Specialist Mathematics Subject Outline — Stage 2 (2017)
Specialist Mathematics Subject Outline — Stage 2 (for teaching in 2017)
ACARA
Course content
Topics
Topic 1: Mathematical Induction /Induction Notes
Topic 2: Complex Numbers
Topic 3: Functions and Sketching Graphs
Topic 4: Vectors in Three Dimensions
Topic 5: Integration Techniques and Applications
Topic 6: Rates of Change and Differential Equations.
2016 Specialist Mathematics Examination Paper
Assessment
Students demonstrate evidence of their learning through the following assessment types:
School-based Assessment | Weighting |
Skills and Applications Tasks | 45% |
Folio | 22% |
External Assessment | |
Examination | 30% |
Year 12 Specialist Mathematics
1 | TRIGONOMETRIC PRELIMINARIES | 9 | |
A | Terminology and radian measure | 11 | |
B | Periodic functions from circles | 13 | |
C | Transforming trigonometric functions | 21 | |
D | Trigonometric identities | 29 | |
E | Sine and cosine equations | 33 | |
F | Review | 36 | |
2 | COMPLEX NUMBERS | 39 | |
A | Complex numbers | 41 | |
B | Complex conjugates | 48 | |
C | The number plane | 50 | |
D | Polar form | 57 | |
E | Complex sets and their graphs | 65 | |
F | DeMoivre’s theorem | 68 | |
G | Solving zn = C | 70 | |
H | Review | 74 | |
3 | REAL POLYNOMIALS | 79 | |
A | Operations with polynomials (Review) | 80 | |
B | Division of polynomials | 82 | |
C | Roots, zeros and factors | 87 | |
D | Polynomial equality | 89 | |
E | The remainder theorem | 93 | |
F | Graphing cubics and quartics | 97 | |
G | Zero, root and factor finding | 104 | |
H | Factoring | 108 | |
I | Cubic and quartic problem solving | 110 | |
J | Quadratic iterations | 111 | |
K | Review | 121 | |
4 | 3-DIMENSIONAL VECTOR GEOMETRY | 125 | |
A | 3-dimensional coordinates | 126 | |
B | 3-dimensional vectors | 130 | |
C | Geometric representation | 131 | |
D | Operations with vectors | 133 | |
E | Parallelism and unit vectors | 137 | |
F | The scalar product | 142 | |
G | Vector product | 147 | |
H | Areas and volumes | 153 | |
I | Lines in space | 156 | |
J | Planes | 164 | |
K | The intersection of two or more planes | 169 | |
L | Review | 171 | |
5 | GEOMETRY (VECTOR AND DEDUCTIVE PROOF) | 175 | |
A | Vector proof | 176 | |
B | Circle geometry | 184 | |
C | Review | 202 | |
6 | CALCULUS | 205 | |
A | Functions of time | 206 | |
B | Pairs of uniformly varying quantities | 210 | |
C | Pairs of non-uniformly varying quantities | 212 | |
D | Discovering derivatives of circular functions | 221 | |
E | Using parametric forms | 223 | |
F | Related rates | 226 | |
G | Review | 232 | |
7 | TRIGONOMETRIC CALCULUS | 235 | |
A | Derivatives of trigonometric functions | 236 | |
B | Maxima/minima with trigonometry | 243 | |
C | Further related rates problems | 247 | |
D | Trigonometric integration | 250 | |
E | Review | 263 | |
8 | DIFFERENTIAL EQUATIONS | 269 | |
A | Introduction to differential equations | 271 | |
B | Obtaining differential equations | 277 | |
C | Slope fields and solutions of | 280 | |
D | Separable differential equations | 286 | |
E | Problem solving | 291 | |
F | Relative growth and the logistic equation | 300 | |
G | Review | 309 | |
9 | SYSTEMS OF DIFFERENTIAL EQUATIONS | 315 | |
A | Further physical examples | 318 | |
B | Solving second order differential equations | 325 | |
C | Solution to linear systems of differential equations | 330 | |
D | Problem solving | 335 | |
E | Slope field for general systems | 338 | |
F | Review |