Senior Maths Challenge Questions/Discussion

OP

Synergetic

no. 19 is A I think - mod x implies that x must be positive (I think), so multiplying it by x would make it look like the x^3 graph. Could be wrong...

You doing the one this year?

I've entered for it, now I'm realising it was a mistake! I can only do 12/13 questions out of 25 :eek2:

Reply 3

Overmars

17

hey, don't worry about it - same here. I did this test last year - and got something like 73 out of 125 (And you start on 20) lol.

I'll be doing the ones this year too. Most of the first ones (1-15) are common sense - just try not to overthink. As long as you pick up the marks on them, you'll get a respectable score.

Good luck dude :smile:

Reply 4

No18.
The smaller sphere fits inside a cube of side length = a.
So diameter of smaller sphere is S1 = a.

Cube fits inside larger sphere, so diagonal of cube = diameter of larger sphere. Diagonal of cube is a√3. So diameter of larger sphere is S2 = a√3.

Hence ratio is S2 :s-smilie:

1 = √3:1, which is the ratio of the diameters,

Since the question asks for the ratio of the volumes, and the volume of a sphere is proportional to the cube of the diameters, then the ratio asked for is the cube of the one above :biggrin:

Ans: ratio = 3√3:1

Reply 5

No 19.
Ans is A.
y = x|x| is the same as y = x² fo x > 0 and y = -x² for x <0.

Reply 6

OP

Yeah, 19 is A, I just downloaded Autograph and checked it out on there! Thanks guys, 1 down 4 to go :p:

Reply 7

No 23.
For this I get Ans = B = pi

Let me know if you want the working.

Reply 8

Dystopia

For 11, consider how you would go about finding the surface area. What is the surface area of the top of the bottom cylinder? Of course, you then have to subtract the area of the bottom of the second cylinder, then add that on again for the top... you should be able to work out the total of the top/bottoms easily by cancelling. For the sides, I found the mean and multiplied.

Reply 9

dvs

For the last one notice how
(a + sqrt(a^2 - 1))(a - sqrt(a^2 - 1)) = 1

Then
1/(a + sqrt(a^2 - 1)) = a - sqrt(a^2 - 1)

So square the answers and look at which one will give you 2005 - sqrt(2005^2 - 1) = 2005 - sqrt(2004*2006). Luckily, the first does just that. So the answer is A.

Reply 10

dvs

For the rest I agree with steve's answers, but I agree with your answer for #11: I got 456pi as well. Maybe we both missed the point?

Reply 11

Dystopia

dvs

For the rest I agree with steve's answers, but I agree with your answer for #11: I got 456pi as well. Maybe we both missed the point?

I also got 456

\pi

. Maybe he was asking for confirmation as to whether they were correct?

Reply 12

dvs

Dystopia

I also got 456

\pi

. Maybe he was asking for confirmation as to whether they were correct?

Oh, yes, yes. :smile:

I misread what he said and thought he had an answer key that said that A was incorrect.

Reply 13

Dystopia

steve10

No18.
The smaller sphere fits inside a cube of side length = a.
So diameter of smaller sphere is S1 = a.

Cube fits inside larger sphere, so diagonal of cube = diameter of larger sphere. Diagonal of cube is a√3. So diameter of larger sphere is S2 = a√3.

Hence ratio is S2 :s-smilie:

1 = √3:1

It asks for the volume (although I agree entirely with your method).

It's one of the things I need to work on - actually reading the questions so I don't lose easy marks. :wink:

Reply 14

OP

Dystopia

For 11, consider how you would go about finding the surface area. What is the surface area of the top of the bottom cylinder? Of course, you then have to subtract the area of the bottom of the second cylinder, then add that on again for the top... you should be able to work out the total of the top/bottoms easily by cancelling. For the sides, I found the mean and multiplied.

I used the same method, got 456 pi but then thought I made a mistake and re-read the question, meh, looks likes gut instinct is always right the first time! :redface:

Thanks for the help guys, you shall all be repped in due course.

Reply 15

OP

steve10

No 23.
For this I get Ans = B = pi

Let me know if you want the working.

Yeah, would like the working out, the method interests me more than the answer :smile:

Reply 16