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Summary Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 2 Unit Test 1: Proof QUESTION PAPER
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Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 2 Unit Test 1: Proof QUESTION PAPER
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Type
Summary
Study Level
A/AS Level
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PEARSON (PEARSON)
Subject
Mathematics
Unit
Topic 1
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Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 1 and Year 2 Unit Test Bundle QUESTION PAPER
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1. Exam (elaborations) - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1(as...
2. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
3. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
4. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
5. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
6. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
7. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
8. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
9. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
10. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
11. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 2 un...
12. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
13. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
14. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
15. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
16. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
17. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
18. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
19. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
20. Summary - Pearson edexcel as and a level mathematics, new spec 2015, pure mathematics year 1 (a...
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Pure Mathematics Year 2 (A Level) Unit Test 1: Proof
1 It is suggested that the sequence produces only prime numbers.
a Show that , and produce prime numbers. (2 marks)
b Prove by counter example that the sequence does not always produce a prime
number. (2 marks)
2 Prove by exhaustion that for positive integers from 1 to
6 inclusive. (3 marks)
3 Use proof by contradiction to prove the statement: ‘The product of two odd
numbers is odd.’ (5 marks)
4 Prove by contradiction that if n is odd, n3 + 1 is even. (5 marks)
5 Use proof by contradiction to show that there exist no integers a and b for which
25a + 15b = 1. (4 marks)
6 Use proof by contradiction to show that there is no greatest positive rational
number. (4 marks)
7 Use proof by contradiction to show that, given a rational number a and an
irrational number b, a − b is irrational. (4 marks)
8 Use proof by contradiction to show that there are no positive integer solutions to
the statement (5 marks)
9 a Use proof by contradiction to show that if n2 is an even integer then n is also an
even integer. (4 marks)
b Prove that is irrational. (6 marks)
10 Prove by contradiction that there are infinitely many prime numbers. (6 marks)
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