Specialist Mathematics

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