Name: date: period: COLLEGE PREP CHAPTER 1 REVIEW SECTION 1.1: You should be able to Determine whether a number is a solution to an equation. Solve linear equations (find a value for a variable that makes the equation true). Determine if an equation is conditional (it has one answer), contradiction (it has no solutions), or an identity (all real numbers are solutions). 1. Determine if is a solution to 2. Determine if is a solution to Solve the linear equations, and determine if they are conditional, contradiction, or identity. Write the solutions as a solution set (in { } ) 3. 4. 5. 6. SECTION 1.2: You should be able to. Translate English statements into mathematical statements Model and solve direct translation story problems Model and solve mixture problems Model and solve uniform motion problems Know the formulas for simple interest (, where I = interest earned, p=principle, r=rate, and t=time in years), and uniform motion ( where d=distance, r=rate, and t=time). Translate into mathematical statements. Do not solve. 7. The sum of three times a number and 7 is 22. 8. The difference of a number and 3 is equivalent to the quotient of the number and 2.
For each of the following problems, translate into a mathematical statement, then solve the equation. Show all your work, including your equation. 9. The sum of five consecutive odd integers is 125. Find the integers. 10. Logan is in an elementary statistics course and has test scores of 85, 81, 84, and 77. If the final exam counts the same as two tests, what score does Logan need on the final to have an average of 80? 11. Angie received an $8000 bonus and wants to invest the money. She wants an overall annual return of 12% ($960). She wants to invest part of the money in bonds that give a return of 8%, and the rest in stocks that have a return of 18%. How much should she invest at 18% to reach her goal? 12. The perimeter of a rectangular window is 76 feet. The window is 8 feet longer than it is wide. Find the dimensions of the window. 13. Suppose Joe buys a sleeping bag for a final cost of $38.34, which includes the sales tax of 6.5%. What was the original price of the sleeping bag (before tax)? 14. Lynn s Chocolate Store sells chocolate covered blueberries for $10.95 per pound and chocolate covered strawberries for $13.95 per pound. Lynn wants to sell a mix of the two that would sell for $12.95 per pound with no loss of revenue. How many pounds of each should be used to make 12 pounds of the mix?
SECTION 1.3: You should be able to. Solve for a variable in a formula. Use formulas to solve problems. (See the story problems section.) 15. Solve for. 16. Solve for. SECTION 1.4: You should be able to Represent inequalities using the real number line and interval notation (graph them). Understand the properties of inequalities (most especially the rule that if you multiply or divide by a negative, you must switch the direction of the inequality). Solve linear inequalities. Solve story problems involving linear inequalities. Write each inequality using interval notation, and graph the inequality. 17. 18. Write each interval in inequality notation, and graph the inequality. 19. 20. Solve each linear inequality. Express your solution using interval notation. Graph the solution set. 21. 22.
23. A high school band sells candy bars at a carnival for $1 each to raise money for new instruments. The band pays $50.00 to rent a booth, and must pay the candy company $0.60 for each candy bar sold. How many bars must the band sell to make a profit? SECTION 1.5: You should be able to Determine the intersection or the union of two sets. Solve compound inequalities involving and (intersections). Solve compound inequalities involving or (unions). Solve story problems involving compound inequalities. Given the following sets:, find 24. 25. Solve each compound inequality. Write the solution in interval notation. Graph the solution set. 26. 27. 28. 29.
SECTION 1.6: You should be able to. Solve absolute value equations. Solve absolute value inequalities involving or (Intersections). Solve absolute value inequalities involving or (Unions). Solve applied problems involving absolute values. Solve the absolute value equations. Remember to isolate your absolute value first! Write your solution as a solution set. 30. 31. 32. 33. Solve each absolute value inequality. Graph the solution set. 34. 35. 36. 37.
COLLEGE PREP CHAPTER 1 REVIEW ANSWER KEY 1. Yes. 2. No. 3. {3} conditional 4. Identity 5. Contradiction 6. {-2} Conditional 7. 8. 9. Integers are 21, 23, 25, 27, 29 10. Logan needs a score of 76.5 or higher. 11. She should invest $3,200 at 18%. 12. Width = 15, Length = 23 13. The original price is $36. 14. 4 lbs. of blueberries, and 8 lbs. of strawberries. 15. 16. 17. (2, 7] 18. 19. 20. 21. 22. 23. 125 candy bars or more must be sold. 24. 25. 26. 27. (-5, -1) 28. (-1, 4) 29. 30. 31. {- 1, -3} 32. 33. 34. (-2, 2) 35. [-5,1] 36. 37.