Exam-Style Question on Number
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 182. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.
This expression can be used to generate a sequence of numbers.$$n^2+n + 5$$
(a) Work out the first three terms of this sequence.
(b) What is the smallest value of \(n\) that produces a term of the sequence that is not a prime number?
(c) Is it true that odd square numbers have exactly three factors? Explain and justify your answer.
(d) Seymour is thinking of a number.
Find the two possible numbers that Seymour could be thinking of.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
Here is a related challenge called the Prison Cell Problem.
©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/