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Alternatively, note that the area of the region enclosed between the lines y = 4 and y = 1 - x in the second quadrant is simply the area of an isosceles right triangle with side length 3 (why?). This will give the desired result.

MATH2621 Ease: 8/10. One of the easier MATH courses to take and a good choice for an elective. Class tests and final were straightforward but you need to be careful of the slightly harsh marking criteria (easy to lose marks if you miss certain things). Content: 8/10. Complex Numbers mixed in...

Let p be the premium the individual is willing to pay so that he is indifferent between paying for the insurance or losing a random amount X following some distribution. We want find such a p such that E[u(w-p)] = E[u(w-X)]. Since the LHS expression is simply the expectation of a deterministic...

Re: HSC 2016 4U Marathon - Advanced Level For 4k+2 The square of an even number is always divisible by 4 and so no number of the form 4k+2=4(k+\frac{1}{2}) , where k is a positive integer, can be a perfect square. For 4k+3 , since this always odd for any positive integer k , for it to...

Re: HSC 2016 4U Marathon - Advanced Level I got one solution to be p(x)=x^{k} (x-1)^k for k\in\mathbb{Z}^+ , but I don't know if that's all the possible solutions.

Currently have exams atm, but I'll write up a more detailed response covering what you do in first-year maths and beyond (for UNSW at least). As Paradox said, maths as a discipline is immensely huge and everything you do will be done step-by-step and with an increased level of rigour (esp. from...

Re: HSC 2016 3U Marathon ANSWER: 1.41246953 \times 10^{30} NEW QUESTION: Prove that \dfrac{\text{d}}{\text{d}x}(\tan{x})=\sec^{2}x from first principles.

Re: HSC 2016 MX2 Combinatorics Marathon Good point, I'll get that fixed. Umm, about the answers, putting in white coloured font (or in a spoiler box) is optional but because people will be explaining how they get to answers in the first place, I'd say it's not necessary. But still a good option.

Re: HSC 2016 MX2 Combinatorics Marathon For (a) you are close, but you forgot to consider all the possibilities in which 'MATHS' can go. Treat 'MATHS' as one letter, then you have 4 places to arrange your 'letters' including the sub word 'letter' 'MATHS'. Pick 2 places in which 'MATHS' can go...

This thread is to encourage you to post all your harder Probability + Permutations & Combinations questions here. Some Things to Consider: 1. Please answer one question at a time. 2. When posting a new question, please make it clear that it is a new question (write in capital letters 'NEW...

What was Q16 about?

Re: HSC 2015 4U Marathon NEW QUESTION: Prove that a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

Re: HSC 2015 4U Marathon Yep, you're method is fine. Here's mine (similiar): Since we have n>3 , we have the following: Case 1: Let n=3k for some positive integer k>1 . Then n is divisible by 3 and we are done. Case 2: Let n=3k+1 for some positive integer k>1 . Then n+2=3k+3 is...

Re: HSC 2015 2U Marathon Basic Idea is a^{0}=1 for a \neq{0} , 1^{n}=1 for all integers n and (-1)^{n}=1 for all even integers n .

Can't distinguish between the B and E labels, please put a clearer image next time :). Does it ask for area ABC or area AEC?

Re: HSC 2015 4U Marathon Prove that if n is a positive integer such that n>3 , then at least one of n , n+2 or n+4 is composite.

Re: HSC 2015 2U Marathon NEW QUESTION: Find the exact value of m for which the graphs y=mx and y=\dfrac{e^x}{x} have a common tangent at their point of contact.

Re: HSC 2015 2U Marathon f(x)=4x+3

Re: HSC 2015 2U Marathon :p

Re: HSC 2015 2U Marathon x=-2,1,3