Proof Yr2 Flashcards

1
Q
A
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2
Q

What are some ways to consider proofs?

A

Expressing the problem algebraically
Expressing the problem geometrically

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3
Q

What are the general steps to direct proofs?

A
  1. Defining the key words algebraically
  2. Applying the second key word to the algebraic expression
  3. Rewording the key words in the question to gives a worded explanation of factorised expressions
  4. A therefore concluding statement
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4
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5
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6
Q

Digit proof

A
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7
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8
Q
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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

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10
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11
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12
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13
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14
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15
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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
  1. show that the proof works for at least 2 examples
  2. show the counter example
  3. write a conclusion
19
Q
A
20
Q

what is the format for a proof by contradiction?

A
  1. assume that the statment is in fact false. “Assume that…. negation of statment”
  2. prove that this will lead to a contradiction. “This contradicts the assumption that….”
  3. conclusion. “Therefore”
21
Q

Using proof by contradiction

A
22
Q

Negate the following statements

A
23
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24
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25
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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
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28
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