VCE Specialist Unit 3 Skills () « back to units

The skills below are aligned with the VCE Specialist Mathematics Study Design 2023-2027. Skills are organised into key areas: Logic & Proof Advanced, Functions & Graphs Advanced, Complex Numbers Advanced, Vectors in 3D, and Differential Calculus Advanced. To master a skill, you will have to gain 10 stars.

There are 3 levels to each skill,

  1. Easy: A star will be taken away if you get 3 consecutive wrong answers.
  2. Medium: A star will be taken away if you get 2 consecutive wrong answers.
  3. Hard: A star will be taken away on each wrong answer.

Most skills have multiple types of questions with varying difficulties. If you keep getting wrong answers, the system may give you the simplest question to answer. The idea is to have you master these skills with a ground up approach. If you get an answer wrong, you can read the solution and helpful tips that briefly explain the skill/topic you are practising.

All the best with your VCE Specialist Unit 3. If you see any issue, please do report it by clicking the red button at bottom left of this page.

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  1. Logic & Proof Advanced

    1. Induction: advanced sums/products
    2. Induction: matrix results
    3. Induction: divisibility (advanced)
    4. Induction: inequality chains
    5. Proof with complex numbers
    6. Proof with vectors
    7. Proof by contradiction (advanced)
    8. Geometric proofs using vectors
    9. Combinatorial proofs
    10. Epsilon-delta concepts
    11. Proof of De Moivre theorem
    12. Proof involving calculus
    13. Constructing multi-step proofs

  2. Functions & Graphs Advanced

    1. Rational functions (sketch and analyse)
    2. Partial fraction decomposition
    3. Graphs of rational functions
    4. Asymptotes (oblique/curvilinear)
    5. Reciprocal function graphs
    6. Modulus function and graphs
    7. Parametric curves
    8. Implicit relations
    9. Graph sketching: advanced techniques
    10. Domain and range (advanced)
    11. Function composition (advanced)
    12. Inverse functions (advanced)
    13. Piecewise functions
    14. Applications of functions

  3. Complex Numbers Advanced

    1. De Moivre theorem
    2. nth roots of unity
    3. nth roots of complex numbers
    4. Factorisation over C
    5. Regions in the complex plane
    6. Exponential form (Euler formula)
    7. Complex loci (circles, lines)
    8. Complex loci (advanced)
    9. Trig identities via De Moivre
    10. Complex number geometry
    11. Fundamental theorem of algebra

  4. Vectors in 3D

    1. 3D vector notation and operations
    2. Magnitude in 3D
    3. Unit vectors in 3D
    4. Dot product in 3D
    5. Cross product
    6. Properties of cross product
    7. Scalar triple product
    8. Vector equations of lines in 3D
    9. Parametric equations of lines in 3D
    10. Cartesian equations of lines in 3D
    11. Skew, parallel, intersecting lines
    12. Vector equation of a plane
    13. Cartesian equation of a plane
    14. Normal vector to a plane
    15. Distance: point to plane
    16. Distance: point to line
    17. Intersection of planes
    18. Angle between planes
    19. Angle between line and plane
    20. Vector proofs in 3D

  5. Differential Calculus Advanced

    1. Implicit differentiation
    2. Related rates
    3. Inverse trig derivatives
    4. Parametric differentiation
    5. Second derivatives and concavity
    6. Curve sketching (advanced)
    7. L'Hopital's rule
    8. Mean value theorem
    9. Optimisation (advanced)

Year 12 Semester 1

Unit 3 represents the pinnacle of Year 12 Semester 1 VCE Specialist Mathematics. These skills cover the most challenging and exam-critical topics.

What Makes Unit 3 Special?

Advanced Proof

Induction, contradiction, and multi-step proofs

Complex Analysis

De Moivre, roots of unity, and complex loci

3D Vectors

Lines, planes, cross products, and 3D geometry

Calculus

Implicit differentiation, related rates, and optimisation

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