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don't forget, 4U ppl aren't considered separate in the 3U course

I believe the answer for the first question is 1/5 choose the 2 spots for A and B such that the condition is satisfied: they can be: (1,5), (1,6), (2,6) -> 3 cases and to choose the 2 spots in general there are (6 C 2) = 15 ways so the probability should be 1/5 the second question...

Try this: ABC is a triangle, D,E and F are points on BC,CA and AB such that AD is perpendicular to BC, BE is perpendicular to CA and CF is perpendicular to AB. From D, perpendicular lines are dropped onto AB,BE,CF and AC, intersecting them at P,Q,R and S respectively. prove that PQRS...

first question: Hmm just differentiate and substitute, verify the LHS = RHS second: they are just setting t=0 when V=0, maths still work if you use some other values, but stick with what they give you for the question. stictly speaking, they should indicate that time is measured in...

circa 89

yep

You'll always be marked down if you put down 2 answers.. You will be marked down if you get the right answer from incorrect working however, if you have the correct answer from correct work, then do something further/irrelevant, it's ignored

hmm... as mentioned above the derivative of |x| is sgn(x) = x/|x| so you just apply chain rule: d/dx |x^2 -1| = sgn(x^2 - 1) * (2x) = (2x)*|x^2 - 1|/(x^2 -1)

Hmm just a diffferentiation question the area will equal 2 * x * e^(-x^2) the answer should be x = (1/sqrt(2)) and area = sqrt(2/e)

I would say you need to show symmetry, asymtopes, the correct concavity (up/down), intercepts and inflexion/stationary points if feasible. if something requires you to solve a cubic don't bother finding the values, just mark down a point. graphs of integrals and derivatives are in the...

there's one at (-1, 2e) EDIT: bah.. my bad

^--- and sometimes a matrix cannot be diagonalized

try mclake he lives near where you are

[cos(2x)]^2 = (1/2)[1 + cos(4x)] so it's primitive is (1/2)[x + (1/4)sin(4x)] + C I will leave you to do the other: hint, expand cos(3x)

what you do is reduce the following to REDUCED row echelon form: 2 5 8 5 1 0 0 0 1 2 3 1 0 1 0 0 2 4 7 2 0 0 1 0 1 3 5 3 0 0 0 1 then the matrix on the right is the inverse. there are otehr ways to do it .. but I think this is the best one in this case and most others

if it is find the integral, just write the answer down if they specified a substitution then show some steps

write the substitution (the u = 3x -1 part), the du = 3dx part is optional unless it's not obvious at all (ie you have to work it out on paper)

that's obviously true... apply the fundamental theorem of arithmetic (each interger has a unique prime number factorisation)

^......Hmm.. no

move it to economics