100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 2 Unit Test 1: Proof QUESTION PAPER $6.18   Add to cart

Summary

Summary Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 2 Unit Test 1: Proof QUESTION PAPER

 171 views  0 purchase
  • Course
  • Institution

Pearson Edexcel AS and A Level Mathematics, New Spec 2015, Pure Mathematics Year 2 Unit Test 1: Proof QUESTION PAPER

Preview 1 out of 1  pages

  • July 23, 2021
  • 1
  • 2020/2021
  • Summary
avatar-seller
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)




© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller PredictedPapers. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $6.18. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

76669 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Recently viewed by you


$6.18
  • (0)
  Add to cart