5 9 c. - + a- 4 9 b d. 1 4 - 2 7 e. 6 11 + a- 1 2 ba2 5 b ÷ 3 f. (-4) + (-5)(2) g. (9 - 12) - (7 - 9) h. (-2)3 - 4 ÷ 2 · 6 i. 1(1 - (-4))2 + (-4 - 8)2 j. 6 - 3(-2) 4 - 22 9. Identify the property that is illustrated. a. 5(6 + 2) = (6 + 2)5 b. 4 · 1 4 = 1 c. 3 + (4 + 7) = (3 + 4) + 7 d. 1 5 + a- 1 5 b = 0 e. 3 · 1 = 3 f. -9 + 0 = -9 g. 4 + (-3) = (-3) + 4 4. Place an appropriate symbol that makes the statement true. a. - 3 -5 b. 12 π 5. Simplify each expression. a. - a- 7 2 b b. -(2 - 5) c. u4 - 5(32) u d. u(-4)3 u 6. Find the prime factorization of 180. 7. Use the fundamental property of fractions to write each fraction in lowest terms. a. 124 200 b. -56 -14 8. Perform each operation. Write answers in lowest terms, if appropriate. a. 12 25 · - 5 3 b. 32 ÷ 1 4 10. Complete the table for the given algebraic expressions. Expression Total Number of Terms Variable Term(s) Constant Term(s) Coeffi cients of Each Variable Term a. -3p b. -a c. y - 1 d. x 2 + 3 e. -2y2 + y - 7 f. 9y3 - y2 + 8y - 4 11. Simplify each expression. a. 4(3x + 7) b. 8(6x - 5) c. - 6a1 3 x + 1 2 b d. x + 2 + 5x - 4 e. 2(5x - 3) - (7x - 9) f. 2x2 - 8x + 1 + x2 - x - 3 g. x + 3 2 x h. 5 + 4(3x + 2) 12. Evaluate the expression 4x2 - 2x + 1 for x = -3. 13. Translate each phrase into a mathematical expression. a. Two more than a number b. The difference of a number and 5 c. The sum of three times a number and 4 d. Twice the sum of a number and 7 e. The ratio of a 4 times a number and 3 f. Six less than one-fourth of a number Solve each problem. 14. The country with the highest rate of decrease in the natural birth rate is the Ukraine. Its population is currently 46.8 million. It is expected to be 33.4 million in 2050. What is the difference between the expected population and the current population? (Source: http:// geography.about.com/od/populationgeography/a/zero.htm) 15. The following chart shows the closing price of Google’s stock for October 26 to November 2, 2009. (Source: http://finance.yahoo.com/q/hp?s=GOOG&a=09&b= 19&c=2009&d=10&e=3&f=2009&g=d) Date Closing Price of Google Stock Daily Change in Price 11/2/2009 $533.99 10/30/2009 $536.12 10/29/2009 $551.05 10/28/2009 $540.30 10/27/2009 $548.29 -5.92 10/26/2009 $554.21 n/a a. Complete the chart by showing how the price of the stock changed from the previous day to the next. b. After completing the chart, find the average daily change in price. 16. If $5000 is invested in a savings account that earns 4.25% annual interest for 3 yr, the amount in the account at the end of the 3 yr is given by 5000(1.0425)3. Simplify this expression to determine how much is in the account after 3 yr. 17. The volume of a sphere is given by 4 3 πr3, where r is the radius of the sphere. Find the volume of a basketball that has a radius of 4.7 in. Round the answer to the nearest hundredth. 90 Chapter 1 Real Numbers and Algebraic Expressions
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