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it is obviously only one branch because the distance to one focus is being subtracted from the other. which means if it was |z-i| - |z+i| = +-4 would indicate both branches

noooo the beloved conics.

there is no 2I on the RHS in your last few lines of working. it's actually just I. (there's a 1/2 right at the front which cancels the 2)

how about n=1, integrate xe^{x² :):)}

confirmed questions: integrate xtanx and e^(x²) good luck guys.

05 was fairly hard though. i still can't do the last question.

90 degrees. aka face in paper.

you made a slight arithmetic mistake, but it's ok. x² + 8x + y² + 8y + 2xy = 0 (x+4)² + (y+4)² + 2xy = 32

it's 11%. (40-36)/36 x 100 as for the CO2 ppm question, i think it's important that conditions were given, so it's a (v/v) concentration thing. to work out the volume of air per L we got 1.28 x 10^-5 moles / L = 1.28 x 10^-5 x 24.79 L / L = 3.17312 x 10^-4 L / L = 317.312 ppm Assess the...

how about a nice shiny bronze 2hander.

the answer to 2 is the third choice, right?

determinant method is probably allowed. you could always memorise its proof, which is quite short anyway.

q1. a bit of a strange question i think: this is my approach. first it is obvious that the seating must be that the men and women alternate. consider the males seated first, with Male 1 sitting at a particular spot. .......M1 M............M ...... M there are 3P3 ways to arrange the men...

q2. first let's pick the 8 people that are to dance. we have 12C4 girls x 15C4 boys = 675675 ways of choosing the 8 people. within the 8 people, we want to find the number of ways to couple them. i had to think about this for a while - i think the following approach is correct. imagine if we...

consider case 1, where there is no C in the group of 5: we have the letters RIKET to form words of 5 letters long. therefore, 5P5 = 120 consider case 2, where there is exactly 1 C: to arrange the remaining 4 spots, we have 5 choices (again RIKET), so 5P4. to arrange the 1 C, it's 5C1...

basically how easily the particle can get through the matter. if it has charges, then electrostatic forces between the particle and nuclei will slow it down, reducing its energy and hence it won't penetrate as far. this is why neutrons are much better at penetration than say, protons. also, it...

what does it say? love = integrate .... d time?? fill in blank please.

don't bother, this year's Catholic paper was extremely badly written, with terrible recommended answers. also, mostly "old questions". i.e. no new unusual/interesting problems. waste of time.

solution to 2: <Img>http://www.geocities.com/sunnysnew/solutions.bmp</Img>