1. The final problem in the pure algebra portion of A Second Course in Algebra (first published in 1937), from the "Binomial Theorem" chapter (which is followed by a chapter on logarithms and another on trigonometry), p. 335:
A man can travel from town A to town B by plane in 2 hours and 10 minutes, or by car in 6 hours and 30 minutes. Bad weather forces him to land when he is 65 miles from B and he completes the trip by car. If he traveled the same length of time in the car as in the plane, how many miles is it from A to B?
2. From the final homework assignment in the final algebra chapter of Interactive Mathematics Project Integrated High School Mathematics Year 4, "The World of Functions," p. 345:
As part of your portfolio, write about your personal development during this unit. You may want to specifically address this issue.
How do you feel you have developed during this unit in terms of your ability to explore problems and prove conjectures in mathematics?You should include here any thoughts you might like to share with a reader of your portfolio.
[The "conjectures" in question involve comparisons among the graphs of certain minimally modified functions, e.g., f(x), f(x) + b, and f(x+b)]
3. Extra Credit:
If your daughter is interested in a career in mathematics or science, would you worry more about the male perspective in the first problem, or the ratio of effort to learning in the second problem?