MAT 1033 Final Review for Intermediate Algebra (Revised April 2013)

Transcription

1 1 This review corresponds to the Charles McKeague textbook. Answers will be posted separately. Section 2.1: Solve a Linear Equation in One Variable 1. Solve: " = " 2. Solve: "# = " 3. Solve: " " = " Section 2.2: Solve Formulas for the Indicated Variable 4. Solve for v: = " " 5. Solve for y: " " = " Section 2.3: Solve Application Problems Involving Linear Equations 6. Find the dimensions of a rectangle if its length is two more than four times the width and the perimeter is 84 feet. 7. A teacher s salary for her second year is $39,520. If this is 4% more than her first year salary, how much did she earn her first year? 8. Your friend invests $6,000 in two accounts. If one account pays 6% per year and the other pays 8% per year, how much was invested in each account if the total interest earned in one year was $410? Section 2.4: Solve a Linear Inequality in One Variable Solve each inequality. Write the answer in interval notation. 9. Solve: " " 10. Solve: + " < 2 Section 3.1: Graph Linear Equations by Finding the Intercepts Graph each linear equation by finding the intercepts. Write each intercept in ordered pair form. 11. " " = " 12. " " " =

2 2 Section 3.2: Find the Slope of a Line Given Two Points on the Line 13. Find the slope of the line through each pair of points. a),,, b),,, For part c) find the slope of the line through these two points. Then, determine the slope of a line perpendicular to this line. c),,, Section 3.3: Graph a Linear Equation Using the Slope and the Y-Intercept Determine the slope and y-intercept for each line. Write the y-intercept as an ordered pair. Then, sketch the graph of each line using the slope and y-intercept. 14. " = 15. " + " = Section 3.3: Find the Equation of a Line Given the Slope and a Point on the Line The slope and one point on a line are given. Find the equation of each line. Write the equation in slope-intercept form. 16., ; = 17., ; = Section 3.3: Find the Equation of a Line Given Two Points on the Line Two points on a line are given. Find the equation of each line. Write the equation in standard form. 18., and, 19., and, Section 3.3: Find the Equation of a Line in Slope-Intercept Form that is Parallel or Perpendicular to a Given Line Containing a Given Point 20. Find the equation of the line parallel to " = containing,. 21. Give the equation of the line perpendicular to = " + with x-intercept of.

3 3 Section 3.4: Graph Linear Inequalities in Two Variables Graph the solution set for each of the following < 2 Section 3.5: Determine Whether a Relation is also a Function 24. Which relations below are also functions? a),,,,, b),,,,,,, c) d) Section 3.6: Use Function Notation to Find the Value of a Function 25. Let = " and = + ". Evaluate the following. a) ( ) b) ( ) c) Section 3.8: Solve Variation Problems 26. x varies directly as y If x is 6 when y is 2, find x when y is y varies inversely as the square of x If y is 4 when x is 5, find y when x is The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 42 pounds when the spring is stretched 2 inches, find the tension when the spring is stretched 6 inches.

4 4 Section 4.1: Solve a System of Linear Equations in Two Variables by the Addition Method Solve each system by the addition method. 29. " " = " 30. " " = " + " = " + " = Section 4.1: Solve a System of Linear Equations in Two Variables by the Substitution Method Solve each system by the substitution method. 31. " = " 32. "# + " = = " + " = Section 4.3: Solve Application Problems Involving a System of Linear Equations in Two Variables For each problem set up a system of two equations and two unknowns. Then, solve the system using either the addition method or the substitution method. 33. The sum of two numbers is 50. One of the numbers is 4 less than twice the other. Find the two numbers. 34. How many gallons of 20% alcohol solution and 60% alcohol solution must be mixed to obtain 16 gallons of 30% alcohol solution? Section 4.5: Graph a System of Linear Inequalities in Two Variables Graph the solution set for the given system of linear inequalities. 35. > + Section 5.1: Simplify Expressions using the Properties of Exponents In questions simplify each expression. Leave all answers with positive exponents "

