Writing a generalised statement about specific number properties

12 questions

1. Match the number properties with their generalised forms.
2. Which of these is true for the expression 4n + 7 where n is an integer?
3. Which of these must be even for any integer value of n?
4. Which of these must be odd for any integer value of n?
5. Which of these represent any two consecutive integers?
6. What is the correct expansion of (3n-1)^2?
7. Which of these represent any 3 consecutive even numbers?
8. Which of these could be the general form for any multiple of 5 greater than 10?
9. Which of these would be a good first step to prove "The product of any two odd numbers is an odd number"?
10. Which of these would be the best first step to prove "The difference between the squares of consecutive odd numbers is always a multiple of 8"?
11. Which of these statements are true for the expression 12n + 15 where n is an integer?
12. Starting with step 1 put these steps in order to form a complete proof for "The product of two odd numbers is always odd".

License: OGL