Chapters 1 and 2 Cumulative Review Exercises 189 third consecutive odd integer. What are the three odd integers? 33. Gloria and Richard go out for an afternoon jog. They begin running at an average speed of 9 mph. After some time, they turn around and walk back home at an average speed of 4 mph. If they were gone for a total of 2 hr, how long did they jog before turning around? CUMULATIVE REVIEW EXERCISES / CHAPTERS 1 AND 2 1. Classify each number as a natural number, whole number, integer, rational number, irrational number, and/or a real number. If the number is a rational number, write it in fractional form. If the number is an irrational number, approximate its value to two decimal places. (Section 1.1, Objective 1) a. 9 11 b. 113 c. - 47°F: the coldest recorded temperature in Elkader, Iowa on February 31, 1996 2. Give an example of a real number that satisfies the given conditions. (Section 1.1, Objective 1) a. An integer that is not a whole number. b. An irrational number that is between 3 and 4. c. A rational number that is between 5/2 and 3. d. An integer that is not a natural number. 3. Graph each number on a real number line. (Section 1.1, Objective 2) a. e-4.11, -1, 17, 5 1 2 f b. e-2π, -3, 111, 40 3 f 4. Compare the values of each pair of numbers. Use a <, >, or = symbol to make the statement true. (Section 1.1, Objective 3) a. π ____ 3.3 b. 116 ____ -u-4u 5. Find the opposite of each real number. (Section 1.1, Objective 4 ) a. 1.33 b. 7.5 c. - 1 2 3 6. Simplify each absolute value expression. (Section 1.1, Objective 5 ) a. u5u b. `- 4 7 ` c. -u-14u 7. Write the prime factorization of each number. (Section 1.2, Objective 1 ) a. 180 b. 98 c. 500 8. For the academic year 2009–2010, it was reported that there were 6896 higher education institutions in the United States and other jurisdictions; 2853 were 4-yr, 2259 were 2-yr, and 1784 were less-than-2-yr institutions. Write a fraction that represents the portion of less-than-2-yr institutions. (Section 1.2, Objective 2 ) 9. Simplify each fraction. (Section 1.2, Objective 2 ) a. 36 90 b. 250 516 10. Perform each operation and simplify the result. (Section 1.2, Objectives 2–7 ) a. 13 18 + 25 42 b. 7 12 - 3 10 c. 4 1 5 · 3 1 3 d. 2 5 6 ÷ 2 1 6 e. 5 1 5 - 4 3 5 11. Use the order of operations to simplify each numerical expression. (Section 1.3, Objectives 1 and 2 ) a. 3.52 b. -a- 2 7 b 3 c. 1 6 (9 - 7)4 - 5 12 d. 2(6)2 - 5(3) + 7 e. 728 - 3u15 - 2(7 - 3)u f. 5 + 152 + 4(3)(8) 2 · 3 12. Evaluate each expression for the given values of the variables. (Section 1.3, Objective 3 ) a. 3x - 5 x + 1 for x = 0, 1, 2, 3 b. 4x + 6y for x = 2 and y = 3 c. b2 - 4ac for a = 2, b = 6, c = 3 13. Determine if the given value is a solution of the equation. (Section 1.3, Objective 4 ) a. x2 - 5x - 12 = 2x + 6; x = 9 b. 5y - (y - 3) = y + 9; y = 4 14. Translate each phrase into an algebraic expression. Let x represent the unknown number. (Section 1.3, Objective 5 ) a. 16 more than three times a number b. The difference of a number and 12 c. 13 less than five times a number d. The sum of four times a number and 8 15. The height of a baseball hit upward with an initial velocity of 96 ft/sec from an initial height of 6 ft is represented by the expression -16t2 + 96t + 6, where t is the number of seconds after the ball has been hit. What is the height of the ball after 3 sec? (Section 1.3, Objective 6 ) 16 The expression P(1 + r)t represents the amount of money in an account when P dollars is invested at an annual interest rate of r (in decimal form) for t yr. Find the amount of money that will be in an account at the end of 4 yr if $2500 is invested at 1.2% annual interest. (Section 1.3, Objective 6 )
hendricks_beginning_algebra_1e_ch1_3
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