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as a counterexample for b; v=1i+1j u=10i+20j

most of the big tutoring centers do not work well for people who are actually struggling with maths - the pace is way too fast, their actual problems can't really be worked on (most common one i see is algebra), and since most centers work at least a term ahead, once they decide they need help...

Q14 (a) Let n=2k+1 (odd) where k is a positive integer. Let n consecutive numbers be a+1, a+2, a+3, ..., a+n for some integer a. The sum of these is; a+1+a+2+a+3+\dots+a+n = \\ na+(1+2+3+\dots+n) = \\ (2k+1)a+(1+2+3+\dots+2k+2k+1) = \\(2k+1)a+(1+2k) + (2+2k-1) + (3+2k-2) + \dots + (k+k+1) +...

the best i am capable of at the end of the day originally 96+, then 98+, now 99+ is in reach

\ni is generally used as "such that", as in "under the condition that", often used interchangebly with :. That would make the first statement read "for all positive integers a, under the condition that b is a positive integer, such that b = a^3". However this makes no definition of b (and little...

No, given the stupidity of some people these days, some disgruntled students would go out of their way to abuse and threaten the examination writers. This already happens to some extent for eg english short answer stimuli authors.

I should clarify - I meant for senior years (Y11/Y12). A lot of these concepts are beneficial to learning if used correctly, but are mostly useless at y11/y12.

From what I've seen Du goes heavily out of syllabus on many topics - none of these are in the current syllabus. No school that I know of teaches these topics & they will never be tested in the HSC

Just to add to that, on the other hand, if you're managing to get to a high band 6 range and you don't feel particularly weak in any content areas, then I've personally found it more beneficial to do whole papers - it helps with speed and silly mistakes, which are probably where you're losing...

hi chatgpt asafoetida, this unsubstantive response should be ignored

yep, as a general rule, you only need use cases if something is dependent on something else. for example, if placing the consonants affected placing of vowels, or smth like that

There are 4 places to place the vowels. Ordering those: 4!/2! There are 5 places to place the consonants. Ordering those: 5! Hence there are 4!*5!/2! = 1440 ways. What drew you to use cases for this question?

Trials is just another internal assessment (that your school gives you) that affects your internal rank. Your final internal rank includes trials.

the marks of a cohort on average is very rarely indicative of the bottom % of a cohort, particularly in the case of the HSC due to the way alignment works. i wouldn't be surprised if for the top ~40 schools, the difference in the lowest atar is the strength of academic support & intervention...

The particle has uniform speed, but not uniform velocity, since direction is constantly changing (and velocity is the vector, speed is the scalar). Kinetic energy is a scalar. Momentum is a vector. (Physics isn't very rigorous about the following) Technically, in the kinetic energy formula, we...

Pretty sure that one of the UNSW scholarships is basically = Dux. Academic achievement award? The scholarship website seems to be a bit broken right now. Regardless of this, no one cares about your year 10 results whatsoever, so you shouldn't stress about not coming third for y10 lol.

Hmm, that graph is less than amazing at depicting it, its pretty hard to see. If you look at just after the two minute mark, in the single grid length, all of a sudden, the equilibrium moves more quickly toward the same equilibrium position it was destined to to begin with. Remember that a...

how many units are you currently taking, and why do you wish to change the subjects? what is your goal for after school/atar (if applicable)? in 98% of schools it is effectively impossible to pick up a subject this late. there is no way for them to teach and assess the year 11 course, and nesa...

i didn't say the concentration of a solid or liquid increases, i just said more of it is made. because for a solid or liquid the concentration is fixed; a particular amount occupies a certain amount of space for an aqueous substance or a gas, more particles of the substance can (usually) be put...

Shifting to one side means that the equilibrium will produce more of the species on that side. So there would be more water & solid carbon in the equilibrium