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From Cambridge, "To find a definite integral by first principles, dissect the interval into n equal subintervals, construct upper and lower rectangles on each subinterval, and find the sums of the upper and lower rectangles. Then their common limit will be the value of the integral." My...

I don't know much about university but is there a difference in terms of career prospects if you average a credit vs high distinction? I heard employers don't really look at your marks :S

You can determine the direction of eddy currents according to Lenz's law. E.g. If a metal sheet is losing flux into the page, it will experience induced eddy currents in a clockwise direction to replace it. However, this doesn't make sense to me logically. :S Consider a straight...

I want to use the holidays to perfect my subjects (especially in physics and chemistry) and was wondering how vital are notes? I don't write them because I feel like what I learn becomes... almost instinctive; natural. Except maybe for some pure theory e.g. history of periodic table. Has anyone...

I was looking at 4u solutions of Terry Lee and noticed he did "Σ a" to denote sum of single roots and furthermore "Σ ab" to denote sum of products of two roots at a time, etc. I.e. Σ a = -b/a Σ ab = c/a . . . How valid is this in 3u? I always wrote out in words "by sum of single roots" :S

Use the sum and product of roots to evaluate: i. cos 2pi/9 + cos 4pi/9 - cos pi/9 This question doesn't make much sense to me as it doesn't look like a traditional polynomial. Give me a hint please (direction) :)

Hi, I don't understand this section of the belonging rubric: "Texts explore many aspects of belonging, including the potential of the individual to enrich or challenge a community or group. Could someone explain this to me? Thanks!

If magnetic field strength is the amount of magnetic flux per unit square, how can we define magnetic field strength at a point within a magnetic field? :S

When calculating the value of g with the motion of a pendulum, why must I consider the the arc angle (the angle string makes with vertical when released from rest)? Sources say to keep it within ~30 degrees but can someone tell me why?

Hi, can someone help me with the following questions :) Illustrate on the Argand diagram the following regions: a) 1 <= |z| <= |z-i| b) |z+i| + |z-i| = 4 for a) I had two circles of radius 1 with centres 0,0 and 0,1 however I don't know how to go from here...

State-rankers, high achievers, and olympiads: How did you find school? Your natural talent and passion for a subject converges into curiosity which you wish you satisfy. You begin to explore; your knowledge surpasses the HSC syllabus, dwelling into (low)-level university content. But you don't...

Hi, I encountered this question that I cannot do: The nth term of a series is given by Tn = 1/(2n-1)(2n+1). Explain why the sum of the first n terms of the series is n/(2n+1). So I listed Sn = 1/3 + 1/15 + 1/35 + ... + 1/(2n-1)(2n+1) There is no common ratio/difference :S Then I tried to...

I am having trouble consolidating my proof. The question is not one of difficulty, but there is a small aspect I'd like to inquire about, so quickly: Question: Prove 2^n > n^2 for all n >= 5 *Base case holds* Suppose n = k true, where integer k>= 5 i.e. 2^k > k^2 Problem starts here For n =...