These Year 12 proof multiple choice questions check your understanding of proof with 10 questions for pupils aged 16-17. Each question has four answers, and the right one is explained as soon as you choose.
Year 12 proof multiple choice questions: the 10 questions
Which expression represents an odd number, where \(n\) is an integer?
Odd numbers are one more than an even number, so \(2n+1\).
Which three expressions are consecutive integers?
Consecutive integers differ by 1.
A counter-example is used to
One counter-example disproves a statement.
Which is NOT a valid proof that a statement holds for all integers?
Checking many cases is not a proof.
The sum of two even numbers \(2a\) and \(2b\) equals
\(2a+2b=2(a+b)\).
Which value of \(n\) is a counter-example to "\(n^2+n+41\) is prime"?
\(40^2+40+41=1681=41^2\).
\((n+1)^2-n^2\) simplifies to
\(n^2+2n+1-n^2=2n+1\).
To prove a result for all integers by exhaustion you can split them into
Even and odd cover every integer.
\(x^2-4x+5=(x-2)^2+1\). This proves the expression is
A square is at least 0 so the whole expression is at least 1.
A proof should end with
State what has been shown.
How to use these Year 12 proof multiple choice questions
First, read each question carefully before you look at the four answers. Then work the answer out on paper, so that you do not simply guess. After that, read the explanation, even when you are right. If you score less than 7 out of 10, go back to the proof lesson.
Finally, practise more with the proof worksheet and the quiz. 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.
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