MathematicsChapter 10: Numerical Methods
Bisection Stopping Criteria
Stop when interval width or function value meets the required tolerance; report an honest precision.
Learning objectives
- State the rule for bisection stopping criteria.
- Solve a bisection stopping criteria problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Stop when interval width or function value meets the required tolerance; report an honest precision.
Where / symbols
- Bisection stopping criteria
- Stop when interval width or function value meets the required tolerance; report an honest precision.
CONCEPT AND RULE
Stop when interval width or function value meets the required tolerance; report an honest precision.
METHOD
For bisection stopping criteria, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
After n steps, width is initial width/2^n.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve bisection stopping criteria
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- After n steps, width is initial width/2^n.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Bisection stopping criteria
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Bisection Stopping Criteria
Sticky Notes · Formula and Worked Revision
Core Idea
- Stop when interval width or function value meets the required tolerance; report an honest precision.
Rule / Formula
- Stop when interval width or function value meets the required tolerance; report an honest precision.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- After n steps, width is initial width/2^n.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Stop when interval width or function value meets the required tolerance; report an honest precision.
- Worked pattern: After n steps, width is initial width/2^n.
- Final check: domain, sign, notation, units, and reasonableness.
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