Unit 3: Proof, Complex Numbers, Vectors & Calculus
VCE Specialist Mathematics Study Design 2023-2027
67 Skills • 3 Levels Each
Units 3 & 4 (Exam-Assessed)
Unit 3 Skill Map
Logic & Proof Advanced, Functions & Graphs Advanced, Complex Numbers Advanced, Vectors in 3D, and Differential Calculus Advanced.
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Logic & Proof Advanced
13 skills
Induction: advanced sums/products21200
Induction: matrix results21201
Induction: divisibility (advanced)21202
Induction: inequality chains21203
Proof with complex numbers21204
Proof with vectors21205
Proof by contradiction (advanced)21206
Geometric proofs using vectors21207
Combinatorial proofs21208
Epsilon-delta concepts21209
Proof of De Moivre theorem21210
Proof involving calculus21211
Constructing multi-step proofs21212
Functions & Graphs Advanced
14 skills
Rational functions (sketch and analyse)21220
Partial fraction decomposition21221
Graphs of rational functions21222
Asymptotes (oblique/curvilinear)21223
Reciprocal function graphs21224
Modulus function and graphs21225
Parametric curves21226
Implicit relations21227
Graph sketching: advanced techniques21228
Domain and range (advanced)21229
Function composition (advanced)21230
Inverse functions (advanced)21231
Piecewise functions21232
Applications of functions21233
Complex Numbers Advanced
11 skills
De Moivre theorem21240
nth roots of unity21241
nth roots of complex numbers21242
Factorisation over C21243
Regions in the complex plane21244
Exponential form (Euler formula)21245
Complex loci (circles, lines)21246
Complex loci (advanced)21247
Trig identities via De Moivre21248
Complex number geometry21249
Fundamental theorem of algebra21250
Vectors in 3D
20 skills
3D vector notation and operations21260
Magnitude in 3D21261
Unit vectors in 3D21262
Dot product in 3D21263
Cross product21264
Properties of cross product21265
Scalar triple product21266
Vector equations of lines in 3D21267
Parametric equations of lines in 3D21268
Cartesian equations of lines in 3D21269
Skew, parallel, intersecting lines21270
Vector equation of a plane21271
Cartesian equation of a plane21272
Normal vector to a plane21273
Distance: point to plane21274
Distance: point to line21275
Intersection of planes21276
Angle between planes21277
Angle between line and plane21278
Vector proofs in 3D21279