of the triangle if it were to be enlarged by a scale factor of 2, and the matrix which represents this transformation, for instance.

Another thing. If you're planning to copy the questions off your Maths textbook, a Maths quiz book, an exam paper etc., try to give citations, for copyright reasons. You may do this after the week's quiz is over to prevent cheating.

************************************************** **************************************
Let's begin this weekly mathematical trip on iSketchForum, and let's make a sincere effort to keep that candle called 'Maths' glowing brightly in our minds, hearts and souls for ever. :smile::biggrin::razz::smile::biggrin:
************************************************** **************************************

Hehe great idea Mathsy! I like your questions too ;p

uni level. who said anything bout having to do uni level probs XD i have like...3 more years before i get into uni or whatevs the equivalent over here.....
/me attempts

but if this gives me a headache im giving up :P

:cry::cry::cry::cry::cry: (I'm not in uni yet!)

awww
/me gives mathsies a hug
dont cryyyyyy :) i'll work on the problems XD once i remember how to use that math thing in word XD


its a lovely competition :D and btw ;) i actually can do some uni math XD i just dont like to brag bout it on here..... since i've got the rep of someone who doesnt have a brain according to sparrowhead up there :P

once i remember how to use that math thing in word XD


i actually can do some uni math XD i just dont like to brag bout it on here.....

Ooo0o0Ooo0Oo0o00Oo0Ooo00oo0oo...! WOW! That's COOL, jenni! :biggrin::biggrin::biggrin: I'd LOVE to see you do uni maths!!! :biggrin::biggrin::biggrin: And what MS-WORD thing are you talking about? OO00ooOO0o0OO000o0o0O0OOoo0OOoo... :?::?::?:

Hmm... I've got an idea. Just in case there's a quiz with uni-level questions, or the like... and many people aren't very satisfied with it, I can have two alternatives for the same question. One can be a high-school level difficult question, and the other can be a uni-level question. Those who are capable of doing the uni-level question (like Sparrow, Saff, db1986, bb, YOU... :razz:) must attempt it; the others can attempt the high-school level question. Isn't that a good way around it?

-_- i didnt say i was good at it. i just know a bit....plus my brother's old math stuff is left around my room.

Good! No probs...! That 'bit' is enough. However, if the question is out of your 'bit' of uni-Maths expertise, you can always learn something new and attempt the question, or opt for the alternative! :razz:

Those who are capable of doing the uni-level question (like Sparrow, Saff, db1986, bb, YOU... :razz:)
I can do Uni-level math? Hmmm, you learn someting new about yourself all the time :P

Nice idea for a thread btw.

I like this idea, it's similar to the iSketch Weekly Quiz (http://www.isketchforum.net/isketch-weekly-quiz-t1518.html).

For question 9...

Q9) What's 1 - 1 + 1 * 1 / 1 + 1 - 1 * 1 + 1 / 1? (2 points)

... does BODMAS apply? Or even BIDMAS? (They are very slightly different)

Working must be shown for every question, unless it's as easy as 1+1 or the like. Proper use of parentheses/brackets is NECESSARY.


Any chance you can alter that rule? Maths is more fun when done on top of the head. Besides, the word "easy" is relative.

And when working out on paper, there is always a chance of...
http://i405.photobucket.com/albums/pp135/Alessadri/image004.jpg

:eek::eek::eek: Definitely a thread I will not be participating in!!! :eek::eek::eek:

lol nah Maths is more fun when you work it out on paper. If you're doing things on top of your head, it is most likely arithmetic - what an accountant does at work! To do the more fun things in Maths - differential equations, calculus, trigonometry, vectors etc., you require paper... and a pen that refuses to get you hanged on a square root symbol. :biggrin::razz: LOL bb, i've seen that one b4, and I simply love it. LOL Don't worry... The question won't get thatttt complex (or will it? :twisted::twisted:)! Yeah, the word "easy" is relative. However, note that the number of points is a good indication of how much work is required.
For instance, a question worth a point asking you to find the area of a square measuring 2 cm on a side doesn't require you to show which formula you used to get the answer. An answer of 4 cm^2 is suffice to give you the point. If it was worth two points, however, you'd have to show your work.
I hope that clears it!

I like the idea of subject specific quizes :)
Even if I haven't heard about math in about... 6 years now... wow... yep... heh... i'll try to answer the easy ones to keep my brain young ;)

Once my question has been answered I can submit my answer.. just about :P it's interesting how much you forget when you don't use it... like I'd forgotten about circle theorems etc. And the parallelogram question confused me since I thought that it always ended up being one of those.. but yis :D
Basically it reminded me of all the old times in maths :D It's all nice maths.. :) I miss nice maths. >.>

theres a parallelogram question? ...hm....i should prob go see what i was doing XD :P
and phooey, i was showing my work on all those questions....adding in little shapess and picturessss XD haha :P oh wells, they look purty anyways :D i should color the shapes...

/me wanders off the finish the quiz

I forgot everything about circles and archs and whatever else... I hope I win some cookies for playing anyway :D

arcs* :razz:

Thanks a lottt, everyone! It's nice to see everybody play! :biggrin:

um,...is it possible to attach a word document to pms?

I think you can't directly.. you could try uploading the word document somehow and putting a link on it, or asking for ILMs email and emailing it, or just printscreen the whole lot and upload that?

But I'm not sure, maybe someone else know for sure if you can or can't :P

For small files, I would imagine that PMing a link to the screenshot would be the easiest way of accomplishing that.

For larger ones, e-mailing would be the best bet in my opinion.

OK, It's been a few years *cough*decades*cough* since I did this sort of stuff. But I'll give it a go. But I'm telling you, Maths - one LOLZ at me, and I'm out! :embarrassed:

Aw Saff...

OK one more question remains... Should I really have to use a piece of paper for the 5th one?

Edit : Er... I guess not.

Okay, I'll try not to laugh... Although I'm smiling... :smile:

Yeah, I don't mind. E-mail/PM... Whatever you find convenient. Some questions (You know of which sort... :twisted:) might have to be e-mailed rather than PMed. You can get my email from my profile. :smile:

EDIT: Oh, I guess you can't...? It's me07me07@hotmail.com

Yeah I got confused with question 5, I pm'd mathsie about it and he gave me it worded better... I think it's worded badly, but if you think about it hard enough you can understand what it means.

I am a little confused about question 5 too, although I've already sent my entry. I hope you see my logic Mathsy and will award me points for that, even if I don't get the correct answer :rolleyes::embarrassed:

I hope my addition is correct, that always fails me in exams. Not usually the hard stuff that we get taught lets me down, just simple addition every time :s

* db1986 thought that 1 + 0.7 = 2.7 :embarrassed:

Hmmm
Reading people's responses, I reckon I'm good for maybe 3/10 correct so far ^^

Okey I'm ALSO confused with question 5 (surprise surprise)
Is this assuming each player has a 50/50 chance of getting the answer correct each time they guess? I'm pretty sure I'm reading this question all wrong -_-

I actually threw out all my maths books and stuff today as well...
I dropped maths for a reason!!

ZOMG... THREW OUT ALL YOUR MATHS BOOKS? HOW RUDE AND DISRESPECTFUL OF YOU!:eek::mad: :cry::cry:

WHY ON EARTH DID YOU DROP MATHS?!?!? :mad:

Oh well, sorry if the iSketch question has caused some problems... Well, almost everyone has gotten it correct...!

Well... I deliberately worded it that way so that you would give an incorrect answer. :twisted::twisted: OKAY, OKAY, down everybody... down. :razz::twisted:

Fine... It's like this. You guess a word, but you're out of time, and you're the seventh person to guess the word correctly.

Is that clear now? :razz:

Ohhhh.. I see.. Ya know it woulda bin better if... hehe o well

/me goes to finish the quiz

PS. Ya might wanna delete the first of those posts as you repeat yourself anyway ^^ :)

Deebs you've got me confused now - I don't think 0.7 came into any of my answers!

Oh no, that happened in one of my exams, not in this quiz :P

I know for a fact I've got Q5 wrong lol.

Lol I hated add maths when I tried it.. xDDD
But I blame the teachers for that, so I can understand why you ripped out pages tasha :P

And It's getting close to the deadline :) I'm excited to see who's won :)

Well, if a question is worth a point, it means that only the final answer is required. Whether you show your working or not doesn't make a difference. You will not score any marks for the working, just the final answer, coz the question is worth only 1 point! Also, 1 point questions are meant to be EASY. Things you can work out in your head, or things that require simple reasoning.

830... Don't worry... I won't LOLZ...All I'll say is... The aim of creating this quiz is to make people aware of the importance of Maths and make them love and enjoy it.

And to be honest, I've just gone through your entries. I haven't really calculated anything so far, but you've all done very well. Some entries were simply amazing!

Thanks!

There are still 2 days left... so anyone who hasn't submitted yet can give this a try!

:biggrin:

Only a couple of hours left...!

Dun dun dunnnnnnnnnnn!!

/me waits for the results to find out she failed XD

Ooooooooooooh it's getting exciting! I know from Mathsy that I haven't got all the points :sad: It better not be method marks I've lost though cos I've argued for (and won) marks back from teachers in the past :twisted:

Haha Capt lol.

But there aren't any method marks in this edition, except for Q9 which is a 2-pointer.

(1-pointers are easy right? So only answers required :D )

Yes, bb, that's right. :biggrin:

And sparrow, let's see how you get your marks back, if any, from ME! :twisted::twisted:

Any results yet?

Edit: Oh you're viewing this page. I'm guessing you're doing that now :embarrassed::razz:

Answer Key (with Working/Explanations)

1) Area of triangle = ½ * base * perpendicular height
= ½ * 6 cm * 8 cm = 24 cm^2.

The slant height is not required for this question.
Moreover, this triangle is right-angled, as 10^2 = 6^2 + 8^2, or (slant height, or hypotenuse, in this case)^2 = (base)^2 + (perpendicular height)^2. It was pleasing to see a ‘pretty’ right triangle interpretation.
You will score a point for 24 cm^2. 24 or 24 cm does not score a point. An answer of ’24 cm^2’ without any working also scores the point.

2) LXIV – XXIII = (50 + 10 + 4) – (10 + 10 + 3) = 64 – 23 = 41.

41, in Roman numerals, is XLI. An answer of 41 scores no points. An answer of 41 and an incorrect Roman numeral for 41 scores no points. An answer of XLI scores a point.

3) The angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc on any point of the circumference of the circle.

If the angle at the centre is 35 degrees, then this is 2x. x, the angle at the circumference, is 35/2 = 17.5 degrees.

http://i452.photobucket.com/albums/qq249/ILoveMaths07/circle-1.jpg

4) This was a simple recall question, but it was disappointing to see several incorrect, or incomplete answers.

A reflex angle is an angle between 180 and 360 degrees (exclusive).
Or A reflex angle is an angle greater than 180 degrees but less than 360 degrees.

OR

A reflex angle is an angle between pi and 2 pi radians (exclusive).
A reflex angle is an angle greater than pi radians but less than 2 pi radians.

In inequality form:

180 degrees < Reflex angle < 360 degrees.
Pi radians < Reflex angle < 2 pi radians.

REJECTED answers:

180 < Reflex angle < 360
pi < Reflex angle < 2 pi
From 180 to 360 degrees, i.e. 180 degrees <= Reflex angle <= 360 degrees
From pi to 2 pi radians, i.e. pi radians <= Reflex angle <= 2 pi radians
An angle greater than 180 degrees or pi rad
From 181 to 359 degrees, i.e. 181 degrees <= Reflex angle <= 359 degrees

As you can see, answers without the unit ‘degrees’ or ‘radians’ have been rejected. 181 degrees <= Reflex angle <= 359 degrees has also been rejected as 180.5 degrees and 359.5 degrees, for instance, are also reflex angles.

5) Almost everyone got this correct. We all know that time and tide wait for none, and time never goes back. Guessing the word correctly, but out of time is not going to fetch you any points, leave alone the 5 points for being the seventh person to guess!

So, the probability of scoring 5 points, given that I’m the seventh person to guess, but out of time, is 0.

