Proofs involving inequalities and graphs (HSC SSCE Mathematics Extension 2): Flashcards
📚Flashcards
Practise the cards
10 cards from this deck
ShowHide
Practise the cards
10 cards from this deck
What are inequalities in mathematics?
What are inequalities in mathematics?
Statements using <, >, ≤, or ≥ to compare numbers.
What does the transitive property state?
What does the transitive property state?
If a > b and b > c, then a > c.
What is the reflexive property?
What is the reflexive property?
Every number a is at least equal to itself, a ≥ a.
What do graphs show in mathematics?
What do graphs show in mathematics?
They visualize relationships between equations or functions.
What are asymptotes in graphing?
What are asymptotes in graphing?
Lines that graphs approach but never touch.
How do you solve 2x + 3 > 5?
How do you solve 2x + 3 > 5?
Simplify to find x > 1.
What is proof by contradiction?
What is proof by contradiction?
Assume the opposite to prove the original statement.
How can calculus help with inequalities?
How can calculus help with inequalities?
Derivatives find max/min values and function behavior.
What is the role of plotting in inequalities?
What is the role of plotting in inequalities?
It shows where functions meet, confirming relations.
How to prove n^2 > 2^n for n > 4?
How to prove n^2 > 2^n for n > 4?
Use base case and inductive step to confirm.