Unit 1: Functions, Algebra & Calculus Intro
VCE Mathematical Methods Study Design 2023-2027
77 Skills • 3 Levels Each
Unit 1 Skill Map
Functions & Relations, Algebra, Circular Functions, Introduction to Calculus, and Probability Foundations.
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Functions & Relations
6 skills
Identify domain and range from a graph FREE20001
Express domain and range using interval notation20002
Determine if a relation is a function (vertical line test)20003
Evaluate functions using function notation f(a)20004
Identify key features of graphs (intercepts, turning points, asymptotes)20005
Sketch linear functions and identify gradient/intercept20006
Polynomial Sketching
6 skillsInverse & Power Functions
3 skillsGraph Transformations
5 skillsFunctions & Graphs (Advanced)
4 skillsAlgebra
21 skills
Expand and simplify algebraic expressions20030
Factorise quadratic expressions (monic and non-monic)20031
Factorise by grouping20032
Factorise sum and difference of cubes20033
Simplify algebraic fractions20034
Simplify expressions involving surds20035
Rationalise denominators20036
Apply index laws20037
Convert between index and surd form20038
Solve quadratic equations by factorising20039
Solve quadratic equations using the quadratic formula20040
Solve equations with surds or indices20041
Solve simultaneous equations (linear-linear)20042
Solve simultaneous equations (linear-quadratic)20043
Solve polynomial equations using factor theorem20044
Apply remainder theorem20045
Long division of polynomials20046
Solve literal equations20047
Simplify rational expressions with polynomials20048
Apply the discriminant20049
Solve inequalities involving quadratics20050
Circular Functions Intro
10 skills
Convert between degrees and radians20055
Identify exact values of sin, cos, tan for standard angles20056
Use the unit circle to find values in all four quadrants (ASTC)20057
Use symmetry properties of circular functions20058
Sketch y = sin(x) and y = cos(x) identifying key features20059
Sketch y = tan(x) identifying asymptotes and key features20060
Apply transformations to circular functions20061
Determine amplitude, period, and phase shift from equation20062
Determine amplitude, period, and phase shift from graph20063
Solve trigonometric equations (basic: sin x = k)20064
Introduction to Calculus
6 skills
Calculate average rate of change over an interval20070
Estimate instantaneous rate of change from a graph20071
Interpret rate of change in context20072
Identify intervals where a function is increasing or decreasing20073
Sketch the gradient function from a given graph20074
Trace a pseudocode algorithm (bisection method)20075
Counting & Probability Intro
11 skills
Set notation for events20080
Identify sample spaces20081
Calculate theoretical probability20082
Apply the complement rule20083
Equally likely outcomes20084
Use tree diagrams20085
Interpret Venn diagrams20086
Apply the addition rule20087
Calculate conditional probability20088
Determine if events are independent20089
Apply the multiplication rule20090