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1 Algebra II Honors Course Prerequisite Assignment We hope that you are enjoying your summer break/fall semester! You are currently enrolled to take Algebra II Honors at Allentown High School during the upcoming school year. This packet is the Course Prerequisite Assignment. You are expected to bring this completed packet with you on the first day of class, as we will be taking questions and reviewing the material at that time. On the second day of class, we will have a test on this assignment. Before coming to class, you should be a master of these objectives. The score on this test is a strong indicator of success in the class. This packet is comprised of many topics in which one should have a mastery of in order to succeed in the course. You are to complete all of the problems in the packet and list each of your final answers on the answer booklet provided. Please show ALL of your work for each question in the packet on the blank back pages and/or attach any and all scrap paper used. *PLEASE NOTE* There is an answer key section immediately following the last problem of the packet. Use this key to check you solutions and guide you along as you progress. ** The decision to take an honors course is a serious one. This class will require: ** Exemplary work ethic and time management skills Personal Responsibility for attendance and accountability for work requirements A genuine desire to learn, self-discipline and a determination to succeed We will be using graphing calculators throughout the course. If you do not own a graphing calculator, it is recommended that you purchase your own. We will do our best to provide as many as we can *IN CLASS ONLY* but will not be able to loan them out for work at home. We highly recommend purchasing one from the TI-84 Plus product line. A great way to help you remember any given problem is to Google the topic. One can also use the search function for and to help guide you through any problems that require a memory refresh If you have any questions regarding the requirements of this assignment, please Lynn Folino, Vice Principal of AHS at FolinoL@ufrsd.net We look forward to meeting you in class! Sincerely, The Algebra II Honors Teachers At Allentown High School

2 Chapter 1 Solving Equations and Inequalities Chapter Expressions and Formulas Evaluate each of the following expressions: 1. ( ) (7 3 2 ) Evaluate each expression if given a = 8.2, b = 3, c = 4 and d = ½. 4. ac bd a 5. 6b 5c d 2 c 1 6. b d 7. A person s basal metabolic rate (or BMR) is the number of calories needed to support his or her bodily functions for one day. The BMR of an 80-year-old man is given by the formula of BMR = 12w (0.02)(6)12w, where w is the man s weight in pounds. Estimate the BMR of an 80-year-old man who weighs 170 pounds. Chapter 1.2 Properties of Real Numbers Name the set or sets of real numbers belonging to each of the following: Simplify the following expressions: 12. 4(10g + 80h) 20(10h 5g) n n 14. (7 2.1x)3 + 2(3.5x 6) a b Chapter 1.3 Solving Equations Write an algebraic equation for each of the following written statements: (do not solve) 16. Four times the square of a number increased by five times the same number is thirteen. 17. Twice the sum of a number and seven is the same as half of that same number. Solve each equation and check your solutions x 2 = 5x 7 3x 19. 3(8x 5) = 4(7 6x) 20. 3(x 5) + 8x = 18 (3 10x) 21. 3(8x 5) + 3 = 22x + 2(x 6)

3 y p = 8.7 Solve each equation for the specified variable. 24. Solve for p given 25. Solve for x if given 3pq c + ax = dx 12 r Chapter 1.4 Absolute Value Equations Evaluate each expression if w = 4, x = 2, y = ½ and z = z 35yz wx 4x 8x 4 Solve each of the following equations and check your solutions. 28. x b x x 1 2x 11 Chapter 1.5 Solving Linear Inequalities Solve each inequality and graph the solution set on a number line (12 3n) < x 2 < 7(4x 2) Four friends plan to spend Friday evening at the bowling alley. Three of the friends need to rent shoes for $3.50 per person. A game of bowling costs $1.50 per person. If the friends pool their $40.50 together, how many games can they afford to bowl? 34. Write an inequality to describe this situation. 35. Solve the inequality and interpret the solution in context of the question. Chapter 1.6 Solving Compound and Absolute Value Inequalities Solve each inequality and graph each solution set on a number line a + 8 < 23 or ¼a 6 > < 4x 10 < x x 1 27

4 Chapter 2 Linear Relations and Functions Chapter 2.1 Relations and Functions Graph each relation/equation and state the domain & range. Is it a function? Explain. 40. {(3, -4), (1, 0), (2, -2), (3, 2)} 41. y = x Find each value if given f ( x) 2x and g( x) 0.4x 1.2 x 42. f (-8) 43. g (2.5) 44. f (2a) Chapter 2.2 Linear Equations Identify whether or not each of the equations are linear. If not, explain y x = y 46. xy 5 = f(x) = 2 8x 2 Find the x and y intercept for the following equations. Then graph the equation x + 7y = y x = 10 Write each equation in standard form. Identify the A, B and C values y = 2x x 18y = y 5 x 4 3 Chapter 2.3 Slope 53. Find the slope of the line that passes through the points (4, -2) and (-4, -8). 54. Find the slope of the line that passes through the points (6, 4) and (3, 4). 55. Determine whether the slope of a line passing through (4, 3) and (1, -3) and the slope of a line that passes through (1, 2) and (-1, 3) is considered parallel, perpendicular or neither. 56. Determine whether a line with an x-intercept of -2 and a y-intercept of 5 and the line with an x-intercept of 2 and a y-intercept of -5 is considered parallel, perpendicular or neither.

