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Bisection Stopping Criteria
Stop when interval width or function value meets the required tolerance; report an honest precision.
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Bisection Stopping Criteria
What is it?
Stop when interval width or function value meets the required tolerance; report an honest precision.
In simple words
- 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.
Important terms
Bisection stopping criteria: Stop when interval width or function value meets the required tolerance; report an honest precision.
What you should learn
- State the rule for bisection stopping criteria.
- Solve a bisection stopping criteria problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
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
How it works
- 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.
Remember
- Bisection stopping criteria
- rule
- worked example
- worked example
How the ideas connect
Worked example: After n steps, width is initial width/2^n.
Deeper understanding
Go beyond memorising Bisection Stopping Criteria. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: After n steps, width is initial width/2^n.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Bisection stopping criteria
- rule
- worked example
- 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 matc
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Bisection Stopping Criteria: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Bisection stopping criteria
- rule
- worked example
- Bisection stopping criteria: Stop when interval width or function value meets the required tolerance; report an honest precision.
Important formulas
- Bisection stopping criteria
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Bisection stopping criteria
rule
worked example
Bisection stopping criteria: Stop when interval width or function value meets the required tolerance; report an honest precision.
Stop when interval width or function value meets the required tolerance; report an honest precision.
- Definition
- Stop when interval width or function value meets the required tolerance; report an honest precision.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Bisection Stopping Criteria.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Bisection Stopping Criteria and say why it fits.
Mistake
Q4. State one common mistake students make about Bisection Stopping Criteria.
Exam note
Q5. Write a short exam note on Bisection Stopping Criteria: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.