Unit 2: Trigonometry, Vectors & Complex Numbers
VCE Specialist Mathematics Study Design 2023-2027
Units 1 & 2 (School-Assessed)
58 Skills • 3 Levels Each
Unit 2 Skill Map
Simulation, Sampling & Sampling Distributions, Trigonometry & Reciprocal Functions, Transformations of the Plane, Vectors in the Plane (2D), and Complex Numbers (Introduction).
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Simulation, Sampling & Sampling Distributions
5 skillsTrigonometry & Reciprocal Functions
14 skills
Sketch graphs of sec(x), csc(x), cot(x) and identify key features21110
Evaluate reciprocal trig functions for standard angles21111
Identify domain, range, and asymptotes of reciprocal trig functions21112
Sketch the modulus function |f(x)| from f(x)21113
Solve equations involving |f(x)| = k21114
Identify and sketch conics: parabolas (general form)21115
Identify and sketch conics: ellipses21116
Identify and sketch conics: hyperbolas21117
Determine the locus of points satisfying a given condition21118
Convert between parametric and Cartesian equations21119
Sketch curves given by parametric equations21120
Convert between Cartesian and polar coordinates21121
Sketch curves in polar coordinates21122
Identify polar forms of common curves (cardioid, rose, spiral)21123
Transformations of the Plane
10 skills
Represent a linear transformation as a 2x2 matrix21130
Apply rotation matrices for angle theta21131
Apply reflection matrices in lines through the origin21132
Apply dilation and shear transformation matrices21133
Find the composition of two linear transformations21134
Find the inverse of a linear transformation21135
Apply a transformation to a graph or region21136
Calculate the area scale factor using the determinant21137
Determine invariant points and lines of a transformation21138
Describe the geometric effect of a given transformation matrix21139
Vectors in the Plane (2D)
15 skills
Represent vectors graphically and in component form21145
Perform vector addition and subtraction (graphical and algebraic)21146
Perform scalar multiplication of vectors21147
Calculate the magnitude of a vector21148
Find unit vectors21149
Calculate the scalar (dot) product of two vectors21150
Find the angle between two vectors using the dot product21151
Determine if vectors are perpendicular using the dot product21152
Calculate scalar and vector projections21153
Resolve a vector into rectangular components21154
Prove geometric results using vectors (midpoints, parallelograms)21155
Apply vectors to displacement and velocity problems21156
Apply vectors to relative velocity problems21157
Apply vectors to forces and equilibrium (statics)21158
Introduction to vectors in 3D (i, j, k components)21159
Complex Numbers (Introduction)
14 skills
Define i and express complex numbers in Cartesian form a + bi21165
Perform addition and subtraction of complex numbers21166
Perform multiplication of complex numbers21167
Perform division of complex numbers (multiply by conjugate)21168
Find the complex conjugate and its properties21169
Plot complex numbers on an Argand diagram21170
Calculate the modulus of a complex number21171
Calculate the argument of a complex number21172
Convert between Cartesian and polar form (r cis theta)21173
Multiply and divide in polar form21174
Solve quadratic equations with complex roots21175
Solve polynomial equations over C (factor theorem)21176
Sketch subsets and regions of the complex plane21177
Verify conjugate root theorem for polynomials with real coefficients21178