A-Level Maths OCR B (MEI) H640

Be able to add, subtract, multiply and divide polynomials.

Expanding brackets and collecting like terms.

[Excludes: Division by non-linear expressions.]

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.]

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, $f:x→y$

Understand and use composite functions.

Includes finding the correct domain of $gf$ given the domains of $f$ and $g$.

Notation:

• $gf(x)$

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:

• $f^{-1}(x)$

Understand and be able to use the modulus function.

Graphs of the modulus of linear functions involving a single modulus sign.

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.]

Be able to use functions in modelling.

Including consideration of limitations and refinements of the models.