This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Find the remainder when dividing two polynomials, by algebraic long division.

This question tests the student's ability to find remainders using the remainder theorem. 

Apply the factor and remainder theorems to manipulate polynomial expressions

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Finding the coordinates and determining the nature of the stationary points on a polynomial function

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Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

From mathcentre.ac.uk

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Integration techniques for monomials and simple polynomials.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Using the chain rule with polynomials and negative powers

A basic introduction to differentiation

A basic introduction to differentiation

Quotient and remainder, polynomial division.

A worked example about polynomials. 

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

This question tests the student's ability to find remainders using the remainder theorem. 

A worked example about polynomials.