5 5 Section 5.1: Write Numbers in Scientific Notation Write each number in scientific notation. 39. a) ", "",, b). "# Section 5.2: Add and Subtract Polynomials 40. Add: Subtract: + + Section 5.3: Multiply Polynomials 42. Multiply: " " " 43. Multiply using the FOIL method: " + " 44. Multiply using the FOIL method: " " Find the special product: " 46. Multiply: " " 47. Simplify: " " Section 5.4: Factor using the GCF Method and the Grouping Method Factor using the GCF method: 48. " " 49. Factor each polynomial: 50. " + "# " 51. +

6 6 Section 5.5: Factor Trinomials using the Trial-and-Error Method or the AC Method Factor each polynomial: 52. " + " 53. " " " " 55. " + "# 56. " + " " 58. "#$ " + "#$ + " Section 5.6: Factor using the Difference of Squares Method Factor each polynomial completely: " Section 5.6: Factor using the Sum or Difference of Cubes Method 62. Factor using the sum of cubes method: + "# 63. Factor using the difference of cubes method: " Section 5.7: Factor a Variety of Polynomials Factor each polynomial completely. 64. " "# + " " " " 67. " " Section 5.8: Solve Equations by Factoring In questions solve each equation by factoring: "# + " = = "

7 7 70. An object projected upward with an initial velocity of 48 feet per second will rise and fall according to the equation = "# ", where h is its height above the ground at time t. At what times will the object be 20 feet above the ground? Section 6.1: State the Domain of a Rational Function State the domain of each rational function: 71. a) b) 72. " + Section 6.1: Reduce Rational Expressions to Lowest Terms Reduce to lowest terms: " + " 72. a) b) " + " " + Section 6.2: Divide Rational Expressions Using Long Division Divide using the long division method: + " " 73. " 74. " " + + " + Section 6.3: Multiply and Divide Rational Expressions Perform the indicated operation. Write each answer in lowest terms. 75. " " + " + " 76. a) b) + " + "

8 8 Section 6.4: Add and Subtract Rational Expressions Perform the indicated operation. Write each answer in lowest terms " " " + + " + " " + + Section 6.5: Simplify Complex Fractions Simplify as much as possible Section 6.6: Solve Equations Containing Rational Expressions 83. Solve: + + " " = Section 6.7: Solve Application Problems Involving Rational Equations 84. The speed of a boat in still water is 20 miles per hour. It takes the same amount of time for the boat to travel 3 miles downstream with the current as it does to travel 2 miles upstream against the current. Find the speed of the current. 85. A pilot can travel 400 miles with the wind in the same amount of time as 336 miles against the wind. Find the speed of the wind if the pilot s speed in still air is 230 miles per hour.

9 9 86. An inlet pipe can fill a pool in 10 hours, and the drain can empty it in 12 hours. If the pool is empty and both the inlet pipe and the drain are open how long will it take to fill the pool? Section 7.1: Simplify Expressions with Rational Exponents (leave positive exponents) 87. a) / / b) " / / c) " / / Section 7.3: Write Radical Expressions in Simplified Form Simplify: Assume all variables are nonnegative. 88. a) " " b) " " c) " " Section 7.3: Rationalize a Denominator that Contains Only One Term Rationalize each denominator: 89. a) b) c) Section 7.4: Add and Subtract Radicals Combine. Assume all variables are nonnegative. 90. " " " " 91. " + " " Section 7.5: Multiply Expressions Containing Radicals 92. Multiply: 93. Multiply:

10 10 Section 7.5: Rationalize a Denominator Containing Two Terms Rationalize each denominator: Section 7.6: Solve Equations Containing Radicals 96. Solve: " + = 97. Solve: + = Section 7.7: Perform Operations with Complex Numbers 98. Multiply. Write your answer in a + bi form. " ( + ") 99. Divide. Write your answer in a + bi form. + + " Section 8.2: Solve Quadratic Equations using the Quadratic Formula 100. Solve using the Quadratic Formula: = ± "# " a) + " + = b) + " = c) + " + =