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 skills

Distinguish population parameters from sample statistics21105 Simulate random sampling using pseudocode21106 Describe the distribution of sample proportions21107 Understand variability between samples21108 Estimate population parameters from sample data21109

Trigonometry & 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)