Summer Assignment for students entering Pre IB Algebra II

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Francine Bond
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1 Summer Assignment for students entering Pre IB Algebra II Part I - Problems Directions: 1. Students, please complete the attached packet of Algebra 1 problems by the first day of school. You are expected to complete all boxed problems on a separate sheet of paper and SHOW ALL WORK. If you need to check your work the answers can be found on the last few pages of the textbook portion. 2. Matrices: You will first find notes for you to read and then two pages from the textbook to complete. Once again use a separate piece of paper to complete and show all work. 3. Linear Programming: You will find notes along with 3 problems to complete. Please do them on a separate piece of paper and show all work. 4. Domain and Range: You will find notes and then practice problems. If you feel there is enough room you may write on this sheet but don t forget to attach it to your other work. This assignment will be checked for completeness, not accuracy. All problems should be completed. Show work on every problem. Write neatly in pencil and box final answers. You will be assessed on the topics presented in this assignment THURSDAY AUGUST 25. We will review this packet and you will be given an opportunity to ask questions in class Wednesday August 24 (the first day of school). However, if you have significant trouble completing this packet you should reconsider your course placement. You should not need extensive help from a tutor as this is a review assignment. Part II Writing Assignment Choose a topic of interest to you and write a paper about how your topic relates to math. For example, the math involved with the various strategies in different sports or the math strategies used to spend $100 at the mall during back to school sales. Your paper must be typed. There is no length requirement as your paper must be complete with enough math to be considered a math paper. The grading rubric will be posted online (Mrs Inglis or Mrs Levin s websites) the week before school starts. Be careful not to choose a topic that is too basic. This assignment (problems and written paper) is due the first day of school. Be sure to bring it to class. No late packets will be accepted. With questions Mrs. Inglis at KInglis@lvusd.org or Mrs. Levin at ALevin@lvusd.org. As this is a summer assignment, please be patient for a response as our work is not checked daily. Mrs. Inglis will post the syllabus with required supplies on her website the week of registration. Please print and bring required supplies to class as well as a signed syllabus the first day of class.

Linear Programming Linear Programming is the process of taking linear inequalities relating to some situation and finding the best value under the given circumstances.

41 Linear Programming Linear Programming is the process of taking linear inequalities relating to some situation and finding the best value under the given circumstances. We often use linear programming models to maximize profits and minimize costs given constraints like cost to produce product and the consumer purchase price. For this reason, most real world examples occur in the first quadrant. The inequalities we graph are called the constraints and the intersection of these graphs is called the feasible region. Typically this region takes on a polygonal shape. When this happens we call it bounded. Each linear programming problem will also have a function or cost equation that typically looks like f(x, y) where we plug in values for both x and y. This equation tells what the maximum or minimum value is and where it occurs (it occurs at the (x, y) coordinate we plug into the problem). Step 1: Graph each equation and find the feasible region remember these are all inequalities so we will need to check for solid and dotted lines as well as shade each equation Step 2: Find the vertices that make the feasible region solve using systems of equations you will need to do this for every pair of equations that form the feasible region Step 3: Plug the vertices into the function equation f(x, y) Step 4: Find the maximum or minimum value 1. x 1 Step 1: y 0 2x + y 6 f(x, y) = 3x + y Step 2: (1, 4) (3, 0) (1, 0) Step 3: (1, 4) = 3(1) + 4 = 7 (3, 0) = 3(3) + 0 = 9 (1, 0) = 3(1) + 0 = 3 Step 4: Max of (3, 0) and Min of (1, 0) 2. y 1 x 6 y 2x + 1 f(x, y) = x + y 4. 2x + 3y 6 3x 2y -4 5x + y 15 f(x, y) = x + 3y 3. x + y 3 x + 2y 4 x 0 y 0 f(x, y) = 3y 4x

Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane

Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant