Reasoning and Geometry grade 11

[Guest]

1. The sum of 2 consecutive even numbers is divisible by 2, but not 4.
Use deductive reasoning to prove this.




2.Give 2 examples that support the conjecture. Then find the counter example that shows the conjecture is false.

If a perfect square is divided by 5, the remaider is 1 or 4




3.What whole number values of x make each of the following compound statements true?

a)x is a factor of 42, and x is a factor of 56


b)x is a factor of 12, or x is a factor of 10

 

[stapel]

1) If the first even number is "2n" (for some integer "n"), what is the expression for the second number? What is the expression for their sum? Can you factor a "4" out?

2) This is just telling you to divide various squares by 5, looking at their remainders, until you have the three necessary examples. Where are you stuck?

3-a) Factor 42 and 56. What combinations of the common factors can you create?

3-b) Factor 12 and 10. What combinations of factors can you create that include non-comme factors?

Eliz.