More mathematically, as one of you have written, P(Points = 5 | out of time ∩ 7th person to guess) = 0


6) In the x-y (2D) plane, x = 3 represents the equation of a whole vertical line at x = 3. This line has all its x-coordinates = 3. x = 3 could have represented a point if this were a 1D plane.

In an x-y plane, the line with equation x = constant is a vertical line parallel to the y-axis. Its gradient is undefined.
In an x-y plane, the line with equation y = constant is a horizontal line parallel to the x-axis. Its gradient is 0.

Y = mx + c is the standard equation for a straight line in 2D.
Putting m = 0 gives y = c, which is a horizontal line parallel to the x-axis.
If m is not defined, then the equation of the line is x = constant, which is a vertical line parallel to y-axis. Besides not having a gradient, such a line also does not have a y-intercept.

So, the answer is a) Vertical.

7) 1.00 * 10^6 = 1,000,000

That’s 1 million, or 10 lakhs.
The number (whole number) that comes before 1 million is 999, 999, which is Nine hundred and ninety-nine thousand nine hundred and ninety-nine.
OR
Nine lakh ninety-nine thousand nine hundred and ninety-nine.

8) This question received several incorrect answers, despite mentioning that the parallelogram is not a square, rectangle or a rhombus.

A parallelogram has no lines of symmetry. Folding a parallelogram along any of these lines will not produce two equal halves. Try it!

http://i452.photobucket.com/albums/qq249/ILoveMaths07/parallelogram.jpg

9) This is one question that seemed to have caused a lot of problems… for me! I’ve had to check this one very strictly as it’s not possible to differentiate the mathematical from the non-mathematical without your working. The reason it carried 2 points is because of the working!

1 - 1 + 1 * 1 / 1 + 1 - 1 * 1 + 1 / 1
= 1 – 1 + (1 * 1 / 1) + 1 – (1 * 1) + (1 / 1)
= 1 – 1 + 1 + 1 – 1 + 1
= 2.

This is what entrants were supposed to show. Some of you have done this correctly. However, some have simply stated ‘2’. In mathematics, the BODMAS/BIDMAS/PEDMAS (whatever you know it as) rule has to be followed for all sums. Coincidentally and unfortunately, for this sum, an answer of ‘2’ is obtained even WITHOUT using the BODMAS/BIDMAS/PEDMAS rule! Here’s the ‘false’ solution:

1 – 1 + 1 * 1 / 1 + 1 – 1 * 1 + 1 / 1
= 0 + 1 * 1 / 1 + 1 – 1 * 1 + 1 / 1
= 0 + 1 / 1 + 1 – 1 * 1 + 1 / 1
= 0 + 1 + 1 – 1 * 1 + 1 / 1
= 0 + 1 + 1 – 1 + 1 / 1
= 0 + 1 + 1 – 1 + 1
= 2.

So, an answer of 2 with correct working scores 2 points.
An answer of 2 with incorrect working scores no points.
An answer of simply ‘2’ scores no points.
Correct working but incorrect answer (probably due to copying down the question incorrectly) scores 1 point.

10) 1 hour after 11:00 pm is 12:00 am.

Acceptable answers: 24:00, 00:00, 12 am, midnight
Rejected answers: 12 pm, noon.

It was nice to see so many people participate in the first iSketchForum Weekly Maths Quiz. All of you have played well, but no one managed to score 11 points out of 11. The mean was 7.7 and standard deviation 1.9. Like I said… Not bad, pretty consistent scores! I hope there’s a much better response in the upcoming quizzes.


http://i452.photobucket.com/albums/qq249/ILoveMaths07/excelspreadsheet-1.jpg

Name Score Percentage PASS OR FAIL? Remarks
Capt_Sparrow 9 82% PASS Well done!
Ches 5 45% FAIL Stop underestimating yourself and work harder! Maths is not for those who give up!
db1986 9 82% PASS Excellent!
Sunny1 8 73% PASS Well done! You need to work a little harder.
830 3 27% FAIL You need to work hard and make mathematical guesses rather than putting In ?s
Saffron 7 64% PASS Not bad! You're going to host the Maths Round of the 'Dux of the Forum' competition, aren't you?
Alessadri 9 82% PASS Be more careful, bb!
Sorsie 8 73% PASS Well done! Be more careful next time!
Tasha 9 82% PASS Not bad, but learn to respect Maths
Medea. 9 82% PASS Very well done! Stop underestimating yourself!
jenni939706 9 82% PASS Very impressive!

Arithmetic mean 7.727272727
Standard deviation 1.911254186



Six people scored 9/11, so there had to be a lucky draw. Candidates were assigned numbers as follows:

Capt_Sparrow – 1
Db1986 – 2
Alessadri – 3
Tasha – 4
Medea. – 5
Jenni939706 - 6

My heart’s beating fast… but I’ve got to do this…

AND THE WINNER IS …

…

…

…



















































ALESSADRI! CONGRATULATIONS BB!

You may now host the next quiz. Go through the rules, make sure you assign an appropriate number of points for each question and make sure you have a comprehensive answer key with working and explanations after the quiz is over. All the best!

I think its a bit unfair to decide a winner just randomly.
May be..
There were 6 winners..
And the lucky one gets to do the next round.


SO MUCH work needed for 2 points ? :O
Lets face it, I got the circle one wrong :eek:

And I'll try and post my questions asap, definitely within this week.

Congrats Aless!

I got the 1 + 1 - 1 * 1 etc. one wrong, even though I got the answer correct :(

Yes, circle and reflex angle one wrong. Don't worry about the BODMAS/BIDMAS/PEDMAS one, bb. You got 2 points for that!

Yes, tortoise bro, BODMAS/BIDMAS/PEDMAS one wrong. You were so close... yet so far. I felt so bad! :sad::cry:

Hmm... It is a bit unfair, but there's nothing else I can do. Imagine each winner posting 1or 2 questions per quiz!

Then I am applying for Re-evaluation :P
(Thanks Sparrow for the idea)

4. 181º to 359º is wrong?

Yes, it's incorrect. Like I said, 180.5 degrees and 359.5 degrees are also reflex angles. Haven't you gone through the answer key...:?:

Touche lb. I missed that bit entirely >.< Its late in the night.

And yes, do let me know if I've incorrectly evaluated any of you (although I know I haven't)... Let me know if I've given you a point less, or a point MORE. :twisted::twisted:

Lolol we had long chats about the 1+1 one.. :P Heh heh

Well done all those who got 9/11.. I would have if I had done silly bodmas... >.>

Name Score Percentage PASS OR FAIL? Remarks
Capt_Sparrow 9 82% PASS Well done!
Ches 5 45% FAIL Stop underestimating yourself and work harder! Maths is not for those who give up!
db1986 9 82% PASS Excellent!
Sunny1 8 73% PASS Well done! You need to work a little harder.
830 3 27% FAIL You need to work hard and make mathematical guesses rather than putting In ?s
Saffron 7 64% PASS Not bad! You're going to host the Maths Round of the 'Dux of the Forum' competition, aren't you?
Alessadri 9 82% PASS Be more careful, bb!
Sorsie 8 73% PASS Well done! Be more careful next time!
Tasha 9 82% PASS Not bad, but learn to respect Maths
Medea. 9 82% PASS Very well done! Stop underestimating yourself!
jenni939706 9 82% PASS Very impressive!



:embarrassed: Hehe! I have a habit of doing that...

But very well done to all, everyone did so well! I bet Aless' quiz will be a little more tricky though -_- eeeep!

ah well :) fun fun fun fun XD lol, units.....and then...hm... that parallelogramythingymabob XD (i love my terminology ;)

/me skips around with db :D

Just missed out on this one. Hurry up Aless :D I want a maths quiz! :)

Awww. :) Joining in already :D Glad you're uhh settling in :D heh heh...

Heh. And I Don't want alessies quiz, I bet it's hard and will take up time I should be using to revise.. >.>

Yeah, I can bet it'll be hard/tricky, too. But I'll make sure I get 100%...! :twisted::twisted::twisted:

lol Sorsie... Then revise first, and do this quiz later?

parallelogramythingymabob... ROFLMAO :biggrin:

Congratulations to everyone, especially those 82%ers! :razz:
Ah Mathsy your mark scheme is so thorough I can't weed out any more marks! I think we have a teacher in the making :p

If Aless's quiz is full of calculus it might be easier for me than this one was.

Oh haha. I've been lurking the forum for a while before I joined >:)
Oh and ILM07, I've PM'ed you some answers (to the other quiz thingerbobber :))

Lol. Well I'm trying to do lots of revision... -____- I'm so silly for wasting my holidays. Tbh. I'll probs do it anyways whatever happens xDDDD :P Heh. Ahh.. Cramming is fun. -___-

I'm excited about this next quiz when it comes, but it'll probably distract me more.. I'm doing too much at one time atm Thus the cause of the flitting. I need to slow down xDDD one day maybe. xD Oooh 111 posts :)

hehe XD cool words ;) i'll try to come up with some new ones for the next quiz :D

and phooey, if its calc....hm...i'll prob do alright XD only know half of it though :P
/me twirls around ...

alessssss, where areee youuu? :P making a maths quiz cant take thatttt long for u aless :P

lol if he's cooking it up and adding his own secret ingredients, then it can take some time, jen! I'm soooo gonna pwn this quiz... hopefully! If there are alternatives, I'll try doing the difficult ones, and then pwning bb! That'll be sooo muchhh funnnnn :twisted::twisted:

mmhmmm....
/me thinks she'll do this just to see how well she can do against maths :P
hes the one with maths in the name XD and im the one that keeps getting called dumbbbbb

LOL ughh I'm scareddddd for this next quiz :rolleyes:


Oooh 111 posts :)

LOL if only it was 1,111 posts then it woulda bin much cooller, I could of documented it in my 11:11 journal.. No kidding I don't have an 11:11 journal!! Really I don't! :P

What's an 11:11 journal?

LMAO
/me tries to hide her angel obsession :embarrassed:

Ugh nothingggg
Haha this is so of topicccc but there's a "theory" about 1,111 angels.. and if you look at the clock a lot at 11:11 they're contacting you or something.. Hehe I was making a joke that I kept a journal of all my "11:11 experiences".. I don't!! :P Lolol

Oh back on topic.. Maths maths maths maths
Next quiz is just going to be SO much fun
I love maths yayaya
*Cough* Nottttttttttt :P

lol a 'lucky' journal? ROFLMAO... SSHHHHH. You can make notes of lots of cool incidents in today's date, medea! :razz:

Yeah, I'm scared of the next quiz, too. After all, it's bb. And he'll do anything to make sure his lb loses! :sad: You know how bbs are...

Anyway, I'm all prepared... Just waiting for the countdown... and the quiz to appear. I think we'll have to wait till tomorrow, though. It's 2:00 AM right now (in India), and he must be fast asleep. Moreover, he's not online on my Yahoo Messenger.

okis then XD go to sleep maths :P goodness XD 2am :P hmmm, i can wait for a bit XD just wondering how hard these maths problems are going to be....*sigh*
/me twirls around to pass the time

LOL... Yeah... It's hard to wait... But... My quote... "Patience is the key to success." We'll have to wait. It's nice to see everyone so excited about a MATHS QUIZ! :razz::biggrin: Looks like my magic worked! :razz:

mmhm XD what magic :P maybe its just that people are bored ;) <3 *hugs*

45%? lol... as I think I got 8 out of 10 correct answers, it must have been my working that let me down - I don't think I'd ever have considered showing working for a sum comprising only the number 1! And one of the ones I got wrong was because I didn't put it in Roman numerals. lol

There's also a theory that if you look at the clock a lot at Pi O'Clock (03:14 but 3:14 pm is also acceptable), you will have moments of mathematical and poetic inspiration. I think I'll make a journal of that like Meddy's "11:11 journal" that she SO has!
:twisted:

hehe XD ches, getting a better score at maths than an admin is fun :D
/me runs away before she gets in trouble for taunting the admin :P

mmhm sparrow :P i bet..that u already have one :D

Yeah, a PI journal for me! Count me in, too! :twisted:

Ches... Wait. I'll tell you which ones you got wrong, and why.

