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www.naikermaths.com Pure Mathematics 2 Practice Paper M7 MARK SCHEME Question 1 Question Number Scheme Marks ‘Assume that there exists a product of two odd numbers that is even (2+1)(2+ 1) = 4 + 2 + 2 + 1 = 2(2 + + ) + 1 2(2 + + ) is even so 2(2 + + ) + 1 must be odd M1 This contradicts the assumption that the product of two odd numbers is even, therefore the product of two odd numbers is odd B1 B1 1.

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Page 1: Pure Practice Paper 2 M7 Mark Scheme - Maths · Title: Microsoft Word - Pure Practice Paper 2 M7 Mark Scheme.docx Created Date: 5/13/2019 9:12:40 PM

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Pure Mathematics 2 Practice Paper M7 MARK SCHEME Question 1

Question Number Scheme Marks

‘Assume that there exists a product of two odd numbers that is even

(2𝑚+1)(2𝑛+ 1) = 4𝑚𝑛 + 2𝑚 + 2𝑛 + 1

= 2(2𝑚𝑛 + 𝑚 + 𝑛) + 1

2(2𝑚𝑛 +𝑚 + 𝑛) is even so 2(2𝑚𝑛 +𝑚 + 𝑛) + 1 must be odd

M1

This contradicts the assumption that the product of two odd numbers is

even, therefore the product of two odd numbers is odd

B1

B1 1.

Page 2: Pure Practice Paper 2 M7 Mark Scheme - Maths · Title: Microsoft Word - Pure Practice Paper 2 M7 Mark Scheme.docx Created Date: 5/13/2019 9:12:40 PM

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Question 2

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Question 3

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Page 6: Pure Practice Paper 2 M7 Mark Scheme - Maths · Title: Microsoft Word - Pure Practice Paper 2 M7 Mark Scheme.docx Created Date: 5/13/2019 9:12:40 PM

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Question 4

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Question 5

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Question 6

Question 7

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Question 8

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Question 9

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Question 10

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Question 11

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