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Proof by Contradiction
Question Paper 1
Level
A LEVEL
Exam Board
Edexcel
Subject
Mathematics
Module
Pure
Topic
Algebraic Methods
Sub-Topic
Proof by contradiction
Booklet
Question Paper 1
Time Allowed:
40 minutes
Score:
/33
Percentage:
/100
Grade Boundaries:
A*
>85%
A
77.5%
B
C
D
E
U
70%
62.5%
57.5%
45%
<45%
1
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1. Use proof by contradiction to show that, given a rational number a and an irrational number b, a − b is
irrational.
(Total 4 marks)
2. Use proof by contradiction to prove the statement: ‘The product of two odd numbers is odd.’
(Total 5 marks)
2
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3. Express
as a single fraction in its simplest form.
(Total 4 marks)
4. Use proof by contradiction to show that there are no positive integer solutions to the statement
(Total 5 marks)
3
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5. Prove by contradiction that if n is odd, n3 + 1 is even.
(Total 5 marks)
2
6. (a) Use proof by contradiction to show that if n is an even integer then n is also an even integer.
(4 )
(b) Prove that Ö2 is irrational.
(6 )
(Total 10 marks)
4