Proving or disproving a statement

12 questions

1. Which of these statements are always true?
2. Which of these is a general form for any odd number (where n is an integer)?
3. The diagram shows a right-angled triangle. Which of these is an expression for the area?
4. The diagram shows a right-angled triangle. Which of these formula show the correct relationship between the lengths of the sides?
5. Which of these shows the first 4 numbers of the form 9^n where n is a positive integer?
6. Andeep has written out the first 4 numbers of the form 9^n where n is a positive integer. Which of these conjectures hold true for these 4 values?
7. To __________ is to formulate a statement or rule that applies correctly to all relevant cases.
8. Why is testing a conjecture often not a good way to prove it is true?
9. Laura wants to prove Pythagoras' theorem. Her first few steps are shown. Which of these is the correct next step of her proof?
10. If p is a prime number and n is a positive integer, which is a counterexample to the conjecture "p^n is always odd"?
11. Which of these is a counterexample to the conjecture "The digit sum of any number of the form 9n where n is a positive integer is always 9"?
12. Aisha writes the conjecture "For all integer values of x, (x-2)^2 > x-2". There is a counterexample to this when x=___.

License: OGL