HSC Maths Extension 2 Section II

Section II is 90 marks of written responses in 37 to 42 items, some of them in parts; at least two items are worth 4 or 5 marks. Show relevant reasoning and calculations: the marks are for the working as well as the answer.

The paper	One written paper, 100 marks, 3 hours plus 10 minutes reading time
Section I	Objective-response questions worth 10 marks
Section II	90 marks in 37 to 42 items; at least two items worth 4 or 5 marks
Provided	A reference sheet; NESA-approved calculators may be used

About 160 minutes

At 1.8 minutes a mark, Section II is worth about 162 minutes. A 4-mark part deserves about seven minutes: enough to write every step of a proof, not enough to try three methods.

Proofs and show-that parts

Write the base case, the inductive step and the conclusion of an induction proof in full.
In a show-that part, reach the given result one line at a time without assuming it; the result is given so you can use it in the next part.
Later parts often use an earlier answer: say which value you used.
Give exact values unless the part asks for a decimal, and then to the accuracy it asks for.

Try 3 questions

Section II · 7 marks · Complex numbers: arithmetic and polar form
Let $z = 3 + 4 i$ and $w = 1 - 2 i$ .
Answer it, every step marked
Section II · 9 marks · Complex numbers: arithmetic and polar form
Let $z = -\sqrt{3} + i$ and $w = 1 + i$ .
Answer it, every step marked
Section II · 9 marks · Complex numbers: arithmetic and polar form
Let $z_1 = r_1(\cos\theta_1 + i \sin\theta_1)$ and $z_2 = r_2(\cos\theta_2 + i \sin\theta_2)$ , where $r_1 > 0$ , $r_2 > 0$ and $\theta_1$ , $\theta_2$ are real.
Answer it, every step marked

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Questions people ask

How many marks is Section II?

90 marks, in 37 to 42 items. At least two items are worth 4 or 5 marks.

How long is the paper?

3 hours plus 10 minutes reading time, for 100 marks: Section I is 10 marks and Section II is 90.