Proof Yr2

Question 1

Answer 1

Question 2

What are some ways to consider proofs?

Answer 2

Expressing the problem algebraically
Expressing the problem geometrically

Question 3

What are the general steps to direct proofs?

Answer 3

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

Question 4

Answer 4

Question 5

Answer 5

Question 6

Digit proof

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

What is a rational number?

Answer 9

A number is rational if it can be expressed as a quotient of two integers with a non zero denominator

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Proof by Exhaustion

Answer 16

Question 17

What is a
* conjecture
* axiom

Answer 17

• 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

Question 18

what is the format to disproof?

“prove that this is false”

Answer 18

1. show that the proof works for at least 2 examples
2. show the counter example
3. write a conclusion

Question 19

Answer 19

Question 20

what is the format for a proof by contradiction?

Answer 20

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”

Question 21

Using proof by contradiction

Answer 21

Question 22

Negate the following statements

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

Question 26

what are some wordings to be cautious of in proofs?

Answer 26

* when something is squared say that it is always positive **or 0**

Question 27

Answer 27

Question 28

Answer 28