#3.1
Be able to add, subtract, multiply and divide polynomials.
Expanding brackets and collecting like terms.
[Excludes: Division by non-linear expressions.]
#3.2
Understand the factor theorem and be able to use it to factorise a polynomial or to determine its zeros.
\(f(a)=0 \iff (x - a)\) is a factor of \(f(x)\).
Including when solving a polynomial equation.
[Excludes: Equations of degree > 4.]
#3.3
Understand the definition of a function, and be able to use the associated language.
A function is a mapping from the domain to the range such that for each \(x\) in the domain, there is a unique \(y\) in the range with \(f(x) = y\). The range is the set of all possible values of \(f(x)\).
Notation: Many-to-one, one-to-one, domain, range, \(f:x→y\)
#3.4
Understand and use composite functions.
Includes finding the correct domain of \(gf\) given the domains of \(f\) and \(g\).
Notation: gf(x)
#3.5
Understand and be able to use inverse functions and their graphs.
Know the conditions necessary for the inverse of a function to exist and how to find it.
Includes using reflection in the line \(y = x\) and finding domain and range of an inverse function.
e.g. \(\ln{x}~(x > 0)\) is the inverse of \(e^x\).
Notation: \(f^{-1}(x)\)
#3.6
Understand and be able to use the modulus function.
Graphs of the modulus of linear functions involving a single modulus sign.
#3.7
Be able to solve simple inequalities containing a modulus sign.
Including the use of inequalities of the form \(|x - a| ≤ b\) to express upper and lower bounds, \(a \pm b\), for the value of \(x\).
[Excludes: Inequalities involving more than one modulus sign or modulus of non-linear functions.]
#3.8
Be able to use functions in modelling.
Including consideration of limitations and refinements of the models.