There's also a theory that if you look at the clock a lot at Pi O'Clock (03:14 but 3:14 pm is also acceptable), you will have moments of mathematical and poetic inspiration. I think I'll make a journal of that like Meddy's "11:11 journal" that she SO has!
:twisted:

Oooo!
Lol Pi o'clock.. that's so ugh... appropriate for this thread!! Haha :biggrin:
PS. I don't have an 11:11 journal!!! lololol

There's also a theory that if you look at the clock a lot at Pi O'Clock (03:14 but 3:14 pm is also acceptable), you will have moments of mathematical and poetic inspiration. I think I'll make a journal of that like Meddy's "11:11 journal" that she SO has!
:twisted:

I keep thinking I should do that with 12:34. It seems I never miss a day without seeing that time! And I'm not a clock-watcher... just notice that time. A lot.

lol, awww XD chessssssy :D (nvm. im not calling him that again..too girly .)
/me gives ches a hug :D
/me needs to fix her quote.....

What about CHEESY? I'll call him 'cheesy bro' or something... LOLZ :razz:

There's also a theory that if you look at the clock a lot at Pi O'Clock (03:14 but 3:14 pm is also acceptable), you will have moments of mathematical and poetic inspiration. I think I'll make a journal of that like Meddy's "11:11 journal" that she SO has!
:twisted:
I think you have to look at the clock pi amount of times to have moments of mathematical and poetic inspiration. :P

That irrational 0.1415926535897932384.. is going to be a pickle.

I think you have to look at the clock pi amount of times to have moments of mathematical and poetic inspiration. :P
I tried to open my eyes by 0.14 but an eyelash went inside one of them and I said, "NEVER AGAINN!"

* Capt_Sparrow considers this not to be spam because pi is of utmost importance in a mathematical thread

Well it's not spam because maybe to do well at this quiz you need to consider the magic of maths and it's wonderous special numbers (0,1,pi,e,i) Maybe if we all tried to be at pi angles whilst doing this quiz and wrote e words a second we would be inspired mathmatically with the right answers :D

/me follows on from Sorsie's example and vanishes in a dust of imagination

Saffron 7 64% PASS Not bad! You're going to host the Maths Round of the 'Dux of the Forum' competition, aren't you?


*cough*
I might just skip the maths round......
LOL not really, but the questions for the Comp are ......er....different. :biggrin:

lol, u guys are odd XD pi :P hm..pi day.....i wonder.........
/me hasnt met a math teacher yet ready to be smashed in the face with a pie on pi day :( ;)

oohhhh, sparrow, u gonna be a math teacher one day? :D

me me me me me me me me me me I'M ALLLLLL ready to be smashed in the face by pi^pi^pi^pi^pi^pi... cakes in the face on pi day. :razz:

oohhhh, sparrow, u gonna be a math teacher one day? :D
NOOOOOOOOOO!!!!!!!!!!!!!! :eek: Although I might be quite good at it :embarrassed:

lolz...! Sparrow = Maths teacher, OOoOOoOooOOoOoOOoo...

lolz...! Sparrow = Maths teacher, OOoOOoOooOOoOoOOoo...
Quiet Mathsy or I'll make you stand in the corner! :twisted:

LOL... OoooOOooOOooOOoo... You're already a teacher, then?!?!? :razz:

Clearly he's going to be one kickass chemical engineer!! Durrr

That involves loads of Maths, too...! :razz:

MATHS MATHS everywhere!!! Maths is the fuel of this cosmos...MUAAAHHAHAHAHAHAHAHAHAA! :razz: :biggrin:

Actually, chem eng can be summed up by:
What goes in, must come out

Much like feeding a baby really.

Much like feeding a baby really.
Or having one :rolleyes:

HAHA
/slap Capt, this is a G rated forum!

HAHA
/slap Capt, this is a G rated forum!
To clarify, I meant, you write a letter to Mr Stork, hang it outside your window and nine months later, a baby appears :smile:

ROFLMAO... HEY THIS IS MY MATHS THREAD!!!!! GO MAKE A BIOLOGY ONE OF YOUR OWN!! :mad::mad::mad:

MATHS MATHS everywhere!!! Maths is the fuel of this cosmos...MUAAAHHAHAHAHAHAHAHAHAA! :razz: :biggrin:
'Nuff said ;)

haha XD oddheads :P that was interesting to read :P

/me cant picture sparrow as a science teacher though...only math :0
;) phooey, where are aless' questions?

sometime this week, he said. Not today, though. He just logged off, and it's midnight in India now... :cry::cry::cry:

Sorry for the delay... I was initially planning one set where each question's answer will depend on the previous question's answer.. but anyway.. may be later.



There are 10 questions, five 1-pointers and five 2-pointers, so a total of 15 points. The questions with red numbers are tie-breaker questions. In case of a tie, the person who answered the most number of these red questions will be the winner. If there is still a tie, I will use a random generator to decide who is to set the next week's set. (Or I will try and think of some other idea, which is a bit less unfair.)

PM me the entries by Thursday 15th January 1200 Noon (UTC)

__________________________________________________ ______


1. Find f(2006) if f(i) = 1 + minimum [ f(i-1) , f(i-2) ] (if i > 2)
= 1 (if i = 1,2)
= 0 (otherwise) (1)

2. How many (x,y) pairs satisfy the equation : x + 3y = 100 , if x,y are positive integers. (1)

3. Find the number of rectangles in a M x N chessboard.(1)

4. One ball is chosen randomly from each of the three boxes shown below. What is the probability that they are all of the same color? (1)
http://i405.photobucket.com/albums/pp135/Alessadri/4.jpg


5.

http://i405.photobucket.com/albums/pp135/Alessadri/5.jpg
ABCD represents a 8cm x 6cm billiards board with holes only at the vertices of the rectangle ABCD. The rectangle is divided into 1cm x 1cm squares for convenience. From the point S, the ball is hit in the marked direction. Which hole will the ball fall into?. Assume that there is no loss of energy by the ball, and its size is negligible. (1)



6. If 4^(x+1) + 4^x = 3^(y+4) – 3^y, find the value of (x-y). x and y are positive integers. (2)
* a^b = a to the power b



7.
http://i405.photobucket.com/albums/pp135/Alessadri/7.jpg
Find the value of angle X (image not to scale) (2)



8. In an iSketch room with P people and R rounds, what is the maximum possible score that one can obtain? Skipping and “Away” status are not to be considered. (2)

9. Find the number of trailing zeroes in 49!
eg : 7! = 5040 has 1 trailing zero (2)

10. A race was held between the Rabbit and the Turtle. It was in their natural elements, covering a distance, say 2d. The Rabbit hops on land at 10m/s and the Turtle swims at 8m/s. At the instant the first person covers half the total distance, an air current blows, making the Rabbit slow down by 2m/s and the water flow helps the Turtle move faster by 2m/s. Who will win the race, and by what margin of time? (Express answer in terms of d) (2)

Woah, this looks intense! I'm gonna give it a go though. Also, great idea for a tie-breaker. A lot less random.

This looks brilliant :D When's the deadline?

That looks like great fun :D I think I will try this this weekend. Whens the deadline? Is it a week from now orr...?
[Slow again xDDD Ignore my deadline bit, sparrow already asked :P]


I think I can do most of the maths too, or should be able to do most of it :P

Ughh ohhh.. errmm O__O

This looks hard :S
Or maybe its just coz it's 5:30am right now and my eyes are sleepy.. Hmm!! Lolol

Oh and nice idea about the tie-breaker questions :)

I think I did something wrong :(


Can't wait to see the solutions!

oh phooey, this is hard. actually, havent really looked at it XD but looks hard :P hm.....i'll try. busy time for me now XD

OMG THIS IS HARD N FUNNN (loovveeee yaaaa bb!!!) OOoooOOooo... there's vectors, too! :biggrin::biggrin: and perm/combo...! :biggrin: uh oh. *sniff* AAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH! But I feel 1 and 2 marks are wayyyy too little for these complex probs...! :sad:

nah, I guess it's algebra, after all...No vectors... well, there are vectors (for another question)...but not really. I thought they're vectors coz of the bold letters...

Questions are easier than they appear.

uh huh. they always are.

Yeah, probably they are easy. I'll know when I actually sit down and do them... lol.
Never judge a book by its cover!

M X N 'chessboard'?

A rectangular chessboard?!? OOooOOOoOOoOooOoooOOOoo...Or did you mean M X M?

Well at least it isn't a 3d chessboard

Nice idea tgf.... may be next time... if I win...

Lol I was thinking of sneaking in fermat's last theorem as a bonus question just for ILM07

..............???????????????????????????????????? ?

This is painful. They're all painful :D

Lolol. I was trying to.. well not just me. Me and my maths boff friend. :D Well firstly he doesn't understand the first question, so I'm stuck on that one.. I'm trying to find someone who may help me with that.. Maybe my maths boff friends going to oxford... >.> Hmm... So yeah.. That stupid chessboard question. xD That's long. xD Well I bet there must be a quicker way to do it, but the way we started doing it was like.. long. Oh p.s. Is a square a rectangle?

phooeymabob.
/me sighs

iiiiiii might not submit anything for this one XD been getting headaches :) good luck though :D

.................................................. ..................................

Is a square a rectangle?

What do you think?


.................................................. ..................................

Next time you post a message in Morse Code, remember to add spaces in between the letters.
Well I tried.. See his hiss... shhhh... his sis is she... after which i lost count of the dots >.<

Haha nice evasion of a question. I'm thinking that some of these are easier than they seem.

Yeah dB most are.. one of my friends just had a look at them and said...
"Wow, you sure got a talent for complicating things!"

What do I think. I think no :P but my friend was like, aren't squares a special kind of rectangle..? Hmm. maybe I'll just look around and try and find the answer to the square rectangle thing. :P

Squares are rectangles, but I'm unsure if we have to count the number of squares for this question.

yeah. aless is evil.

lol hehehhehehee... yeah he evaded our questions... Do we have to count the squares?
And the first one has too many '=' signs. I don't get the question... It has a mini-algorithm too...! :cry::cry::cry:

coz u tore your maths books into pieces... and your handwriting + work showed that you were not interested at all... :razz:

lol don't worry... I can make out which ones of you are interested even if you type the answers...! :razz:

hehehehehe lol... That's what I could make out from your handwriting + work ... lol :razz:

yeah. aless is evil.
Yes Yes Yes :twisted: :twisted: :twisted:

lol hehehhehehee... yeah he evaded our questions... Do we have to count the squares?
And the first one has too many '=' signs. I don't get the question... It has a mini-algorithm too...!

To quote from wiki "In geometry, a rectangle is a quadrilateral where all four of its angles are congruent right angles."

And Q1 is not an algorithm.. the value of the function depends on the value of the variable...

Hmm... My maths skillz are not up to scratch :\
Or maybe I just can't get my head around all the over-complications..

/me gives this one a miss..

:) Right, I have 5 answers so far.. ish.. Some are iffy, very iffy. xD But I'm going on a few assumptions as I can't be bothered to follow them through if it's the complex answer... I may just enter 5 xD Heh heh. but I am slowly working at them :) Thank you for this challenge aless :) It's better in someways that it's harder as it makes you think.

Edit: Just got another... <3333 Excel xD

evil aless :( i thought u were nice!
/me runs off

jk XD too tired :P but im still not answering the questionsss. no time. plus exam review time...*sigh* :P

lol i'll do it...!

Right. I think I have got all the answers :D As I told you earlier :) I think time to pm them so I don't forget. xD

/me officially will not be participating in this one :(

but i wanna do the next one ^_^ maybe...depending on how long it takes me to study for exams...

AAHHHHH... I don't have time... I wanna participate in this one!!! I'm just v busy... If only bb could postpone the final date by the number of days late he put on this quiz...

I took nearly two days... (47 hours and 57 minutes..)

