Year 13 proof by contradiction quiz to download as PDF

This Year 13 proof by contradiction quiz has 10 short questions for pupils aged 17-18. Type your answer, check it straight away and read the explanation when you get one wrong.

Year 13 proof by contradiction quiz: the 10 questions

Is the number 0.4 rational or irrational?
What is the negation of "x is rational"?
If n squared is even, is n even or odd?
How many counterexamples are needed to disprove a "for all" statement?
What common factor leads to the contradiction in the proof that root 2 is irrational?
Is 30031 = 2x3x5x7x11x13+1 prime? (yes or no)
Is the sum of a rational and an irrational number rational or irrational?
Is it valid to prove a general result by checking 10 examples? (yes or no)
Write the negation of "there are infinitely many primes".
What type of number is a/b with integers a, b and b not 0?

How to use this Year 13 proof by contradiction quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the proof by contradiction lesson and try again later. After that, try the multiple choice questions or the proof by contradiction worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.