MathematicsChapter 10: Numerical Methods
Bisection Method
Repeatedly halve a sign-changing interval and keep the half that still changes sign.
Learning objectives
- State the rule for bisection method.
- Solve a bisection method problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Repeatedly halve a sign-changing interval and keep the half that still changes sign.
Where / symbols
- Bisection method
- Repeatedly halve a sign-changing interval and keep the half that still changes sign.
CONCEPT AND RULE
Repeatedly halve a sign-changing interval and keep the half that still changes sign.
METHOD
For bisection method, 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
For x^2-2 on [1,2], first midpoint is 1.5 and new bracket is [1,1.5].
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 method
- 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:
- For x^2-2 on [1,2], first midpoint is 1.5 and new bracket is [1,1.5].
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 method
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Bisection Method
Sticky Notes · Formula and Worked Revision
Core Idea
- Repeatedly halve a sign-changing interval and keep the half that still changes sign.
Rule / Formula
- Repeatedly halve a sign-changing interval and keep the half that still changes sign.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For x^2-2 on [1,2], first midpoint is 1.5 and new bracket is [1,1.5].
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
- Repeatedly halve a sign-changing interval and keep the half that still changes sign.
- Worked pattern: For x^2-2 on [1,2], first midpoint is 1.5 and new bracket is [1,1.5].
- Final check: domain, sign, notation, units, and reasonableness.
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