Further Maths proof by induction quiz to download as PDF

This Further Maths proof by induction quiz has 10 short questions for pupils aged 16-18. Type your answer, check it straight away and read the explanation when you get one wrong.

Further Maths proof by induction quiz: the 10 questions

What is the first step of an induction proof?
Evaluate \(\sum_{r=1}^{5}(2r-1)\).
What is the remainder when \(5^n-1\) is divided by 4?
If \(\sum_{r=1}^{k}r=\tfrac12k(k+1)\), what is \(\sum_{r=1}^{k+1}r\) before simplifying?
For which smallest integer \(n\) is \(2^n\lt n!\)?
What is the top-right entry of \(\begin{pmatrix}1&1\\0&1\end{pmatrix}^{10}\)?
Evaluate \(\sum_{r=1}^{3}r\,r!\).
For \(u_{n+1}=3u_n+2\), \(u_1=1\): find \(u_3\).
Is \(2^n>n^2\) true for \(n=3\)? (yes/no)
\(\dfrac{d^3}{dx^3}(xe^x)=f(x)e^x\). Find \(f(x)\).

How to use this Further Maths proof by induction 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 induction lesson and try again later. After that, try the multiple choice questions or the proof by induction 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.