5 Chapter 2.4a Graphing Linear Equations Graph each line on the corresponding coordinate plane provided in the answer booklet. 57. Graph a line that has a y-intercept of -5 and a slope of ¾. 58. Graph a line that has a slope of -3 and a y-intercept of x = y = y = ¼x y = 3x 63. 4x y = x 7y + 21 = 0 Chapter 2.4b Writing Linear Equations in Slope Intercept Form 65. Write the equation of a line in slope intercept form that passes through (2, 5) with a slope of Write the equation of a line in slope intercept form that passes through the points (-1, 9) and (2, 0). 67. Write the equation of a line in slope intercept form that passes through the points (3, -2) and (-3, -6). 68. Write the equation of a line in slope intercept form that passes through (-4, 2) and is parallel to the line whose equation is y = ½x Write the equation of a line in slope intercept form that passes through (3, 1) and is perpendicular to the graph of y = -3x + 2.

6 2.5 Creating Scatter-Plot Graphs 70. The table below shows the number of women serving in the United States Congress during the years of Create a scatter-plot graph of this data on the plane provided. 71. The table below shows the years of experience for eight technicians at the Lew Techomatic as well as the hourly rate of pay for each corresponding technician. a. Draw a scatter-plot to show how years of experience are related to hourly rate of pay. Draw a line of best fit. b. Write a prediction equation to show how years of experience, (x), are related to hourly rate of pay (y). 2.7 Graphing Linear Inequalities Graph each inequality on the coordinate plane provided in your answer booklet. 72. y < 3x x + y > y x y 2x 1 Chapter 3 Systems of Equations 3.1 Solving a System of Equations by Graphing Graph the system of equations and state the solution for each. Then describe the system as consistent and independent, consistent and dependent OR inconsistent. 76. y = 3x + 4 6x + 2y = x + 2y = 3 6y 6 = 3x 78. 2x 3y = 0 6y = 4x

7 3.2 Solving a System of Equations Algebraically Utilize substitution or elimination to find the solutions to each of the following systems. 79. Solve the system below using substitution. 80. Solve the system below using substitution. 3x y = 4 2x 8y = 4 y = 4 + x x + 16y = Solve the system below using elimination. 10x 2y = 34 3x + 2y = Solve the system below using elimination. 8x + 2y = 18 4x + y = Solve the system below using the algebraic method of your choice. 3x 5y = 6 2x 4y = Solving a System of Inequalities by Graphing Graph each of the following systems on the coordinate planes provided. 84. x < x 3y < 0 y > 2 y > x y < -2x y > -2x y > -1 x + y < 3

8 Find the coordinates of the vertices (feasible region) of the figure formed by the systems below. 88. y < -3x x > 3 y < ½x y < -1/3 + 3 y > -2 y > x 1 Spiral Review Factoring Factor each of the following completely. If not factorable, indicate simplest form. There is space provided in your answer booklet to allow work to be shown for this section. Take advantage! 90. x x 2 y x 3 75x 93. 6x 2 7x x 2 16x 95. x 2 3x x 2 8x x 2 40x x 2 6x x x x 2 30x + 24

9 Name Algebra II Honors Course Prerequisite Assignment - Answer Packet Chapter 1.1 Expressions and Formulas Date Course Prerequisite Assignment Chapter 1.2 Properties of Real Numbers Chapter 1.3 Solving Equations Chapter 1.4 Absolute Value Equations Chapter 1.5 Solving Linear Inequalities Chapter 1.6 Compound Inequalities and Absolute Value Inequalities

10 Chapter 2.1 Relations and Functions Chapter 2.2 Linear Equations Chapter 2.3 Slope Chapter 2.4a Graphing Linear Equations

11 Chapter 2.4b Writing Linear Equations Chapter 2.5 Creating a Scatter-Plot Graph a. 71b. 2.7 Graphing Linear Inequalities Solving a System of Equations by Graphing Solving a System of Equations Algebraically Solving a System of Inequalities by Graphing

12 Spiral Review Factoring Remember, show all of your work in addition to answers The end! Looking forward to a great semester!

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