I am having a patchy connection.. so the answers will (hopefully) be up within a 48 hour delay.. which is 1200 UTC 17-01-09

OOooOOooOooOOoOOoOoo...

Awww.. I remembered the answers would be coming soon and I was very excited, but I don't mind waiting for them :) So yaay for extensions so more people can enter :)

AAHHHHHH This is toooo difficult... I don't think I'll be able 2 do it. I've only finished the billiards Q until now... :razz: I'm UNDER A LOT OF TENSIONNNN AND PRESSUUURRREEE AAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHHHHHHHHHHHHHH

Take them down one at a time. Now get back to work. :P

Yea cmon mathsy, you can do it bro!
(Besides if you fail.. that'll just be embarrassing for you XP I kid I kid.. relax hehe)

lol heh I have a lot of schoolwork 2 do also... I can do the probability one... The first one... snooker one, 49! trailing zeros one (using calcu :razz:), the tortoise/hare one mayb but me is 2 lazy 2 do that, x+3y = 100 one but i'm too lazy 2 do tht also... and maybe the M X N chessboard one... dunno abt the rest... :cry:

lol I can't do any of them. Don't panic!

AAAHHHHH I'm not like the restttt, Saffff! :cry::cry::cry:

:) If you take it nice and slow and work on each one as you go through them it's not too hard. You should look at it, try and do it, if you get stuck, move on then come back to it...

AAHHHH me just told bb me won't be able 2 do this... :cry::cry::cry: I told him I'll do the winner's quiz... :cry::cry::cry:

Well, Sorsie, I'm already tensed coz I have a lot of other work 2 do. My head isn't really working... and I'm in the mood of finishing everything FAST... FAST FAST FAST! I don't have the time to think, nor do I have time to actually count and do some longgg Qs like the x + 3y = 100 ones... and I don't want combinatorics to eat my head right now...! :cry::cry::cry:

Hmm... I suppose.. I think it's very busy at the moment for everyone.. Maybe you should just save the questions for later when you have time to work on them (I know the deadline will have gone, but atleast you would have had a chance to try them :) )

Sorry for the delay again.

Here are the answers :
( I did have a proper answer key, but as my methods are.. well unorthodox, for some questions I am posting excerpts from the solutions I received )

1. Find f(2006) if f(i) = 1 + minimum [ f(i-1) , f(i-2) ] (if i > 2)
= 1 (if i = 1,2)
= 0 (otherwise) (1)

This simply states that f(1)= 1 ; f(2) = 1;
f(3) = 1 + min [ f(1),f(2) ] = 1 + 1 = 2
f(4) = 1 + min [ f(2),f(3) ] = 1 + 1 = 2

We find that f(i) = i/2 rounded-up.
So f(2006) = 1003

2. How many (x,y) pairs satisfy the equation : x + 3y = 100 , if x,y are positive integers. (1)

x+3y=100
x = 100-3y
Considering x and y as positive integers, we have for every value of y between 1 to 33, there are equivalent values for x. So the answer is 33


3. Find the number of rectangles in a M x N chessboard.(1)

Every rectangle in the chess board is defined by two horizontal lines and two vertical lines. The total number of lines in each direction to chose from is equal to (M+1) and (N+1) respectively and we need to select two of these in each dimension. Therefore:
The total number of rectangles = [(M+1) Choose 2] x [(N+1) Choose 2)]
*submitted by marauders

4. One ball is chosen randomly from each of the three boxes shown below. What is the probability that they are all of the same color? (1)

P (all three of same colour) = P(all three are red) + P(all three are blue) + P (all three are green)
= (3/12)*(3/12)*(4/12) + (5/12)*(4/12)*(4/12) + (3/12)*(5/12)*(4/12)
= 1/9

5. The billiards board problem
http://i405.photobucket.com/albums/pp135/Alessadri/98412249hz1.jpg
The ball will not fall into any of the holes.
*submitted by tgfcoder

6. If 4^(x+1) + 4^x = 3^(y+4) – 3^y, find the value of (x-y). x and y are positive integers. (2)

4^(x+1) + 4^x = 3^(y+4) – 3^y
4^x (4 + 1) = 3^y (81-1)
4^x = 3^y * 16
4^(x-2) = 3^y
taking logarithms..
x = y(log 3 / log 4)+2
Integer solutions exist only if y=0. (x = 2)
However, considering x and y as positive integers, no solutions exist.

7. Triangle question :

As angle A is a right-angle, we can as well imagine a circle around ABC such that BC is the diameter.
BD = DC implies that D is the mid-point of the diameter, and hence the centre.
AD is also the radius and so AD = BD.
Since AB = AD, we obtain an equilateral ABD. So X = 60 degrees

8. In an iSketch room with P people and R rounds, what is the maximum possible score that one can obtain? Skipping and “Away” status are not to be considered. (2)

In the maximum case, each round gives you 10 points, and you get additional points during drawing.

So the score is 10R + (additional drawing points)

Drawing points :
No of drawing chances = ceiling[R/P]
Score obtained for a draw (in addition to the 10 points)
= min [(P-2) , 5 ] ( P-2 because it includes you and the first guesser )

So, ultimately.. Max Score = 10R + c[R/P]*min[(P-2),5]

9. Find the number of trailing zeroes in 49!

The zeroes are attributed to the factors of 5 and 2 among the numbers from 1-49. As 2s are abundant, lets consider the number of 5s.

5,10,15..45 will give 9 5s and 25 will have an extra 5. So 10 5s in all.As many trailing zeroes.

10. A race was held between the Rabbit and the Turtle. It was in their natural elements, covering a distance, say 2d. The Rabbit hops on land at 10m/s and the Turtle swims at 8m/s. At the instant the first person covers half the total distance, an air current blows, making the Rabbit slow down by 2m/s and the water flow helps the Turtle move faster by 2m/s. Who will win the race, and by what margin of time? (Express answer in terms of d) (2)

Breaking the journey up into 2 stages:
Stage 1
Time (rabbit) for first part of journey=d/10
Let the distance travelled by the turtle in this time be x- as the times are the same
Time(turtle)=x/8=d/10 therefore 10x=8d and x=0.8d
Stage 2
Time (rabbit)=d/8 (as rabbit has distance d left- and new speed is 8)
Time (turtle)=1.2d/10 (as turtle has distance 2d-0.8d left and new speed is 10)
Total Time (Rabbit)=d/10+ d/8=0.225d
Total Time (Turtle) =0.8d/8 + 1.2d/10=0.22d

Therefore Turtle wins by 0.225d-0.22d=0.005d seconds
*submitted by marauders


Results :
http://i405.photobucket.com/albums/pp135/Alessadri/1st.gifmarauders (13 points)
http://i405.photobucket.com/albums/pp135/Alessadri/2nd.giftgfcoder (12 points)
http://i405.photobucket.com/albums/pp135/Alessadri/3rd.gifIambic and Sorsie (10 points)

yayyy marauders gets to post the next set of Qs! Lucky me... Me read your post (Sorsie) before me could read bb's answers... Let's see if me/we can fill this page quickly so that me doesn't see bb's answers...



























































































Oh, but me saw the tortoise question methinks. me saw that tortoise won... did he? Me dunno... Okay, me won't look at the answers and will do them when me gets plenty of TIME AND PEACE. Then me will honestly send the answers to bb and see what me scores...



CONGRATS marauders! :biggrin:

Thanks for playing! :razz:

I see I see. :) I'm glad I got most of that right :D Well done Marauders and coddddeeeey :) And Iambic :)

Looking forward to the next one...^_^

EDIT: I'm glad mathsie :) Just don't look at it and jump to the bottom, I'm sure the answers you will see you could have guessed anyways. :)

Aw, I completely forgot about submitting this one, sorry Aless.
I would have only got 9 points though :(

Yes, me is leaping to the bottom... I just hope you keep posting like you did earlier, and bring this page to an end ASAP. :razz:

But me is still feeling guilty coz methinks me saw The tortoise won... for the last Q... :cry::cry: nyway doesn't matter... maybe he didn't who knws? tortoises r slow idiots, anyway... :twisted:

Yeah, can't wait for marauders' quiz...!

Hmmm... But what if someone posts something about one of the Qs... and me reads that...? :cry: SPOILER TAGS, PLEASE!

:) I think that will happen. Like I said Mathsy, any answers you may or may not have seen, would be easy enough to work out, I think for you anyways :)

And aww -pats db- Get ur maths on ;)

The tortoise won... tortoises r slow idiots, anyway...


Ahem.. the Turtle won, and they are decent swimmers as far as speed is concerned.

OOoOOoOOoOOooo... So the tortoise won just coz the wind was in his favour? idiotttt... anyway, don't give out answers bb :cry:. me will work it out for myself later. :razz:

Lololol. Ahh poor mathsie xDD

Turtles always win ;) Never forget that ;) xDD Tortoises are the slow ones :P

Yay congrats marauders! :razz:
Unlike Mastermind, I started the quiz but couldn't finish cos of time but hopefully will do in the next one! Get questioning mara ;p

Hi everyone : )- as I’m going to be overseas from the 23rd to the 1st of February and won’t be able to log onto the forums during this time, I’m giving everyone an extension. As you have two full weeks for these relatively simple questions, there will hopefully be a good number of entries (even with the other fun distractions). Please submit your worked solutions by:

3.14pm on Monday, 2nd February Western Australian Time :razz:

I *think* this is the equivalent to
7.14pm on Monday, 2nd February New Zealand Time
5.14pm on Monday 2nd February East Australian Time
11.44am on Monday 2nd February Indian Time
6.14am on Monday 2nd February UK Time
1.14am on Monday 2nd February Eastern US Time
10.14pm on Sunday 1st February Western US Time

Like the previous quiz, this one has 5 x questions worth 1 mark, and 5 x worth two marks so the maximum possible score is 15. Hope you have fun doing them and good luck! :)
__________________________________________________ ______________________

1. The numbers 2^2009 and 5^2009 are written out one after the other (in decimal notation). How many digits are written altogether? (2 marks)

2. Find the number of integers between 100 and 500 such that the sum of their digits is 10. (1 mark)

3. Three athletes Amy, Bridget and Chloe are preparing to take part in a pole vault competition.
At the same time some of the spectators are discussing their chances:
Spectator 1 : ‘I think Amy will be first’,
Spectator 2: ‘I am sure that Chloe will not be the last’,
Spectator 3 : Bridget will not take first place’.
After the competition it turned out that only one of the spectators was right, while the
other two were wrong. Where did Chloe finish? (explaining your reasoning) (1 mark)

4. You are given 25 coins of the same denomination, and are told that one of them is counterfeit and that it is lighter than the others. You have a pan balance which means you can put any number of coins on each side and the balance will tell you which side is heavier, but not how much heavier. Explain how to find the counterfeit coin by using at most 3 weighings on the pan balance. (2 marks)

5. What is the units digit of 1! + 2! + 3! + ... + 1986!? [3! means 1 × 2 × 3] (1 mark)

6. XYZ is a three-digit number. Given that XXXX + Y Y Y Y + ZZZZ = Y XXXZ, what is X + Y + Z? (1 mark)

7. Find the least possible value of the expression x^2 - 8xy + 19y^2 - 6y + 10. (2 marks)

8. Ella has 20 coins in her purse. They are 10c, 20c and 50c coins and the total value is $5. If she has more 50c coins than 20c coins, how many 10c coins does she have? (2 marks)

9. Susie has four children, one is a teenager (13 to 19 years old) and the product of their ages is 1848. How old is the teenager? (1 mark)

10. Two buses start travelling at the same time, but bus 1 travels from city A to city B while bus 2 travels from city B to city A using the same road/route. Both buses travel at constant speeds and they meet 7km from A before continuing in the same directions and speeds. After both buses reach their destinations (cities B and A respectively, possibly at different times), they immediately start travelling back along the same road and with the same speeds. If they meet again 4 km from B, find the distance between the cities A and B. (2 marks)

uh oh. This is worse than bb's... lol... :cry::cry::cry:

I'm sure it's similar in the sense that the answers aren't as hard as you think... :P but.. it takes a while to get there. :P Or not. xD Iono. I wont touch this bad boy ;) until after next week.. xD -hugs 2 week deadline-

