Friday, August 29, 2008

Outstanding classwork

Hi Emile,
Here is what we discussed last week:

Geometry: Aug 25 (due by Wed, Aug 27). Read paragraph 22. Solve exercise 51 and write down your solution.
For the proposition: "If a whole number is divisible by 3 then the sum of its digits is divisible by 9," write down the converse proposition.
For each of the direct and converse proposition, if it is true, prove it, and if its is false, give an example where it is false. Write down the proofs and examples.

Added on Tue: Give an example of two angles whose halves add up to 90 degrees, but whose bisectors are not perpendicular.
In your solution to the 2nd question in exercise 51, find where you use the hypothesis that the angles are supplementary.

Algebra: (due by Th, Aug. 28). Section 10. Write down solutions of Problems 31--33. Hint for 31: Start with designating a multiplication to be performed last.
If done with 31--33, try the variant of Problem 31 with 6 numbers to multiply.

Geometry: (due by Mon, Sept 1).
Read paragraph 31. Write down definitions:
- of a broken line, its sides, and its vertices;
- of a convex broken line;
- of a closed broken line.
Draw an example that satisfies the definition, and another example that does not (for instance, draw an example of a closed broken line and of a broken line that is not closed). Solve exercise 53.

Since Monday, Sept. 1 is Labor Day, may I suggest that you spend enough time on Sat, Sun, and Mon to finish all this before school resumes on Tue?