Algebraic Proof – Quiz

Test out your knowledge of Algebraic Proof with our final quiz! (if you haven’t completed the worksheets yet, I strongly recommend you do this first…)

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Question 1 of 9

1. Question
1 point(s)
Select the algebraic expression/equation that proves that the sum of any two consecutive odd numbers is always even.
- 2n + 1 + 2n + 3 = 2 (2n+2)
- 2n + 1 + 2n + 3 = 4n+4
- 2n + 2n + 4 = 2 (2n+2)
- n + 1 + n + 3 = 2 (n+2)
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Question 2 of 9

2. Question
1 point(s)
Select the algebraic expression/equation that proves that the difference between any two consecutive odd numbers is always two.
- 2n+3 +2n+1= 4(n+1
- n+3 – n-1= 2
- 2n+3 – n-1= n+2
- 2n+3 –2n-1= 2
Correct

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Question 3 of 9

3. Question
1 point(s)
Select the algebraic expression/equation that proves that the mean of three consecutive integers is always the middle number
- n+ 2n + 3n= 6n
- 3n + 3 = 3(n+1)
Correct

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Question 4 of 9

4. Question
1 point(s)
Select the algebraic expression/equation that proves that the sum of any three consecutive even integers is always even.
- n + 2 + n+ 4 + n + 6 = 3n + 12
- 2n+2n+2+2n+4 = 2(3n+3)
- 2n+2n+2+2n+4 = 3 (2n+ 2)
- n + 2 + 2n + 2 + 3n + 2 = 2 (3n + 3)
Correct

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Question 5 of 9

5. Question
1 point(s)
Select the algebraic expression/equation that proves that 8 (n+7) – 5(n+4) is always a multiple of 3
- 8n+54-5n+ 20=3n + 74
- 8n+54-5n-20=3n + 45
- 8n+54-5n-20=3(n+8)
- 8n+54-5n-20=3n + 24
Correct

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Question 6 of 9

6. Question
1 point(s)
Select the algebraic expression/equation that proves that the sum of the squares of any two positive integers is always even
- 8n^2 + 16n + 10= 2(4n^2 + 8n +5)
- 8n^2 + 16n – 10= 2(4n^2 + 8n -5)
- n^2-2-(n-2)^2 = 2(2n^2-1)
- n^2-2-(n-2)^2 = 2n(2n+2)
Correct

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Question 7 of 9

7. Question
1 point(s)
Select the algebraic expression/equation that proves that n²-2-(n-2)² is always an even number
- n^2 – 2 – n^2 – 4n – 4 = 2 (-2n-3)
- n^2 – 2 – n^2 – 4n + 4 = 2 (2n+1)
- n^2 – 2 – n^2 + 4n – 4 = 2n^2 -6
- n^2 – 2 – n^2 + 4n – 4 = 2 (2n-3)
Correct

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Question 8 of 9

8. Question
1 point(s)
Select the algebraic expression/equation that proves that the sum of four consecutive integers is not a multiple of four
- n+n+1+n+2+n+3 = 4(n+1) + 2
- n+n+1+n+2+n+3 = 2(2n+2)
- n+n+1+n+2+n+3 = 4(n+6)
- n+n+1+n+2+n+3 = 4n -1
Correct

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Question 9 of 9

9. Question
1 point(s)
Select the algebraic expression / equation that proves that the difference between the squares of any two consecutive odd numbers is always a multiple of 8
- 3n^2- n^2 = n(3n – 1)
- 4n^2 + 12n +9 – 4n^2 + 4n + 1 = 8n (n+1)
- 4n^2 + 12n +9 – 4n^2 – 4n – 1 = 8 (n+1)
- 4n^2 + 12n +9 – 4n^2 + 8n – 1 = 8 (2n+1)
Correct

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