LOLOLOL... I don't believe I'm behaving like this... Why is Maths getting hard for me? :cry: It's been a long time since I've done Maths... and a very long time since I've done any tricky puzzly Maths questions... :cry:

That's exactly it mathsies :P Some of these are more puzzley... So some parts are more logical, although all maths related.. :P

I don't think it's getting hard, u just have to work at it and haven't had the time :) And it's good if they're challenging :) It's good to have fun. :P

Hi everyone : )- as I’m going to be overseas from the 23rd to the 1st of February
All fun for some! :p

LOLOLOL... I don't believe I'm behaving like this... Why is Maths getting hard for me? :cry: It's been a long time since I've done Maths... and a very long time since I've done any tricky puzzly Maths questions... :cry:
Maybe you're over the hill :twisted:. But I have to say, these Q's are not like the typical exam questions so you have to actually think before answering them! :p

I don't know why I even bother viewing this thread anymore

All fun for some! :p
It's a family oriented trip and it's quite short, but I'm not complaining :razz:. Quite looking forward to it actually


Maybe you're over the hill :twisted:. But I have to say, these Q's are not like the typical exam questions so you have to actually think before answering them! :p
That's what I kind of aimed for- I tried not to make them too difficult (at least in the mathematical, even if not in the logical stakes) as I really didn't want to put people off

I don't know why I even bother viewing this thread anymore

Aww Saff :( They are much easier than you think- promise :). And as I just heard that you're extending the due date for the Dux of the Forum Comp (thanks so much */hug), hopefully you'll have a chance to look at them :). There's still a full 2 weeks left afterall

/me glares at maps
awww
/me kisses mapsies :D
sorry maps XD i'm going to be busy for the next week or so....cant really do any math stuff XD but lovely questions aless and mapsies ^_^ :D

This one looks fun (not that the others didn't)
And ooh, we have 2 whole weeks :D

Enjoy your trip mapfeatures :D

Wah this last minute attempt is doing my head in haha. well a couple of them are..

1. The numbers 2^2009 and 5^2009 are written out one after the other (in decimal notation). How many digits are written altogether? (2 marks)
http://i118.photobucket.com/albums/o118/naraysl/q1Answer.jpg


2. Find the number of integers between 100 and 500 such that the sum of their digits is 10. (1 mark)
Putting the numbers in blocks. We have 10 numbers with 1st digit being 1: 109,
118, 127,..., 190, then 9 with 1st digit being 2: 208, 217,..., 280, then 8 with 1st
digit being 3, and 7 with 1st digit being 4. The total number of integers is then 10
+ 9 + 8 + 7 = 34.



3. Three athletes Amy, Bridget and Chloe are preparing to take part in a pole vault competition.
At the same time some of the spectators are discussing their chances:
Spectator 1 : ‘I think Amy will be first’,
Spectator 2: ‘I am sure that Chloe will not be the last’,
Spectator 3 : Bridget will not take first place’.
After the competition it turned out that only one of the spectators was right, while the
other two were wrong. Where did Chloe finish? (explaining your reasoning) (1 mark)
There are three possible cases to consider:
Case 1. 1 is right, while 2 and 3 are wrong. Then Amy must be first, Chloe is last and
Bridget is first, impossible.
Case 2. 2 is right, while 1 and 3 are wrong. Then Chloe is not last, Amy is not first
and Bridget is first. Hence Chloe is second and Amy must be last. This case is possible.
Case 3. 3 is right, while 1 and 2 are wrong. Then Bridget is not first, Amy is not first and
Chloe is last, impossible.
Thus, only the second case is possible, so Chloe must have taken second place.



4. You are given 25 coins of the same denomination, and are told that one of them is counterfeit and that it is lighter than the others. You have a pan

balance which means you can put any number of coins on each side and the balance will tell you which side is heavier, but not how much heavier. Explain how

to find the counterfeit coin by using at most 3 weighings on the pan balance. (2 marks)

TRIAL ONE: Divide the coins into 3 groups, the first two groups containing 9 coins each, while the third group contains 7 coins. (Other divisions are

possible, e.g. 8+8+9.). Place the coins of group 1 on one pan of the pan balance and the coins of group 2 on the other pan. If the pans do not balance, the

counterfeit coin is in the lighter pan. If the pans balance, the
counterfeit coin is in the third group. In the latter case, take two coins from either group to get a group of 9 coins containing the counterfeit one. So,
with one weight trial we determine a group of 9 coins that contains the counterfeit coin.

TRIAL TWO: Divide the coins into three groups of 3 coins each (groups, 4, 5 and 6). Place e.g. the coins of group 4 on one of the pans of the pan ballance

and the coins of group 5 on the other pan. If the pans do not balance, the counterfeit coin is in the lighter pan. If the pans balance, the
counterfeit coin is in the third group. So we’ve determined a group of 3 coins that contains the counterfeit coin.

TRIAL THREE choose any two of these 3 coins and place them on the two pans. If the pans balance, the third coin is the counterfeit one; if not, then the

lighter coin is the counterfeit one.



5. What is the units digit of 1! + 2! + 3! + ... + 1986!? [3! means 1 × 2 × 3] (1 mark)
Since 5! and n! for all n > 5 are divisible by 10, the required units digit is the units digit of 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33. hence the answer

is 3.

6. XYZ is a three-digit number. Given that XXXX + Y Y Y Y + ZZZZ = Y XXXZ, what is X + Y + Z? (1 mark)
Adding 3 4-digits numbers together means that Y must be either 1 or 2, X+Y=10 and Y+Z+1=10 so Y+Z=9, using trial and error only Y=1 works so
X=8 Y=1, Z=9 hence X+Y+Z=18
Though db1986 pointed out that X=Y=Z=0 also fits this equation, 000 isn't a three digit number (though it is a three digit code) so this solution wasn't

required to gain the mark.

7. Find the least possible value of the expression x^2 - 8xy + 19y^2 - 6y + 10. (2 marks)
x^2 - 8xy + 19y^2 - 6y + 10 = x^2 - 8xy + 16y^2 + 3(y^2 - 2y + 1) + 7
=(x-4y)^2+3(y-1)^2+7
Each of the squared terms must equal at least 0 (in this case, when y=1 and x=4, so minimum value possible is therefore 7.

8. Ella has 20 coins in her purse. They are 10c, 20c and 50c coins and the total value is $5. If she has more 50c coins than 20c coins, how many 10c

coins does she have? (2 marks)
10x + 20y + 50z = 500
x + y + z = 20
x = 20-(y+z)
the first equation becomes
y + 4z = 30
For y,z integers and z > y. We get a solution of (y,z) = (2,7)
Ans = 20-(7+2) = 11 10c coins (submitted by Alessadri)

9. Susie has four children, one is a teenager (13 to 19 years old) and the product of their ages is 1848. How old is the teenager? (1 mark)
1848 = 2x2x2x3x7x11
Only teen factor possible is 2x7=14 or alternatively divide 1848 by each of 13, 14...right up into 19, and note that 14 is the only teen which divides to

give an integer result.

10. Two buses start travelling at the same time, but bus 1 travels from city A to city B while bus 2 travels from city B to city A using the same

road/route. Both buses travel at constant speeds and they meet 7km from A before continuing in the same directions and speeds. After both buses reach their

destinations (cities B and A respectively, possibly at different times), they immediately start travelling back along the same road and with the same

speeds. If they meet again 4 km from B, find the distance between the cities A and B. (2 marks)
http://i118.photobucket.com/albums/o118/naraysl/q10Answer.jpg
__________________________________________________ __________________________________________________ __________________________________________
RESULTS (with questions incorrect in brackets so that players can double check that I didn't award the incorrect number of marks to someone)

:embarrassed:

Alessadri-12/15 (q2 and 7)
db1986- 12/15 (q1 and 3)
Dean- 12/15 (q5 and 10)
tgfcoder -11/15 (q4 and 7)

A three-way tie! And you almost got different combinations of questions incorrect too xD
I was going to leave deciding who is declared the "winner/writer of the next quiz" to chance- but considering Alessadri wrote the previous quiz, and Dean

submitted a few mins after the deadline, I'll ask db to put up the next questions if this is ok with him? I was going to post that- in case of a tie, the

person who submits first would be the winner (but changed my mind in the end). Even using this rule though, db1986 is the winner as he sent his answers in

earlier than Alessadri and Dean.

Congratulations to db1986, Alessadri and Dean- and over to db1986 for the next set of questions :)

OK, I haven't forgotten about setting this week's questions, but what with the Valentine competition, 1 Vs. The Forum and uni work to be getting on with I haven't had much time to.
I now have some free time and the questions will appear here by tomorrow at the latest.

Mine were Not Late XD. I was sending them over to you on msn right on Pi:P

OK, here are this week's Maths questions. There are a total of 10 questions, where the maximum score is 20 marks.
Where appropriate, please show your working.
__________________________________________________ __________________________________________________ ___________________________________________

Q1. Calculate the result of the following equation. (1 mark)

...1 + 2 + 4 + 6 + 8 = ?
.....''''.3.'''.5..'''7.'''.9

Q2. Find the coordinates and determine the nature (maximum, minimum or point of inflexion) of the two turning points of the curve y = x³ - 6x² + 9x + 14. (2 marks)

Q3. Find the area of the largest circle that will fit inside a rectangle whose area is 144cm² and whose ratio of length to width is 9:4.
Give your answer in terms of π. (1 mark)

Q4. Mary has a normal 52-card deck of playing cards. She chooses 3 cards at random without replacing the card each time.
Calculate the probability that Mary receives:
....a. 3 diamonds (1 mark)
....b. 3 eights (1 mark)
....c. 1 eight, 1 six and 1 jack (1 mark)
Give your answers in the lowest fraction form.

Q5. Work out a formula for this set of numbers. (1 mark)

....x: .1..'''2..'''3..'''4..'''5..'''6..'''7..'''8
....y: -1..''0..'''3..'''8...15.''24.''35.''48

Q6a. Write down the value of the radius of the circle x² + y² = 2. (1 mark)
.................................................. ....................'.2.....4
....b. Find the two sets of coordinates where the line y = 2x - 4 intersects the circle x² + y² = 2. (2 marks)
.................................................' .................................................. .............2...''.4
Q7a. How many values of x are there, if sin x = 0.4? (1 mark)
....b. Find the lowest numerical solution (to 2 decimal places) to the equation sin x = 0.4. (1 mark)

Q8. By multiplying by the complex conjugate of the denominator, simplify the expression 2 + 6i - 6 + 2i into the form a + bi, where i = √-1. (2 marks)
.................................'................ .'''.............................................. ..................8 + 4i..'.4 + 8i

Q9. Using complete factorisation, find the three integer roots of the function f(x) = x³ - 5x² - 2x + 24. (2 marks)

Q10. The hour and minute hands on a regular clock point in the same direction on 12 occasions in one entire revolution.
On one of these occasions, the time will be exactly 12o'clock and on another occasion the hands will meet at roughly 1:05.
Find the time (to the nearest second) when the hour and minute hands exactly meet between 1:00 and 2:00. (3 marks)
__________________________________________________ __________________________________________________ ___________________________________________

Please PM all answers to me by the 14th February at 3:14pm in your timezone.
In the event of a tie, the red questions will help determine the winner.

Good luck :razz:

__________________________________________________ __________________________________________________ ___________________________________________

Here are the answers:

A1.''315 + 210 + 252 + 270 + 280 = 1327 or 4 67
.'''.''.315.'''.315''.'.315.''.'315.''.'315.'''''' 315.''''.'''.315

A2. Differentiate with respect to x and set the differential to 0.

dy = 3x² - 12x + 9 = 0
dx

(3x - 3)(x - 3) = 0

x = 1 or 3

Substituting these values into the equation gives y = 18 and 14.

