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1. I'm going to assume you're talking about this diagram from Q25 in Exercise 14E i) You must move down a total of 6 times, and right a total of 4 times for a total of 10 moves. The order in which 6 down moves can be placed into a seqeuence of 10 moves is \binom{10}{6} =210 . You may also...

Firstly, vector diagrams always help. Here is one for this situation The blue line is line l The projection is the vector from A to the intersection of the purple and blue lines in the bottom right The purple line is the 'perpendicular distance' we aim to solve for The black line is vector AP...

Alternatively, by a geometrical method; This diagram illustrates the situation. Then you must prove the two angles in red are equal because the bottom angle in red is arg(z+1), and the two angles combined are arg(z), making Arg(z) = 2arg(z+1) The lower red angle is equal to the green angle by...

@pheii Schools generally timetable 2u, 3u and 4u math in their own seperate periods. This means tests throughout the year happen whenever you have that subject period, definitely not at the same time. Trials and HSC exams are also planned with the consideration that some students do more than...

To find the limit in (a) \frac{}{}1^3 + 2^3 + 3^3 ... + n^3 = \frac{n^2(n+1)^2}{4}\\ \frac{1^3 + 2^3 + 3^3 ... + n^3}{n^4} = \frac{n^2(n+1)^2}{4n^4} =\displaystyle \lim_{n \to infinity}\frac{n^2+2n+1}{4n^2} =\displaystyle \lim_{n \to infinity}\frac{1}{4}+\frac{1}{2n}+\frac{1}{4n^2} The two...

Some pointers; Intro Make it clear why police are important (i.e. prevent crime situationally, investigate crime) These powers can be used through LEPRA, you may also list some powers such as the ability to arrest individuals and gather evidence Brief mention of issues with police powers -...

I make notes under the dot points of 'students learn about', and then practice the questions under 'students learn to'. That 2nd column is very directive and is very good for writing practice essays on. It's almost a checklist - can you sufficiently respond to and elaborate on those 'students...

Are you referring to the death of Roberto Curti (2010)? I literally just say 'Death of Roberto Curti' when referencing it, I don't know the case name.

@amdspotter |z-a| = |z-b| is a locus of numbers where the distance to a is the distance to b, for any point on the locus. Obviously the midpoint of a and b is included, and it follows that the perpendicular bisector of the a and b retains the same distance from a and b.

At the very least, part (iii) is more than just writing the answer, because you would write \frac{6}{1-i} and then have to realise the denominator. For (i) and (ii) it never hurts to put more information if you're afraid of losing a mark.

You were on the right track with equating parts; x^2 - y^2 = 0 x^2 = y^2 Suggesting that the Real and Imaginary parts of your root will be equal or opposite in sign. 2xy = 1 xy = 1/2 Hence, x = y = \frac{1}{\sqrt{2}} or x = y = -\frac{1}{\sqrt{2}} This can be verified by thinking about roots...

Could anyone provide feedback for my practice crime essay? I handwrote it in 40 minutes under exam conditions (but have typed it up now to make it easier to read). The question was... Assess the effectiveness of the criminal investigation process as a means of achieving justice. (straight from...

I have an FX 82-AU and it can do complex. It involves using the buttons 'POL' (polar form) and 'REC' (rectangular form).

Treat it as (1+(2x-x^2))^5 Then use the methods you would use for any (1 + x)^n expansion. You may end up having to apply BE multiple times. Hopefully someone can provide a more efficient method.

I could get this far using an internet archive link. Whether the actual pages for resources are archived or not is something that you'll have to try yourself, because most pages are dead ends. https://web.archive.org/web/20201128121522/http://139.99.203.12/yr12/adt-resources/Resource-Collection/

Disagree. Just because most students slacked off does not mean that every teacher had an easy lockdown. Maybe it became a bludge for some lazy teachers, but I know a lot of year advisors and head teachers had a lot of stress.

It just died on you without any warning? That's pretty scary. Are you sure the screen wasn't fading or there wasn't any other indication of low battery?

So it seems a single essay for each chapter is ineffective. What should I aim to make each plan based on instead? I was thinking of commonly asked broad essay questions, and then doing about 2-3 essay plans for each chapter.

My plan for making eco essay plans is to focus on just a single 'central essay' for each chapter. It would be a very broad question that I can easily adapt. For example, my economic growth central essay would be; Explain the causes and effects of economic growth in the last 10 years, as well as...

Looking at past scanned papers of student reponses, the parts outside of those bolded borders in the corners are generally included, but that grey area is not.