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Endpoints
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
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Endpoints
What is it?
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
In simple words
- (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0.
- = sits in the solution
- closed includes the root
- U for two pieces
Important terms
Endpoints: (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
What you should learn
- Define and explain endpoints.
- Apply endpoints to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Examples
- = sits in the solution
- closed includes the root
- U for two pieces
CORE UNDERSTANDING
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
Learn the idea, then use it:
WHAT — ENDPOINTS
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
CORE UNDERSTANDING
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
Remember
- = sits in the solution
- closed includes the root
- U for two pieces
Examples
- = sits in the solution
- closed includes the root
- U for two pieces
- ENDPOINTS: (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- = sits in the solution
- closed includes the root
- U for two pieces
- keep the ideas separate
- = sits in the solution
- closed includes the root
- U for two pieces
- correct term
Deeper understanding
Go beyond memorising Endpoints. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- = sits in the solution
- closed includes the root
- U for two pieces
- keep the ideas separate
- Endpoints: (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Rou
- WHAT — ENDPOINTS: (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Rou
Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Endpoints: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- = sits in the solution
- closed includes the root
- U for two pieces
- keep the ideas separate
Important formulas
- = sits in the solution
- closed includes the root
- U for two pieces
Common exam traps
- Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
= sits in the solution
closed includes the root
U for two pieces
keep the ideas separate
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
= sits in the solution
- Definition
- (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0. A square bracket is a filled circle. Round is open.
- Formula
- = sits in the solution
- Example
- = sits in the solution
- Critical warning
- Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Endpoints.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Endpoints and say why it fits.
Mistake
Q4. State one common mistake students make about Endpoints.
Exam note
Q5. Write a short exam note on Endpoints: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.