UniGeniusHSC Maths Extension 2

HSC Maths Extension 2

HSC Maths Extension 2 practice questions

Original questions for all five focus areas: Section I questions where each wrong option names its slip, and Section II written responses in parts, with proofs, follow-through from earlier parts and every step marked.

The paperOne written paper, 100 marks, 3 hours plus 10 minutes reading time
Section IObjective-response questions worth 10 marks
Section II90 marks in 37 to 42 items; at least two items worth 4 or 5 marks
ProvidedA reference sheet; NESA-approved calculators may be used

Try 4 questions

  1. Section I · 1 mark · Complex numbers: arithmetic and polar form

    Let z=5−12iz = 5 - 12 i. What is Im(1z)\mathrm{Im}\left(\dfrac{1}{z}\right)?
    Answer it, every step marked

  2. Section II · 7 marks · Complex numbers: arithmetic and polar form

    Let z=3+4iz = 3 + 4 i and w=1−2iw = 1 - 2 i.
    Answer it, every step marked

  3. Section I · 1 mark · Complex numbers: arithmetic and polar form

    What are the two square roots of −5+12i-5 + 12 i?
    Answer it, every step marked

  4. Section II · 9 marks · Complex numbers: arithmetic and polar form

    Let z=−3+iz = -\sqrt{3} + i and w=1+iw = 1 + i.
    Answer it, every step marked

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Are these past HSC questions?

No. Every question is original, written for the 2024 syllabus, first examined in 2027.