Proof Yr2 Flashcards
1
Q
A
2
Q
What are some ways to consider proofs?
A
Expressing the problem algebraically
Expressing the problem geometrically
3
Q
What are the general steps to direct proofs?
A
- Defining the key words algebraically
- Applying the second key word to the algebraic expression
- Rewording the key words in the question to gives a worded explanation of factorised expressions
- A therefore concluding statement
4
Q
A
5
Q
A
6
Q
Digit proof
A
7
Q
A
8
Q
A
9
Q
What is a rational number?
A
A number is rational if it can be expressed as a quotient of two integers with a non zero denominator
10
Q
A
11
Q
A
12
Q
A
13
Q
A
14
Q
A
15
Q
A
16
Q
Proof by Exhaustion
A
17
Q
What is a
* conjecture
* axiom
A
- a conjcture is a statment believed to be true based on patterns and observations but it has not yet been proven, awaits verification
- an axiom is a statement that is accpted as true without proof from the start
18
Q
what is the format to disproof?
“prove that this is false”
A
- show that the proof works for at least 2 examples
- show the counter example
- write a conclusion
19
Q
A
20
Q
what is the format for a proof by contradiction?
A
- assume that the statment is in fact false. “Assume that…. negation of statment”
- prove that this will lead to a contradiction. “This contradicts the assumption that….”
- conclusion. “Therefore”
21
Q
Using proof by contradiction
A
22
Q
Negate the following statements
A
23
Q
A
24
Q
A
25
Q
A
26
Q
what are some wordings to be cautious of in proofs?
A
- when something is squared say that it is always positive or 0
27
Q
A
28
Q
A
