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Thats exactly right. I know im wrong, but i dont want to result to calculators

I didnt halve. I integrated over the full contour defined, got the integral over the two semi circles =0, applied let z=-z then combined the integrals to get limits epsilon to R. In the process you get these other integrals, some which go to zero, and some which go to, collectively, pi cubed on...

I cannot believe I forgot to say this. Contour defined on epsilon <= |z| <= R, epsilon goes to 0 and R goes to infinity. If you integrate over the full contour you would get 0 according to jordans lemma

Using the method I suggested, you would get alpha > some real value. Then you would notice the vector from the mans top to the building top has a magnitude to be determined, height of building from mans perspective is 13 (15 - height of man) with horizontal path 20. Call top of building width x...

For second bit (question is blurry so I cant provide direct links), write I n-1 in terms of the recurrence, then I n-2 and provide a few more examples. You will notice that a factorial sequence starts, and then youre done. Try proving gamma function = (x-1)!, its much easier btw.

Can someone please help with the question above, but replace ln( x ) with ln^2 (x). I am asked to prove it equals pi cubed on 8, but when I calculate residue, this is what I get up (maybe with negative) until i apply contour integration, to which the integral converges to 0. Also, you must use...

Polynomials arent in 4u unless complex numbers. Only 3u real polynomials.

I recommend you dont memorise formulae, instead learn how to deduce them. Nearly every year projectiles you are asked to first prove a formula then use it. As for the question above, use horizontal range to find an expression for range and solve for horizontal range > 20, then test for which...

Literally just substitue the line equation and solve for lambda in |v - c| = r for i, then for ii make a sphere of radius r and centre a, b, c, then use vector rules to find expressions for other points in the question, sub into the formula and prove that it equals 0. Just tests the theory...

I will look at 2.1 and 2.2 later when I have a bit more time. 2.3 a) There is statistical evidence that there is a difference. b) If it were an experiment, the elderly people would know that this was being undertaken, and the Hawthorne effect would therefore be evident (Hawthorne effect is...

What happens to the answers we submit? Do we get them back? I know I have asked quite some questions on this exam, but I am just really intrigued and hope it continues this year for the experience. Sorry 🤣

Thank you so much!!! Can I ask, do you follow a process of moderation when marking the BOS trials, or do we get raw marks?

The 4 unit vectors component is titled 'Vectors and Vector Equations of Lines' in the NESA syllabus. This does not say anything about planes, and nor do the subsequent outcomes. The only condition under which a plane can be examined is when referring to a plane as the equation of 'locus' of...

Wouldnt there then be uncertainty when entering HSC exams as to whether or not you have covered content? There are no explicit outcomes which assess planes or surfaces/cylinders, which therefore implies that is left to calculus 3. Why teach it if you could spend time polishing useful content? I...

A teacher that I know is teaching his class planes, and some of my friends are learning planes. Im also fairly sure they are not directly in the syllabus, so could be extension work.

Would you say that cambridge covers enough of planes to get through this syllabus successfully? I think 'prove geometric results in the plane' does not specifically refer to planes in 3D, instead refers to the whole 3D system itself (R3), and constructing proofs would be vector geometric proofs...

Would you recommend cambridge for this syllabus, given its the first year?

I dont either. Someone had said they are learning it, and a teacher told me he is teaching it. From what I know, lines were in the syllabus.

Hello, I have the Fitzpatrick Mathematics Extension 2 textbook for the new syllabus, however the topic planes is missing from the vectors chapter. Would anyone using the Cambridge textbook recommend this textbook for the new syllabus? Also, does it cover planes in vectors? One last question...

Would it still be possible to run an exam, whether or not is tests all content, regardless of situation and in a supervised environment? Restrictions would have definitely gone down by then, so it would be possible to formulate a system of assessments. If not, it can be a possibility to split up...