MathematicsChapter 4: Linear and Quadratic Inequalities
Endpoints
(x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0.
Learning objectives
- Define and explain endpoints.
- Apply endpoints to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
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.
Where / symbols
- 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.
Relationship
- = sits in the solution
Overview
Learn the idea, then use it:
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.
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.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
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.
In simple words
Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
Key points
- = sits in the solution
- closed includes the root
- U for two pieces
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Endpoints
Sticky Notes · Quick Revision
Core Idea
- (x-2)(x-5)>=0 includes 2 and 5: (-inf,2] U [5, inf) if a>0.
Key Points
- = sits in the solution
- closed includes the root
- U for two pieces
Simple Check
- Explain endpoints in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge endpoints with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- (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
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