Exam 1A - Fall 95: Mathematics Problem Solving, Exams of Mathematics

Download Exam 1A - Fall 95: Mathematics Problem Solving and more Exams Mathematics in PDF only on Docsity! Exam 1A Fall 95 Name Instructions: Do all work in the space provided as much as possible. If more space is required, write "see attached" and number your problems. SHOW ALL WORK TO RECEIVE FULL CREDIT! 1. a)(6) Solve: Mrs. Burton has five daughters. They were all born the number of years apart as the youngest daughter is old. The oldest daughter is 20 years older than the youngest. What are the ages of Mrs. Burton's daughters? b)(2) Which of the problem-solving strategies discussed so far in this course did you use to solve the problem above? (guess & test, use a variable, draw a picture, look for a pattern, make a list, solve a simpler problem, draw a diagram, use direct reasoning). Name the strategy or strategies you used here, and circle the portion of your work above which illustrates its (their) use. c)(6) The last step of Polya's four-step process involves looking back to try to see general principles that will help us solve future problems. How old would the daughters be if the oldest were 25 years older than the youngest? If she were 30 years older? If she were 5n years older? 2.(2 pts. ea) Let A = {a,b,c} and B = {c,d}. Find: a) AUB b) A-B c) n(A x B) 3.(6) Name and illustrate 2 < 5 in two different ways. 4. At an automotive repair shop, 50 cars were inspected. Suppose that 23 cars needed new brakes and 34 cars needed new exhaust systems. a)(2) What is the least number of cars that could have needed both? b)(2) What is the greatest number of cars that could have needed both? c)(2) What is the greatest number of cars that could have needed neither? d)(3) If exactly 10 cars needed both types of work, draw a Venn diagram to illustrate this situation and determine how many cars needed neither. 5.(5) A student has chosen 6 flats, 4 longs and 12 units to illustrate the number 182 in base 5. Is she correct? If yes, why? If not, how would you explain what she needs to do? 6. Suppose all the letters of our alphabet were used as our single-digit numerals. a)(2) What would be the name of our base system? b)(4) What would be the base ten numeral for the "alphabet" numeral zz?