Spring ’02 Math 201 Exam 2 Review Prof. Brick
1. Use a block model to illustrate 145 −68.
2. Simplify 28
·272
3. You are told that 143 + 432 = 1130. What is going on ?
4. Using the fact that 98 is close to 100, describe how you could multiply 98 ·42 quickly.
Explain why this works.
5. Describe a quick way of computing 63 −47 and explain why it works.
6. Explain how to estimate 63 + 173 + 41 + 189 + 30 + 12. Why does the method work ?
7. Since 39 + 51 = 40 + 50, why isn’t 39 ·51 = 40 ·50 ?
8. Explain how to use a (four function) calculator to find the remainder in division of
integers.
9. Explain how a numberline model with a car handles 5 −3 and 7 −(−2).
10. Use patterns to show how to compute 7 + (−3).
11. Explain why multiplication by 5 can be done by dividing by 2 and then moving the
decimal place.
12. Describe a quick way of calculating a fifteen percent tip. Show with examples how to
estimate it and how to compute it exactly.
13. Factor x2
−100
14. Explain why the product of two negatives is positive. Give at least three different
approaches.
15. For what values of the digit a is the integer 875147341379532a divisible by 3.
16. Show how to use the Sieve of Eatosthenes to find primes.
17. Suppose you want to test whether or not 397 is prime. At what point should you stop
looking for factors ?
18. How many prime numbers are there ? Why are primes and factorings and related
concepts important to the average person (without them knowing usually) ?
19. Use the Euclidean algorithm to find the g.c.d. of 8532 and 3876.
20. Find the l.c.m. of 12 and 32. Show it using lists of mulitples.
21. Working modulo 12, compute 7 + 9 + 4 + 7 + 11 and 8 ·3.
22. Review all the homework, all the quizzes, and your notes from class.