A-Level Maths AQA 7357

Locate roots of $f(x) = 0$ by considering changes of sign of $f(x)$ in an interval of $x$ on which $f(x)$ is sufficiently well-behaved.

Understand how change of sign methods can fail.

Solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams.

Solve equations using the Newton-Raphson method and other recurrence relations of the form $x_{n+1} = g(x_n).$

Understand how such methods can fail.

Understand and use numerical integration of functions, including the use of the trapezium rule and estimating the approximate area under a curve and limits that it must lie between.

Use numerical methods to solve problems in context.