Math 522 Final Exam Review

• Number theory/modular arithmetic/doing-undoing—Solve one of the following:
• Show that 2 is the only prime p such that p ≡ 2 mod 4.
• Prove that the difference of the squares of any two odd numbers (not necessarily consecutive) is divisible by 8.
• Reflect on the algebraic thinking (Driscoll and multiple representations) in the problem above.
• A suspension bridge has parabolic cables stretched between support towers (thick lines) with suspender cables (dashed lines) hanging vertically from the cable to the road, as shown below. Find the total length of vertical suspender cables required to support one side of the road if the support towers are 100m high, the bridge is 1000m wide, the lowest point of the parabolic cable is 4m above the road, and the cables are placed 20m apart.

Final Exam: Take-home portion

• Short essay: At least one article we’ve run across has mentioned the importance of looking at mathematics problems from multiple perspectives, and learning to translate back and forth between and among the multiple representations. Identify all the work we have done with quadratics, and discuss it in terms of the multiple representations and translating (making connections) between them. Some work may not fit neatly into just one area, or may not fit the multiple representations well at all; they should be discussed anyway. Also, your answer may vary depending on the approach(es) you used to solve particular problems. Your response to this question should be typed and turned in with your final exam. It will count as ¼ of your final exam grade, i.e. 55 points.