Week 9:

Due Monday, October 16: Read section 12.1 and do the practice problems. Do but don't hand in: Problems 1 and 2 on page 551 and Class activity 12D on page 387 of the activity manual.

Due Wednesday, October 18: Read section 12.2 and do the practice problems. Do but don't hand in: Problems 3 and 4 (using the definitions of LCM GCF), 9, 11, 12. Hand in:

1) Solve and explain your solution: You have a fixed amount of money that you will spend on meat. You are considering one kind of meat when you notice another kind that costs $1 less per pound. You figure that you can buy 3 more pounds of this less expensive meat. Then you notice another meat that costs $1 more per pound than the first meat. You can buy 2 pounds less of this meat than of the first meat. How much money do you have to spend on meat?

2) To solve the simultaneous equations 2x + 5y = 9 and 3x - 4y = 2, you could instead solve the equations 6x + 15y = 27 and -6x + 8y = -4 which are obtained by multiplying both sides of the original first equation by 3 and multiplying both sides of the original second equation by -2. (a) Explain clearly why it is legitimate to replace the first set of equations with the second set. Discuss graphs and tables in addition to the equations themselves. (b) Why is it useful to replace the first pair of equations with the second pair?

3) The simultaneous linear equations x + y = 4 and x - 2y = 1 have a single solution, namely (3, 1) (i.e., x = 3, y = 1). Does this always happen? In other words, do two simultaneous linear equations ax + by = c and dx + ey = f, where a, b, c, d, e, and f are constants (fixed numbers) necessarily have exactly one solution? If not, what are all the possibilities for how many solutions the equations can have? Explain.

4) Problem 8 on page 555. Be sure to word your problem very carefully and precisely.

Due Friday, October 20: Study for quiz next week.

Week 10:

Due Monday, October 23: Read section 12.3 and do the practice problems. Do but don't hand in: Describe the "trial division" method for determining if a counting number is prime by using an example to illustrate. When can you stop checking? Explain why it is valid to stop then. Hand in: Refer to parts 3 and 4 of Class Activity 12G on pages 392, 393 (of the activity manual): 1) Describe a relationship between the number of dots, the number describing how the petals were made (e.g., by connecting every 8th dot or every 15th dot), and the number of petals in the flower design. 2) Explain why the relationship you found in (1) holds.

Due Wednesday, October 25: Read section 12.4 and do the practice problems. QUIZ on sections 13.5, 13.6, 12.1, 12.2, 12.3, deriving the equation for a line via similar triangles, different forms of equations for lines and their uses, simultaneous linear equations (Singapore textbook handout), the "slide method" for finding GCF and LCM, and other work done in class or assigned for homework related to this material (Sept 25 - Oct 23) but not including our work on spirographs or the related flower designs.

Friday, October 27: fall break