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.

Live

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 skills

Sketch quadratic functions (turning point form)20007 Sketch quadratic functions (factored form)20008 Sketch quadratic functions (general form)20009 Sketch cubic functions (factorisable)20010 Sketch quartic functions (factorisable)20011 Sketch power functions20012

Inverse & Power Functions

3 skills

Identify graphs of power functions20013 Find the inverse of a function algebraically20014 Sketch inverse functions by reflecting in y = x20015

Graph Transformations

5 skills

Apply translations to graphs (horizontal and vertical shifts)20016 Apply dilations to graphs (stretches and compressions)20017 Apply reflections to graphs (x-axis and y-axis)20018 Determine the equation from a transformed graph20019 Combine transformations in correct order20020

Functions & Graphs (Advanced)

4 skills

Match equation to graph (polynomial family)20021 Identify odd and even functions20022 Determine axis intercepts of polynomial functions20023 Sketch piecewise-defined functions20024

Algebra

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