Review for the Final Exam
1. Factor completely into primes:
2. What’s the largest 3-digit number that has exactly 3 different factors?
3. Using the intersection-of-sets method, find:
(a) GCD(9, 15) and LCM(9, 15)
(b) GCD(12, 32) and LCM(12, 32)
4. Using the prime factorization method, find:
(a) GCD(30, 1470) and LCM(30, 1470)
(b) GCD(54, 3300) and LCM(54, 3300)
5. Vanilla Ice has a nervous tic that makes him say “Yup yup” every 10
minutes and
shave his eyebrows every 14 minutes. If he simultaneously says “Yup yup” and
shaves his
eyebrows at 12 noon, what time will it be when he next does these things
simultaneously?
6. Find two numbers a and b such that GCD(a, b)=LCM(a, b).
7. What’s the largest 4-digit number that has exactly 4 different factors?
8. Express each of the following fractions in simplest form:
9. List the following fractions in increasing order:
10. Find a rational number inbetween:
11. Find two rational numbers inbetween
12. Draw an area model to show that
13. Solve for x in each of the following:
14. Britney Spears got 7 out of 16 answers correct on her driver’s license
exam, and her
lawyer, Jackie Chiles, got 42 out of 99 answers correct on his bar exam. Who did
better?
15. Express as improper fractions:
16. Express as mixed numbers:
17. Perform the following additions and subtractions (express all answers as
fractions in
reduced form):
18. Perform the following additions and subtractions (express all answers as mixed numbers):
19. Approximate each of the following fractions by 0,1/4,2/1,3/4,or 1. State
whether your
estimate is high or low. Explain.
20. By estimating, determine whether the given sum is closer to 0, to 1/2, or to 1.
21. Multiply or divide and express the answer in reduced form:
22. Multiply or divide and express the answer as a mixed number:
23. Each Mariah Carey CD sells 1/3 as many copies as the previous one. If her
15th CD
sells 12 copies, how many copies did her 8th sell?
24. Martha bought 1232 shares of Enron stock at 17 1/4 a share and sold them
at 224 1/8
a share. What was her profit on these stocks?
25. Pop Tarts are on sale for 3/4 of their original price of $2.80 per box.
What is the sale
price per box?
26. Pop Tarts are on sale for 3/4 of their original price. If the sale price
per box is $1.98,
what’s the original price?
27. Stade bought the new Fergie CD used for $10. (Not really.) If used CD’s
sell for 2/3 of
new price, what is the new price of Fergie’s CD?
28. List the following numbers in increasing order:
(a) 1.333334, 1.33344, 1.34, 1.34443, 1.4, 1.3.
(b) −12.123, −12.1229, −12, −12.13, −12.1, −12.2.
29. Determine whether each of the given fractions can be
written as a terminating decimal.
If it can, write it as one; if it can’t, explain why. (You can check your answer
on your
calculator if you want, but show the work that you would do WITHOUT a
calculator.)
30. Write each of the following numbers in scientific
notation.
31. Round 7.45454 to the nearest:
(a) ten-thousandth
(b) thousandth
(c) hundredth
(d) tenth
(e) integer
32. Perform by hand each of the following divisions. (Use
long division; you can check
your results by calculator if you want.)
(a) 7.29÷3 (b) 818.18÷1.1 (c) 0.3703÷23 (d) 1.500002÷0.7 (e) 0.023÷4.6
33. List the following numbers in increasing order:
34. Find a decimal number between:
35. Express each of the following repeating decimals as a fraction:
36. Express each of the following fractions as a repeating
decimal (do the long division by
hand; you can check your work with your calculator):
37. Somebody claims that
How can you prove, without
a calculator, that this is false?