To find the nature of these points, differentiate again with respect to x, and substitute 1 and 3 into the expression.

d²y = 6x - 12
dx²

When x = 1, d²y < 0, therefore it is a maximum.
'''''''''.''''.''''.....dx²
When x = 3, d²y > 0, therefore it is a minimum.
'''''''''.''''.''''.....dx²

A3. Using the 9:4 ratio and the fact that the area is 144cm², the length of the rectangle is 18cm and its width is 8cm. Therefore the diameter of the largest circle is 8cm and hence the area is 16πcm².

A4a. 13 x 12 x 11 = _1716_ = 11
.'''..'''.52.''.51.''''50.'''.132600.''.850
...'b. .4.'x.'3.'x.'2 ''= __24__ = _1_
.'''..'''.52'''''51'''''50'''''''132600'''''5525
...'c. .4.'x.'4.'x.'4 ''= __64__ = __8__
.'''..'''.52'''''51'''''50'''''''132600''''''16575

A5. x² - 2x or (x-1)² - 1 or any equivalent.

A6a. Oops, my bad it isn't a circle :embarrassed:

....b. Substitute y = 2x - 4 into x² + y² = 2, and solve for x.
..........................................'.2..... 4
x² + (2x - 4)(2x - 4) = 2
'2''''''''''''''''..''''4

2x² + (2x - 4)(2x - 4) = 8

2x² + 4x² - 16x + 16 = 8

6x² - 16x - 8 = 0

3x² - 8x - 4 = 0

(3x - 2)(x - 2) = 0

x = 2 or 2
...''.3

Substitute these values into either of the two equations to get y = -8 and 0.
.................................................. ......................................'''.3

The coordinates are (2 , -8) and (2 , 0)
.....................'''......3.'...3

A7a. There are an infinite number of solutions.

....b. 23.58° or 0.41 radians.

A8. (2 + 6i)(8 - 4i) - (6 + 2i)(4 - 8i)
''''''''''''''''''''''''80'''''''''''''..'..''.''' '..'80

= 24 + 16 + 48i - 8i - (24 + 16 - 48i + 8i)
'''''...''''''''''''80'''''''''''''..'..'..''.'''' ''''..'80

= 24 + 16 + 48i - 8i - 24 - 16 + 48i - 8i
'''''''''''''''''''''........'''..'''80

= 80i = i
'''.80

A9. Use trial and error to find one of the factors. If the value of the function is 0, you have found a factor. Using that factor, divide the function by this factor to leave a quadratic. Then factorise the quadratic to yield the other two roots.

For example:

f(1) = 1³ - 5(1)² - 2(1) + 24 = 18
f(-1) = (-1)³ - 5(-1)² - 2(-1) + 24 = 20
f(2) = 2³ - 5(2)² - 2(2) + 24 = 8
f(-2) = (-2)³ - 5(-2)² - 2(-2) + 24 = 0

Therefore (x + 2) is a factor.

x³ - 5x² - 2x + 24 = (x + 2)(x² - 7x + 12)
x³ - 5x² - 2x + 24 = (x + 2)(x - 3)(x - 4)

Therefore the three roots of this function are -2, 3 and 4.

A10. In one hour, the minute hand travels 360°, equivalent to 6° per minute.
In one hour, the hour hand travels (360/12) = 30°, equivalent to 0.5° per minute.

So every minute, the minute hand gains 5.5°.
For an overlap to occur, it must have gained 360°.

So time taken for that is 360/5.5 = 65+(5/11) minutes per overlap.
After 12o'clock, the next overlap occurs at
01:05:(5/11)
which is
01:05:27
__________________________________________________ _______________

The winner is Alessadri with all 20 points :D Well done Aless!

Ah.. I only saw this today.. thanks jen...

Hm... I'll try and put up the next round asap.

lol :D
/me 'll play...if she has time XD

bb... When will you put up the next set of questions?

:sad::cry: It's been over a month, bb! :cry::sad:

Feel free to take over to keep the thread going ILM.
I'm sure BB won't mind

Ah. Apologies for the delay. And I am caught in my uni work/exams, so this quiz wouldn't be Mathematical in the usual way. The following 15 images belong to the iSketch "Mathematics" wordlist.

The thumbnails of each image are posted here, the original image (iSketch screen size) can be obtained by clicking the image you want.

Img1 is monosyllabic, Img15 is bisyllabic, the number of syllables for other images are given.

A maximum of 5 guesses is allowed for each question. Each question carries one mark with no part-points. Tie-breakers will be decided by the total number of guesses for all questions. The lesser, the better.

Deadline : Monday, April 20th 2009, Midnight (UTC)


http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/01.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/01-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/02.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/02-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/03.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/03-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/04.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/04-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/05.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/05-1.jpg)
http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/06.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/06-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/07.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/07-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/08.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/08-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/09.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/09-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/10.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/10-1.jpg)
http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/11.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/11-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/12.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/12-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/13.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/13-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/14.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/14-1.jpg) http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/15.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/15-1.jpg)


Edit : Image 12 : The first word is monosyllabic. Apologies.

Ah, nice one Aless, your drawings are always good :)

The following 15 images belong to the iSketch "Mathematics" wordlist.

* db1986 opens his wordlist file :razz:

Ahhhh so cheating -_- >.>

I think I might give this one a shot. :) It doesn't look too bad. :)

I can actually name a few of those without the wordlist :P

Ah... You breathed life into my exponentially electronically decaying weekly maths quiz! I guess only iSketch brings life into an iSketchForum... :sad:

Ooh.
I might try this one, Sadri!
hehe #5, loveit

Aless, I think image 12 has a slight syllable error.
I think word 1 is supposed to have only one syllable and not two :P

Ah thanks db. I must have been half-asleep playing against myself. >.<

And oh, depending on the entries, I might allot part-points to specific images, which I will explain with the results.

If we make several guesses for one picture and are correct with the first guess, will the subsequent guesses still count against us?

Yes they do, Sparrow.


And also, I guess I might extend the deadline for another week, due to my exams.

Ach nice, 'Sadri.
But it isn't helping me........ lol
But hey, Good luck with your exams ^^

Round closes in 24 hours.

Apologies for the delay, and thanks for the patience.

I have decided to give part points for the guesses.

The Solutions :

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/01.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/01-1.jpg) Mousetrap

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/02.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/02-1.jpg) Quintuple

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/03.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/03-1.jpg) Radius

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/04.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/04-1.jpg) Super Egg

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/05.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/05-1.jpg) Poisson

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/06.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/06-1.jpg) Golden Ratio

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/07.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/07-1.jpg) Cardinal Numbers

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/08.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/08-1.jpg) Fibonacci Sequence

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/09.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/09-1.jpg) Simpson's Rule

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/10.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/10-1.jpg) Heron's Formula

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/11.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/11-1.jpg) Impulse

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/12.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/12-1.jpg) Bridge of Asses

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/13.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/13-1.jpg) Napoleon's Propeller

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/14.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/14-1.jpg) Gaussian Distribution

http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/15.jpg (http://i405.photobucket.com/albums/pp135/Alessadri/MathsQuiz/15-1.jpg) Locust


The Results :
(In the order of submission)

storm : 11 (15)
db1986 : 14 (16)
Bellicimo : 11 (15)
Capt_Sparrow : 14 (15)
Medea. : 9 (15)

*Number of guesses in parentheses


Using the tie-breaker,

Over to you, Capt_Sparrow

Nice one Birdy! Although honestly I would have got only about 11/12, I did cheat a little bit :P
Well we can't be having the wordlist gathering cobwebs can we? :razz:

storm: 11 (15)

Think I did all right, for never having played in the Maths room!

Got Simpson's Rule, Impulse, Gaussian Distribution, Locus, and Napoleon's Propeller wrong.

No. 2 is missing from the answer list?

I didn't get Locus.

No. 2 is missing from the answer list?

Yes, it is :)

Edit: Bah, you changed it at the same time I posted :P

Ah thanks :). I guessed Napoleon's Theorem rather than Propeller :s but it was really fun to solve them all! :p Impulse was brilliant! :razz:

Hmm... now the bit I dread... making maths questions!

Hmm... now the bit I dread... making maths questions!

Nah, it's not that bad. I actually devised my own questions, but it only took about 2 hours :razz:
Lol, you could always hijack steal retrieve some from the net :P

Ooo well done to Capt and everyone else who entered!

And rofl @ giving part points for the guesses.. :razz:

Captie Spawwow bwother, where are your questions? It's been an era since the last quiz!

If you don't put up the questions soon, I'm afraid I'll have to put them up.

Mr. Chemical Engineer Capt_Sparrow is being as obstinate as a mule, and apparently doesn't want to put up any questions online, so I guess I'll have to give this thread a fresh start. I hope you'll all participate. I know many of you just dread Maths, but it isn't as bad as it looks. Trust me. And many of you have studied a lot of Maths. I thought jen939706 doesn't know any calculus, but surprisingly, she does! So get your thinking caps on, try battling this quiz and amuse Maths haters and Mathsophobes around you! Yes, that's the aim of this thread... to drive Mathsophobia away, and make Mathematics interesting for all! And make everyone realise its importance in this cosmos. :biggrin:

All the best. You have one week to answer all the questions and PM them to me. Last date/time for entries is 11/08/09, Tuesday, pi time (GMT +0400). Answer all questions. For question 7, answer either 7A or 7B. Please do not forget to show all your working for every question!

1) What are the coordinates of the point (-32472304832904, 4721934872894) when reflected in the x-axis? (1 mark)

2) What is the standard formula for the area of a triangle, two angles of which measure 60 degrees each? (Hint: It's got a surd/radical/root in it) (1 mark)

3) What's XIV + VX? Answer in Roman numerals please. (1 mark)

4) The length of a side of a square whose area is 169 cm^2 is equal to the length of a side of a heptagon. What is the perimeter of this heptagon? (1 mark)

5) I have one blue ring, one red ring and one black ring. In how many different ways can I put all three rings on one finger? (1 mark)

6) The scores on a Maths quiz, out of a possible 50, were as follows:

23, 28, 27, 26, 25, 21, 20, 19, 23, 28, 24, 25, 25, 21, 24, 25, 21, 25, 26, 28, 28, 25, 26, 27, 29, 21, 25, 49, 24

a) Is the number of students who took this quiz a prime number? (1 mark)
b) What is the probability that this quiz was taken on my favourite day of the week? (NOTE: I DO HAVE A FAVOURITE DAY OF THE WEEK! :razz::biggrin:) (1 mark)
c) What is the mean test score? Reject the obvious outlier. (2 marks)
d) What is the median of these scores? Reject the outlier. (2 marks)

7A) A blue car starts from a point O. It travels 2 km North and 3 km West. This can be represented in vector notation as 2i - 3j. A red car, also starting from O, travels 4 km North and 2 km South. (Note: i and j are unit vectors, of 1 km, in the North and East directions respectively.)

a) What is the shortest distance between the blue car's starting point and its new position? (1 mark)
b) How can you represent the displacement of the red car in vector notation? (1 mark)
c) What is the angle between the vectors that represent the new position of the two cars? (3 marks)


OR (For our juniors or mathsophobes):

7B) a) When 0 < x < 0.9, write the following in order of size with the smallest first.

cos x°, x^2, x^−1 (2 marks)

b) (512)^(-2/3) = 2^p. Find the value of p. (2 marks)

c) If 2^x = 6, and 2^y = 15, find the value of 2^(x + y). (1 mark)

TOTAL MARKS = 16

ALL THE BEST! :biggrin::razz:

The victors are those who fight and face their fears,
Sublime is their might and they don't shed any tears,
Exploring and discovering are two of their qualities,
Trying something new, for them, is a necessity.

NOTE: All answers must be rounded off to three significant figures, unless an exact answer is required, or unless the answer is an integer or a number with two significant figures, for instance.

All angles must be rounded off to one decimal place.

Attach diagrams if necessary. For instance, Q 7A) requires a diagram, but Q2) doesn't (However, using a diagram would certainly be to your advantage).

Please show all your working, even if the answer is worth a mark, because I want to know how you arrived at the answer (unless it's very obvious). Sometimes (like it happened in my first quiz), you may arrive at the correct answer with an incorrect method!

