# VCE Mathematical Methods Units 3 and 4 – Algebra

2.1 Polynomials

2.2 Inverse Functions

2.3 Inverse Trigonometric Functions

2.4 Functions

2.5 Trigonometric Graphs

2.6 Simultaneous Equations

In this area of study students cover the algebra of functions, including composition of functions, simple functional relations, inverse functions and the solution of equations. They also study the identification of appropriate solution processes for solving equations, and systems of simultaneous equations, presented in various forms. Students also cover recognition of equations and systems of equations that are solvable using inverse operations or factorisation, and the use of graphical and numerical approaches for problems involving equations where exact value solutions are not required or which are not solvable by other methods. This content is to be incorporated as applicable to the other areas of study.

This area of study includes:

- review of algebra of polynomials, equating coefficients and solution of polynomial equations with real coefficients of degree n having up to \(n\) real solutions
- use of simple functional relations such as \( f(x + k) = f(x), f (x^n) = nf(x), f(x) + f(–x) = 0, f(xy) = f(x)f(y) \), to characterise properties of functions including periodicity and symmetry, and to specify algebraic equivalence, including the exponent and logarithm laws
- functions and their inverses, including conditions for the existence of an inverse function, and use of inverse functions to solve equations involving exponential, logarithmic, circular and power functions
- composition of functions, where f composition g is defined by \( f(g(x)) \), given \( r_g ⊆ d_f \) (the notation \( f \circ g \) may be used, but is not required)
- solution of equations of the form \( f(x)= g(x) \) over a specified interval, where \(f\) and \(g\) are functions of the type specified in the ‘Functions and graphs’ area of study, by graphical, numerical and algebraic methods, as applicable
- solution of literal equations and general solution of equations involving a single parameter
- solution of simple systems of simultaneous linear equations, including consideration of cases where no solution or an infinite number of possible solutions exist (geometric interpretation only required for two equations in two variables).

*source – VCE Mathematics Study Design*

VCE Mathematical Methods Units 3 and 4 Courses

VCE Mathematical Methods Units 3 and 4 Syllabus

## Course Content

### Polynomials

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