These Further Maths proof by induction multiple choice questions check your understanding of proof by induction with 10 questions for pupils aged 16-18. Each question has four answers, and the right one is explained as soon as you choose.
Further Maths proof by induction multiple choice questions: the 10 questions
In an induction proof the basis step shows that:
Which is the correct assumption step?
\(\sum_{r=1}^{k+1}r^3\) equals:
To prove \(f(n)=7^n-1\) divisible by 6, a useful expression is:
If \(\mathbf M^k=\begin{pmatrix}1&3k\\0&1\end{pmatrix}\), then \(\mathbf M^{k+1}\) with \(\mathbf M=\begin{pmatrix}1&3\\0&1\end{pmatrix}\) is:
Which statement is true for all positive integers \(n\)?
For the second-order recurrence \(u_{n+2}=au_{n+1}+bu_n\) a proof by induction needs:
In proving \(n!>2^n\) for \(n\ge4\), the basis case is:
\(\sum_{r=1}^{n}r(r+1)=\tfrac13n(n+1)(n+2)\). When \(n=4\) the sum is:
Which is the correct conclusion?
How to use these Further Maths proof by induction 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 by induction lesson.
Finally, practise more with the proof by induction 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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