In terms of the HSC exam, integration and complex are the most straight foward.
Polynomials seem easiy but some of the "prove this identity" are quite confusing and are generally more likely to come up as a harder question in the HSC.
In summary:
-Integration, HSC componenet has been the most straightforward (question 1)
-Complex, similar to integration. May have a more interesting part.
-Curve Sketching, what can I say? Annoys me because I tend to be to fussy when drawing my diagrams.
-Mechancs. HSC questions haven't seemed to difficult compared to ones from text books.
-Polyomials, farily straight foward. Some proofs may be "interesting".
-Harder 3u, fun proofs.
-Conics, easy to grasp. Algebra bashing makes it hard. Some proofs are elegant though. (see below)
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Consider the ellipse E, of equation x²/a² + y²/b² = 1, with centre O, and let P (x1, y1) and Q (x2, y2) be two points on E.
a) Sketch the ellipse given a>b>0.
b) Prove that the equation of the tangent to the ellispe at P is: xx1/a² + yy1/b² = 1
c) The tangents at P and Q intersect at T. Find the coordinates of T.
d) Let M be the midpoint of PQ. Show that T lies on OM produced.
e) Given that R is a point on E such that QR is a diameter of the ellipse, and that RP produced intersects QT produced at N, show that T is the midpoint of QN, with or without the use of part (d)