# VCE Mathematical Methods Units 1 and 2 – Algebra

2.1 Algebraic Expressions

2.2 Parameters

2.3 Transformations

2.4 Polynomials

2.5 Simultaneous Equations

2.6 Inverse Functions

2.7 Equations

2.8 Exponents

2.9 Logarithms

## Unit 1

This area of study supports students’ work in the ‘Functions and graphs’, ‘Calculus’ and ‘Probability and statistics’ areas of study, and content is to be distributed between Units 1 and 2. In Unit 1 the focus is on the algebra of polynomial functions of low degree and transformations of the plane.

This area of study includes:

- use of symbolic notation to develop algebraic expressions and represent functions, relations, equations and systems of simultaneous equations
- substitution into and manipulation of these expressions
- recognition of equivalent expressions and simplification of algebraic expressions involving different forms of polynomial and power functions, the use of distributive and exponent laws applied to these functions, and manipulation from one form of expression to an equivalent form, including expansion of \( (x + a)^n \) where \( n \in N \)
- use of parameters to represent families of functions and determination of rules of simple functions and relations from given information
- transformations of the plane and application to basic functions and relations by simple combinations of dilations (students should be familiar with both ‘parallel to an axis’ and ‘from an axis’ descriptions), reflections in an axis and translations, including the use of matrices for transformations
- the connection between the roots of a polynomial function, its factors and the horizontal axis intercepts of its graph, including the remainder, factor and rational root theorems
- solution of polynomial equations of low degree, numerically (including a numerical approximation of roots of simple polynomial functions using bisection), graphically and algebraically
- solution of a set of simultaneous linear equations (geometric interpretation only required for two variables) and equations of form \( f(x) = g(x) \) numerically, graphically and algebraically

## Unit 2

This area of study supports students’ work in the ‘Functions and graphs’, ‘Calculus’ and ‘Probability and statistics’ areas of study. In Unit 2 the focus is on the algebra of some simple transcendental functions and transformations of the plane. This area of study provides an opportunity for the revision, further development and application of content prescribed in Unit 1, as well as the study of additional algebra material introduced in the other areas of study in Unit 2 as follows:

- use of inverse functions and transformations to solve equations of the form \( Af(bx) + c = k \), where \( A, b, c, k \in R \) and \( A, b \ne 0 \) and \( f \) is sine, cosine, tangent or \( a^x \) , using exact or approximate values on a given domain
- index (exponent) laws and logarithm laws, including their application to the solution of simple exponential equations
- numerical approximation of roots of cubic polynomial functions using Newton’s method.

*source – VCE Mathematics Study Design*

VCE Mathematical Methods Units 1 and 2 Courses

VCE Mathematical Methods Units 1 and 2 Syllabus

## Course Content

### Algebraic Expressions

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