Please do not make any assumptions to any of the questions posted. Any assumptions have been clearly stated in the questions. If still in doubt, feel free to ask me.

Oooh I like the look of this. :)

Suppose I should give it a go before I go..
After several hours of maths nudging me :P ahaha.

Oh maths doesn't like the wording of that...
SEVERAL DAYS OF NUDGING. xD

woohoo!

Math is fun!

And a little friendly competition never hurt anyone did it? haha....
the more the merrier!

1) What are the coordinates of the point (-32472304832904, 4721934872894) when reflected in the x-axis? (1 mark)

A point in the second quadrant is reflected in the x-axis, so it ends up in the third quadrant, where both coordinates are negative.

Answer – (-32472304832904, -4721934872894) [1]

2) What is the standard formula for the area of a triangle, two angles of which measure 60 degrees each? (Hint: It's got a surd/radical/root in it) (1 mark)

If two angles of a triangle measure 60 degrees each, the third angle apparently measures 60 degrees, as well. This is an equilateral triangle. The formula for the area of an equilateral triangle is ‘Area = ((√ 3) / 4) * (side)^2’. [1] You will not lose the mark for stating only this formula from memory.

OR

Divide an equilateral triangle into two congruent 30-60-90 isosceles triangles. The area of each isosceles triangle is ½ * base * height = ½ * (1/2 * side) * (side sin 60) = ¼ (side)^2 * √3 / 2 = √3/8 * (side)^2. Therefore, the area of the whole triangle (or two 30-60-90 isosceles triangles) = 2 * √3/8 * (side)^2 = √3/4 * (side)^2, where side = length of a side of the equilateral triangle. [1]

OR

The area of a triangle is given by ‘Area = ½ * a * b * sin C’. So, the area of an equilateral triangle is:
Area = ½ * side * side * sin 60
= ½ * (side)^2 * √3/2
= √3/4 * (side)^2 [1]

If candidate uses x or l or the like for ‘side’, then candidate must state what x or l is. No credit will be awarded if the variable is not defined.

3) What's XIV + VX? Answer in Roman numerals please. (1 mark)

Not possible, because VX does not exist. [1] Note: 5 = V.

4) The length of a side of a square whose area is 169 cm^2 is equal to the length of a side of a heptagon. What is the perimeter of this heptagon? (1 mark)

Cannot be determined; heptagon is not regular (not mentioned in the question). [1]

If the heptagon were regular:

Side of square = √Area = √169 = 13 cm.
Perimeter of heptagon = 13 * 7 = 91 cm.




5) I have one blue ring, one red ring and one black ring. In how many different ways can I put all three rings on one finger? (1 mark)

Three different rings to be worn on one finger, so the number of different ways = 3! = 6. [1]

Both 3! And 6 must be written down to score the mark.

6) The scores on a Maths quiz, out of a possible 50, were as follows:

23, 28, 27, 26, 25, 21, 20, 19, 23, 28, 24, 25, 25, 21, 24, 25, 21, 25, 26, 28, 28, 25, 26, 27, 29, 21, 25, 49, 24

a) Is the number of students who took this quiz a prime number? (1 mark)

The number of students who took this quiz = 29.
Yes, 29 is a prime number [1], because it only has 1 and itself as its factors.

Accept ‘Yes’ only. [1]

b) What is the probability that this quiz was taken on my favourite day of the week? (NOTE: I DO HAVE A FAVOURITE DAY OF THE WEEK!) (1 mark)

Provided that the quiz could’ve been conducted on any day of the week, including the weekend, and that I have one day of the week that is my favourite, P (quiz on my favourite day of the week) = 1/7. [1]


c) What is the mean test score? Reject the obvious outlier. (2 marks)

Mean = (23 + 28 + 27 + 26 + 25 + 21 + 20 + 19 + 23 + 28 + 24 + 25 + 25 + 21 + 24 + 25 + 21 + 25 + 26 + 28 + 28 + 25 + 26 + 27 + 29 + 21 + 25 + 24) / 28 [1] = 24.6 (correct to 3 sig. fig.) [1]

Accept 689/28 [1] = 24.6 (correct to 3 sig. fig.) [1]

No credit awarded if the outlier of 49 is included in the calculation.
No credit awarded if the sum (excluding the outlier) is inadvertently divided by 29 instead of 28.

d) What is the median of these scores? Reject the outlier. (2 marks)

Arrange the scores in ascending or descending order: [1]

29/19
28/20
28/21
28/21
28/21
27/21
27/23
26/23
26/24
26/24
25/24
25/25
25/25
25/25
25/25
25/25
25/25
24/25
24/26
24/26
23/26
23/27
21/27
21/28
21/28
21/28
20/28
19/29

The median is the mean of the two middle numbers, 25 and 25, which is 25. [1]

No credit awarded if the outlier of 49 is included in the calculation.

7A) A blue car starts from a point O. It travels 2 km North and 3 km West. This can be represented in vector notation as 2i - 3j. A red car, also starting from O, travels 4 km North and 2 km South. (Note: i and j are unit vectors, of 1 km, in the North and East directions respectively.)

a) What is the shortest distance between the blue car's starting point and its new position? (1 mark)

Using Pythagoras’ theorem, shortest distance = hypotenuse = √(2^2 + 3^2) = √13 km = 3.61 km (3 sig. fig.) [1]
No credit awarded if ‘km’ not stated.

b) How can you represent the displacement of the red car in vector notation? (1 mark)

4i – 2i = 2i [1]

Accept ‘2i’ only or ‘2i km’.

c) What is the angle between the vectors that represent the new position of the two cars? (3 marks)

The dot product of two vectors a and b is given by:
a.b = |a| |b| cos θ, where θ is the angle between the two vectors.
Rearranging this gives θ = arccos (a.b) / ( |a| |b| )
a.b = (2 * 2) + (-3 * 0) = 4. [1]
|a| |b| = √13 * 2 = 2√13 [1]
Therefore, θ = arccos (4/ (2√13)) = arccos (2/√13) = 0.983 rad (3 sig. fig) = 56.3 degrees (1 d.p.) [1]
Accept 1.0 rad.

Accept answer obtained by a right triangle and a suitable trigonometric ratio. [3]




OR (For our juniors or mathsophobes):

7B) a) When 0 < x < 0.9, write the following in order of size with the smallest first.

cos x°, x^2, x^−1 (2 marks)

Let x = 0.00000001 or something similar.

Then, cos x° is nearly 1, x^2 is a very small value and x^-1 is a very large value. [1]

Therefore, x^2 < cos x° < x^-1 [1]

No credit awarded for guesswork. All three must be in the correct order. No credit awarded if only one is in its right place. If all three in correct order, but no explanation, then candidate will only be awarded half the credit.

b) (512)^(-2/3) = 2^p. Find the value of p. (2 marks)

512 = 2^9
So, 512^(-2/3) = (2^9)^(-2/3) = 2^(-6). [1]
Therefore, p = -6. [1]

OR

(512)^(-2/3) = (∛512)^(-2) = 8^(-2) = (2^3)^(-2) = 2^(-6). [1]
Therefore, p = -6. [1]

Accept any other equivalent method.
Accept answer that has made use of logarithms.


c) If 2^x = 6, and 2^y = 15, find the value of 2^(x + y). (1 mark)

2^(x + y) = 2^x * 2^y
= 6 * 15 = 90. [1]

No credit awarded if ‘90’ stated only.

Scores:

Jmac = 12/16
Sorsie = 3/16

Thanks for playing! Over to you, Jmac!

alright, didnt notice the results part until just now, woops!
well i will start getting those questions and hopefully they will be up in a few hours....

ALRIGHT THIS WEEKS QUIZ IS HERE!!!!!

There will be 10 questions starting out easy and getting harder as we advance, good luck to all who try and play!

Elementary School:
1) What is 3+7-2?

2) What is 19*7/34

Middle School:
3) Solve for X: 3x-5=18

4) graph the function: Y = 2x^3 - x

5) what is the area of a normal pentagon whose perimiter is 740cm?

High School:
6) Determine the point(s) at which the graph of the function has a horizontal tangent. f(x) = x^2 / (x^2 + 1)

7) Suppose that f(t) measures the level of oxygen in a pond, where f(t) = 1 is the normal (unpolluted) level and the time t is measured in weeks. When t=0, organic waste is dumped into the pond, and as the waste material oxidizes, the level of oxygen in the pond is-
f(t) = (t^2 - t + 1) / (t^2 + 1)

a) what percent of the normal level of oxygen exists after 1 week?
b) after 10 weeks?
c) what is the limit as t approaches infinity?

8) With a 7% raise, an engineer will make $50,000 a year. what is his salary before the raise?

9) A person inherits $15000 with the stipulation that for the first year the money must be invested in two stocks paying 8% and 12% annual interest. What is the greatest amount that can be invested at 8% if the total interest is to be at least $1,620?

10) Two ordinary balanced six-sided dice are rolled. Calculate the probability, p, of getting a sum of 3. For a large group of insured taxi-cabs assume that the probability of filing a claim during a calendar year is p.

Two ordinary balanced coins are flipped and the number of observed tails x is recorded. Assume that when a claim is filed, the insurance company has to pay $9,000x to settle the claim.

If a company issues insurance policies to a large number of taxi-cabs, how much should each policyholder pay just to cover the cost of settling filed claims?


Bonus Question: (worth 5 bonus points)
The time to failure of my Energy Booster in my new Time Travel Machine has an exponential distribution with a median of four hours. Calculate the probablility that the Energy Booster will work for at least five hours without failing.



All answers must be sent to me by way of PM before September 1, 2009 at midnight your time
GOOD LUCK!:biggrin:

oh and scoring goes like this:
elementary school: 1 point each.
middle school: 2 points each.
high school: 3 points each.


p.s. sorry for double posting, but i wanted to bring the thread to the top and make sure people knew the questions were up:sad:

5) What do you mean by a 'normal' pentagon? Do you mean a 'regular' pentagon?
9) Is that simple or compound interest?
10) :eek: I wish x were the probability of getting a tail... :cry::cry:

5) yes normal as in regular as in all sides are the same, all angles are the same.
9) its annual interest. compounded annually, not monthly, not daily, but annually.
10) Just flip two coins and use the number that you get:twisted::twisted:
haha... it is a tricky one, but i find it easier than the bonus.

10) :eek::eek::eek: I'm gonna seek help! I'll first try it myself, though. I don't understand business/finance/economics/accounting/commerce terminology - policy, refund, claim, policy holder insurance, blah blah. And you could get 1 tail, or 2 tails... or no tails... uhh...

9) You mean a fixed % each year over a period of years?


WHERE I = PRT/100? :twisted::biggrin::smile::razz:

woops, sorry i didnt see these questions until now.

9) yes, thats what i mean.

10) that part is rather tricky, for those of you who havent submitted just because of that last part about the coins, in your work that you send me explain "i chose the number 2 (or 1 or 0 or whatever) because i was not sure how to do it" and then finish the question using that number. Youre points will be adjusted accordingly.


The Deadline has been extended due to noone:sad: submitting their answers until September 1st at midnight your time

awww. :cry: SEPTEMBER 1st scares the crap out of me! :cry::cry::cry:

:cry: "Your points will be adjusted accordingly" ---> YEAH, RIGHT! As if I'll ever let you take a mark off my answers. :biggrin::twisted:

It's so sad to know that the best of engineering students here on iSketchForum don't want to play this. And still very surprising to see them try their hand at the Dux challenge.

I just want to say I hate maths. xD

If no one else has answered it though I might give it a whack and have my score under mathsies. xD

If you work hard, you can even get your score way above mine. -.-

I'm giving this one a go!
For Q4, should we draw the function in something like MS Paint and then upload it to the net and link you to it Jmac?

yeah, that works. You can just put it on photobucket or somtehing like that and send me the link in your PM.

also for other questions if you need to draw something you can do the same thing.

It's been a hard week for me... very hard... and probably still is. If you can just give me under 24 hours, I'll try to submit this ASAP.

go for it, i have some stuff going on as the uni started this week too... so answers may take a few days to post.

