# Specialist Mathematics Specialist Mathematics Subject Outline — Stage 2 (2017)

Specialist Mathematics Subject Outline — Stage 2 (for teaching in 2017)

## Course content

Topics

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