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9 Proof Ws

This document contains 14 math problems asking students to prove various statements about consecutive integers and their sums, differences, and squares algebraically. The problems cover topics such as proving the sum of consecutive integers is odd or a multiple of certain numbers, and that sums or differences of squares of consecutive integers have specific properties. The document provides up to 3 marks for each correct proof.

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noha heshmat
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47 views1 page

9 Proof Ws

This document contains 14 math problems asking students to prove various statements about consecutive integers and their sums, differences, and squares algebraically. The problems cover topics such as proving the sum of consecutive integers is odd or a multiple of certain numbers, and that sums or differences of squares of consecutive integers have specific properties. The document provides up to 3 marks for each correct proof.

Uploaded by

noha heshmat
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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mathsgenie.co.uk Please do not write on this sheet mathsgenie.co.

uk
1 Prove algebraically that the sum of any two consecutive integers is 8 Prove that the sum of 3 consecutive even numbers is always a multiple
always an odd number. of 6.

(2 marks) (2 marks)

2 Prove algebraically that the sum of any three consecutive even integers 9 Prove algebraically that the sum of the squares of any 2 even positive
is always a multiple of 6. integers is always a multiple of 4.
(2 marks)
(2 marks)
3 Prove that (3n + 1)2 – (3n – 1)2 is always a multiple of 12, for all 10 Prove algebraically that the sum of the squares of any 2 odd positive
positive integer values of n. integers is always even.
(2 marks) (2 marks)

4 n is an integer. 11 Prove that the sum of the squares of any two consecutive integers is
Prove algebraically that the sum of n(n + 1) and n + 1 is always a always an odd number.
square number.
(2 marks) (3 marks)

5 Prove that (2n + 3)2 – (2n – 3)2 is always a multiple of 12, for all 12 Prove that the sum of the squares of two consecutive odd numbers is
positive integer values of n. always 2 more than a multiple of 8
(2 marks) (2 marks)

6 n is an integer. 13 Prove that the difference between the squares of any 2 consecutive
Prove algebraically that the sum of (n + 2)(n + 1) and n + 2 is always integers is equal to the sum of these integers.
a square number.
(2 marks) (3 marks)

7 Prove that the sum of 3 consecutive odd numbers is always a multiple 14 Prove algebraically that the sums of the squares of any 2 consecutive
of 3. even number is always 4 more than a multiple of 8.
(2 marks) (3 marks)

Grade 9 Proof

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