Uh oh - I better post the answers ASAP before this guy returns...

Oh, I forgot to ask... For Q4), will a sketch suffice?

yes, and im just waiting on you to submit your answers so that i can post the answers.

I'll post my answers soon, in 30 minutes or so. But... I'm stuck on that damn policy holder question, and I don't want to guess! :cry::cry::cry:

ALRIGHT THE ANSWERS ARE HERE!
(by the way, i have always grown up using a two decimal places rule (i.e. 123.45) and not 3 significant figures, but i will accept either, just my answers will have 2 decimal points.)

Elementary School:
1) What is 3+7-2?
The answer: 8
2) What is 19*7/34
The answer: 3.91

Middle School:

3) Solve for X: 3x-5=18
3x=23
x=23/3
x=7.67

4) graph the function: Y = 2x^3 - x
(insert graph)

5) what is the area of a normal pentagon whose perimiter is 740cm?
each side = 740/5
=148 cm.
By definition, the area of any polygon of N sides where the sides (S) are equal in length is:
area=S^2*N/(4 tan(pi/N))
(where tan is the tangent function calculated in radians)
so for this case:
area=148^2 * 5/ (4tan(pi/5))
=37685.33 cm^2


High School:
6) Determine the point(s) at which the graph of the function has a horizontal tangent. f(x) = x^2 / (x^2 + 1)
(x) = x^2 / (x^2 + 1) = (x^2 + 1 – 1) / (x^2 + 1) = 1 – 1/(x^2 + 1) = 1 – (x^2 + 1)^-1

simplifying we get f(x) = 1- 1/(x^2 + 1) or f(x) = 1-(x^2 + 1)^-1
df/dx = 2x/(x^2 + 1)^2
set that equal to 0.
only real number that works for that equation is 0.
so it has a tangent at the point (0,0)


7) Suppose that f(t) measures the level of oxygen in a pond, where f(t) = 1 is the normal (unpolluted) level and the time t is measured in weeks. When t=0, organic waste is dumped into the pond, and as the waste material oxidizes, the level of oxygen in the pond is-
f(t) = (t^2 - t + 1) / (t^2 + 1)

a) what percent of the normal level of oxygen exists after 1 week?
when t=1 f(1)=(1^2 - 1 + 1)/(1^2 + 1) = 1/2
=50%
b) after 10 weeks?
f(10) = (10^2 - 10 + 1)/(10^2 + 1) = 91/101
=90.1%
c) what is the limit as t approaches infinity?
lim (t^2 - t + 1) / (t^2 + 1) = lim (1-(1/t) + (1/t^2))/(1+(1/t^2))
=(1-0+0)/(1+0)
=1

8) With a 7% raise, an engineer will make $50,000 a year. what is his salary before the raise?
salarybefore*1.07=50000
salarybefore= 46729

9) A person inherits $15000 with the stipulation that for the first the money must be invested in two stocks paying 8% and 12% annual interest. What is the greatest amount that can be invested at 8% if the total interest is to be at least $1,620?

There are many ways to solve this one. here is one way:
x=amount invested in stock of 12%, y=amount invested in stock paying 8%
x + y = 15000
.12x + .08y = 1620
forms the augmented matrix (pretend the numbers below have a box around them):
1 1 :15000
.12 .08 :1620
replace Row 2 with -> 25/3*Row 2 - Row 1
~
1 1 :15000
0 -1/3 :-1500
~
1 1 :15000
0 1 :4500
Therefore the greatest amount that can be invested at 8% is 4500 dollars


10) Two ordinary balanced six-sided dice are rolled. Calculate the probability, p, of getting a sum of 3. For a large group of insured taxi-cabs assume that the probability of filing a claim during a calendar year is p.

Two ordinary balanced coins are flipped and the number of observed tails x is recorded. Assume that when a claim is filed, the insurance company has to pay $9,000x to settle the claim.

If a company issues insurance policies to a large number of taxi-cabs, how much should each policyholder pay just to cover the cost of settling filed claims?

There are two possible combinations to get a sum of 3 out of a possible 36 combinations. so the probability p=1/18

a coin has a 50% chance of landing tails. Over a large number of coin tosses, 25% will land with 2 tails, 50% with 1 tail, and 25% with 0 tails.
.25*9000*2 + .50*9000*1 + .25*9000*0 = 9000.
so over a large number of claims the average payout will be $9000.

$9000*1/18 = $500
so each policyholder should pay $500 to cover the cost of settling filed claims.

Bonus Question: (worth 5 bonus points)
The time to failure of my Energy Booster in my new Time Travel Machine has an exponential distribution with a median of four hours. Calculate the probablility that the Energy Booster will work for at least five hours without failing.

The distribution function of an exponential random variable
T with parameter θ is given by F (t) =1− e^(−t/θ) , t > 0
Since we are told that T has a median of four hours, we may determine θ as follows:
1/2 = F(4) = 1-e^(-4/θ)
1/2 = e^(-4/θ)
-ln(2) = -4/θ
θ = 4/ln(2)
therefore, Pr(T >= 5) = 1 - F(5) = e^(-5/θ) = e^(-5ln(2)/4) = 2^(-5/4) = 0.42


alright if you read this and this part on the bottom is in, it means i havent inserted the graph yet for number 4

Capt. Sparrow - 22/23
IloveMaths - 25/23 (saved by the bonus question at the end)

congrats ilovemaths

zomgoodness...! HOW STUPID OF ME! I correctly calculated the length of a side of the pentagon as 148 cm, and ended up using 140 cm in the calculation...! :cry::cry::cry: Did I lose all points for that question? :cry:

And, why did you multiply the $9000 by 1/18? uhh...?

Congratulations Mathsy! :) Look forward to your set of questions :p

The $9000 was multiplied by 1/18 because the probability of filing a claim is 1/18.

I worked so hard for the pentagon question, and I think I lost both my points there (I didn't even get one!), and two points definitely in that dumb policyholder question - lol. I tried plugging in 148 into 1.72 * x^2, and I got a different area, and I was wondering how... but then I revised my working (several several times), and it looked all fine to me... Gah! :cry: I'm gonna be depressed about that for a while, lol

Didn't you attempt the bonus question? :biggrin: I loveeeeeed that question!

uhh I still don't get it. Why do you need to multiply it by 1/18? ... $9000 is what a policyholder needs to pay if a claim is filed. Isn't that it? What if I had to pay $10 if the coin showed 'tails' instead of 'heads'... Would I pay $5, because the probability of getting a tail is 1/2? I don't get this... Heeeeelp!

Didn't you attempt the bonus question? :biggrin: I loveeeeeed that question!
I did but made the schoolboy error of thinking the median was the mean θ, a bit like you plugging in the wrong value for the length of the side of a pentagon :p.

uhh I still don't get it. Why do you need to multiply it by 1/18? ... $9000 is what a policyholder needs to pay if a claim is filed. Isn't that it?
The bold bit is where the 1/18 comes into it, because a probability is assigned to the event of a claim being filed, as well as the value that claim would be.

What if I had to pay $10 if the coin showed 'tails' instead of 'heads'... Would I pay $5, because the probability of getting a tail is 1/2? I don't get this... Heeeeelp!
In this question, we're calculating how much each policy is worth, based on the probability of our making a claim. So, in the scenario you've described (which is hypothetical because we haven't actually tossed a coin yet), the policy would be worth $5 and that is how much we would have to pay if we wanted to buy this policy.

After we've bought the policy, we toss the coin. If we get a tails, the insurance company is obliged to pay us $10; if we get a head, the insurance company pays us nothing.

Jmac might want to confirm all this is correct though :smile:

So that's how the policy thing works, eh? NO THANKS a tonnneeeeeeee for clearing that out, spaow bwother! :biggrin:

I was thinking of exactly that when I typed "if a claim is filed" - I was wondering if the two events are independent, but then I thought they aren't. I guess they are... Then the multiplying by 1/18 makes sense, I guess...

Yeah, let's just wait for Jmac brother and see what he has to say about this... Interesting question, btw (I know I've called it dumb before, but that's just because... I couldn't work it out! :twisted::razz:).

This is actually a very practical question that is why i put it in (sure the math behind real insurance policy calculations is a bit more complicated, but it helps you get the general idea of how/why you pay what you pay for your insurance policy)

Basically you can think of it like this:
say 72 people bought car insurance for their taxis, so that if they got in a wreck the insurance company would have to pay them. There is a 1/18 chance that they will get in a wreck, or in other words 1 out of 18 people will file a claim, or get in a wreck and ask the insurance company to pay for the damage.
so out of 72 people, 4 people get in a wreck. one (no tails) has very little damage at all so he gets no money. two (one tails) have a good amount of damage to their cars and so the insurance company pays them $9000 each to cover the cost. One (two tails) had a huge amount of damage done to his car, so the insurance company pays him $18000.

In total the company spent $36000. However, they dont know beforehand WHO is going to get into the wreck, just that 1/18 people WILL. So, they charge everyone who has a policy, a certain amount of money, usually referred to as a premium, to cover the cost of it all. So if each person paid $500 at the beginning, and there are 72 people, that comes out to $36000. Or basically the cost of all claims is spread out amongst all the policy holders.


hope that helped, im off to class now, but later ill be back so just post the questions if you dont understand.

look forward to your quiz maths!

(oh and you only lost one point for the pentagon one maths, i saw your work but slight error in moving the numbers)

Where did I lose my other marks then? Don't tell me I lost them in sketching the curve... where else have I made an error?

I've lost 4 marks in all - 1 in the pentagon; 2 in the policyholder... Where's the last one...? :eek::eek::eek:

I did think about docking you a point for your sketch, as it was fairly rudementary, however then i realized that i hadnt specified exactly what i was looking for in the sketch, and that it was in the middle school section, so i let you keep both your points there.

where you lost the point was when i thought that the bonus question gave 4 extra points and on further review (right now) it was worth 5 points.:embarrassed:

but hey, you still won, so we are waiting for your questions.

I'll be making this quiz very interesting, and different, so it'll take me a week-ish (or so... or less!) until the questions are up! I just hope I get as many participants!

This will be back soon. I promise. I have all the questions ready, but... 1) I'm too lazy to type them. 2) I wanna type them neatly - the mathsy way, and I don't know how to do that.

I wanna type them neatly - the mathsy way, and I don't know how to do that.

The best program for typing math stuff is called LaTeX, but an easier way (you dont have to learn how to write in LaTex, and you dont have to download it) is to just insert symbols in Microsoft Word.

Ah... Damn. How do I get Latex? I have the stupid MS Office 2000. :( Any ideas?
And how do I copy/paste the Word/Latex text into this forum?

∫_(-7)^5▒〖x dx〗

(x+a)^n=∑_(k=0)^n▒〖(n¦k) x^k a^(n-k) 〗

hmmm that is what it looks like when you just paste the word symbols in...
you could clean it up to this: ∫(-7)^5 x dx

as for what LaTeX would look like copy and pasting, i am not sure. it prints it out to a pdf though. I would do an example to test it, but I am not at home and so i dont have LaTeX with me right now... to get it just google "LaTeX" and it should be the first result. It takes between 2-8 hours to download, depending on your internet connection. (2 being you have the fastest internet in the world, 8 being a good connection, but still slow. It took me 6 hours on what I consider a good speed internet connection)

or you could just post the document somewhere online and then link it to us so we can see it.

Ugh... that looks horrible!

I don't have that equation thing in my MS Word.

What do you mean by post the document somewhere online? How? Scan and then links to photobucket files? I don't care about downloading LaTeX, but how long does it take to learn it? lol...

I know that db or saffron wrote an equation neatly once, in one of the game threads. It was a picture, but it wasn't the whole page, just part of it containing the formula. How did they get that? Whenever I link to another page or include the picture in my post, the whole page is displayed, even if the picture is small. That wastes a lot of space. How do I get around that?

wow word 2000, maybe its time to upgrade? at least to 2003, or 2007, or 2010....

a quick google search will let you know how to save it online, its better explained that way, and I do not really feel like typing it all out.

For just writing math equations, LaTeX should take about an hour or two to learn.