P3.6 - Numerical methods

Location of roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x in which f(x) is continuous.

Use locating roots using sign changes to connect the rule to the data and decision in the question.

This matters because locating roots using sign changes determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply locating roots using sign changes to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Locating roots using sign changes is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Approximate solution of equations Solution of equations by use of iterative procedures, for using simple iterative methods, which leads will be given. including recurrence relations of the form x = f(x) n + 1 n.

Use iteration and approximate equation solving to connect the rule to the data and decision in the question.

This matters because iteration and approximate equation solving determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply iteration and approximate equation solving to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.