Making conjectures about patterns and relationships

12 questions

1. Which of these numbers are prime?
2. Which of these are square numbers?
3. Which of these are triangular numbers?
4. The number 100 has exactly ___ factors.
5. Which of these expressions must represent a number 'one more than a multiple of 5' when n is an integer?
6. What is the value of 3^n when n=4?
7. What sort of numbers always have an odd number of factors?
8. Give an example of a number less than 100 which is both square and triangular.
9. A conjecture is a (mathematical) statement which __________.
10. Lucas writes the conjecture "All numbers of the form 2^{n}-1 (where n is an integer greater than 1) are prime". Which of the following are true?
11. Which of these shows the first 4 numbers of the form 7^n where n is a positive integer?
12. Jacob has written out the first 4 numbers of the form 7^n where n is a positive integer. Which of these conjectures hold true for these 4 values?

License: OGL