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3. There're two blue and four yellow marbles arranged in a row. How many different arrangements of just 5 of these marbles are possible? (Answer: 25) hmm one way...(again no calc) 6P5 / (4!x2!) or consider the two cases. case1. one yellow is left out...5!/(2!.3!) case2. one blue is left...

4. 5 travellers arrive in a town where there're 5 hotels. If two of them are husband and wife and must goto the same hotel. How many arrangements if the other three can go to any of the other hotels? (Answer: 320) ok let the wife / hustband go into a hotel..therefore there are 4x4x4 ways of...

"5. There're 8 seats, 4 facing the front and 4 facing the back. Find the probability that 2 particular people will sit opposite each other if seating is arranged randomly. (Answer: 1/7" let the first person sit in any seat he want...then there are 7 seats left..so there is a 1/7 chance to...

"6. In 12 people, 8 have seen film A and 9 have seen film B. Everyone in the group has seen at least one of these movies. If one friend is chosen, find the probability that this person has seen: - Both movies - Only film B" Draw a venn diagram.. and you should be able to see that 3ppl only...

7. In how many ways can 3-letter combinations be made from the word AUSTRALIA? (Answer: 60480) again excuse my poor wording/expalations.. there are 9P3 ways of getting the 3 values.. and then theres 6!/3! (accounting for the triple a) ways of arranging these.. .:. 9P3 x 6!/3!...(sum1...

ill have a go..this topic is hard to explain...you just sort of get it... 1. Letters of "promise" are arranged in a row. What's the probability that there're 3 letters between p and r? (Answer: 1/7) now this is 6! / 7! ..as obviously its over 7! (total arangements) now let p and r be...

you dont need to memeroise this stuff..just think...let roots be @ and -@...therefore sum = 0 and -ve time +ve is -ve

b/sin@ = a/2sin@cos@ = c/(3sin@-4sin^3@) b = a/2cos@ = c/(4cos^2@-1) a/b = 2cos@ b = c / ((a^2/b^2) - 1) giving a^2 = b(b+c) i wish we got qns like that in our papers

also can anyone post some hard circle geo qns (from trials etc)....there isnt many in cambridge :) thanks!

just use the standard l=@r ...also note the angle will be minimally smaller than the one you find! george..i may be misinterpriting this but l = 24pi

post the test if you can it will be easier to say

tehy have to bring back the slide rule

"IYO, would u say time is ur worst enemy in an ext 1 exam, or the difficulty of the paper?" neither really..if you do alot of papers you get very quick..when i started doing 3u papers it took all of 2hrs and mussing a few marks only getting in the 80%~ now after about 12 papers i got to about...

2) x = (t + 1/3) as when expanding the cubic the 3C2 will cancel with the 1/3 getting x^2 - x^2

3a) y = 6x+21, y = x^3 - 6x + 5..solve simul 6x+21 = x^3 - 6x + 5 f(x) = x^3-12x-16 (representing points of intersection) f(-2) = 0 f'(x) = 3x^2 - 12 f'(-2) = 0 as f(x) has a double root at x = -2 and f(x) rep point of interection..hence two lines at x=-2 is a tangent

no he isnt as only 5ppl do ext maths

thanks wogboy! also do you have a website with similar proofs?

hmm..should we put acedemic hobbys or are they looking for like cricket, footy, music or watver? (deciding wteter to put 2nd in state in chess down)

if 3hrs is such a concern just leave after 1.5 hrs...it shouldnt take u longer than this anyway

hi..i dont want to type this qn..too long, but if someone has cambridge 3u on them can you help / give hints / post soln for ex 10A 26d..i can get a,b,c and im getting pretty close for d ie within 0.2 but i just cant seem to get it right.. :( edit: nvm i see what i did