Welcome to Honors Algebra 2, May 2018 Hello, and Welcome to Honors Algebra 2. Honors Algebra 2 is the next course in your path to college-level mathematics. If you are entering Honors Algebra 2, then you have been successful in Algebra I and Geometry, probably both at the honors level. As you prepare for Honors Algebra 2, we have included some helpful starting points, as well as, a summer assignment to help refresh your memory and allow us to jump right into math when school begins next fall. 1. This assignment is due on the first day of class in August 2018 and MUST be in your journal. You may use the internet to help complete some of this assignment and we ve included some examples and notes to get you started. ALL WORK MUST BE SHOWN in your journal for these problems. (Answers without supporting work shown will not be accepted.) 2. Each student will need a journal. This must be a large 5-subject spiral notebook (pockets are okay but not required). We will use this journal all year with the online textbook and classroom resources so make sure that it is durable with lots of pages. 3. Problems in this packet should be familiar and cover basic skills that you will need in Honors Algebra 2. The grade on this summer packet will count as your first journal grade and points will be deducted for late submissions. You are encouraged to join the Summer Honors Algebra 2 Google Classroom (code: jr01i6) where you can send either of us a message and will find this assignment posted. We look forward to working with each of you! Mrs. Erin Dyke and Mrs. Mimi Henshaw dykee@fcpsk12.net and henshawa@fcpsk12.net Mathematics Department James Wood High School
Honors Algebra 2 Summer Assignment: 1. On the first page of your journal, please include the following: a. Your full name b. A personal goal for the 2018-2019 school year c. An academic goal for the 2018-2019 school year d. On the back of the first page, make a list of usernames and password clues (do not write down your actual passwords) for all websites you will be using (google classroom, online textbook, etc.) For now, you may not have much here but you will want to leave space to fill this in once the school year starts. 2. On the second page, create a title page for your Summer Assignment Notes and Practice Problems. Subtitle: A review of Algebra I and Geometry. a. Subsequent pages will be an outline of the minimum topic requirements. b. Part I: Students are to compose a reference book containing information and examples of the methods and concepts described in this assignment. c. The student entries should contain detailed information and examples or graphs (if applicable). d. Students are to use color neatly for illustration, highlighting, and presentational purposes. e. Part II: All practice problems are to be listed and then all work shown neatly to justify the solution. Titles for the practice problem sections should be visible and easy to find.
Part I: Reference Book For each of the following words or mathematical phrases, complete the following: a. definition including proper notation b. example written out and explained c. labeled picture or graph, if starred (*) below Using color or highlights can help in explaining and should be neat and organized for reference as needed throughout the course. 1. polynomial 2. monomial 3. binomial 4. trinomial 5. linear function * 6. quadratic function * 7. cubic function * 8. solution, solutions, solution set 9. solve 10. literal equation 11. distributive property 12. operations of polynomials 13. factors 14. terms 15. radical 16. perfect square 17. perfect cube 18. x-intercepts (include all possible names for this) *
Part II: A. Solving Literal Equations - A literal equation is an equation that contains more than one variable - You can solve a literal equation for one of the variables by isolating that specific variable on one side of the equation - this is called solving for a variable. Ex. 1 3xy = 18 Solve for x Ex. 2 5a 10b = 20 Solve for a 3xy = 18 5a 10b = 20 3y 3y + 10b +10b x = 6 5a = 20 + 10b y 5 5 5 a = 4 + 2b PRACTICE SET 1 Solve each equation for the specified variable. 1. P = (g 9)180, solve for g 2. 3x + y 6h = 10y, solve for x 3., solve for p 4. ml mx = B, solve for m
I. Reviewing the Distributive Property B. Binomial Multiplication - The distributive property is used when you want to multiply a single term by throughout an expression Ex. 1 8(5x + 9x) 8 5x + 8 9x 40x + 72x II. Multiplying Binomials the FOIL Method - When multiplying two binomials (an expression with two terms), we use the FOIL method. This method uses the distributive property twice. - FOIL is the order in which you will multiply the terms F first terms of each binomial O the outer terms of the problem I the inner terms of the problem L the last terms of each binomial Ex. 1 (x + 6)(3x + 10) First: x 3x 3x (x + 6)(3x + 10) Outer: x 10 10x Inner: 6 3x 18x Last: 6 10 60 3x + 10x + 18x + 60 3x + 28x + 60 PRACTICE SET 2 Multiply. Be sure to simplify like terms as you write your final answer. 1. 2.
- When asked to multiply polynomials having more than 2 terms, the FOIL method does not work. Some students will set up a chart in order to multiply the terms. Ex. 2x 2 + 5x 4 2x 5x -4x 6x 15x -12 = 2x + 5x + 6x - 4x + 15x - 12 = 2x + 11x + 11x 12 3. 4. C. Rules of Exponents Multiply common bases: Division of common bases: Power to a power: Negative power: Power of Zero: PRACTICE SET 3 Simplify each expression. 1. 2. 3. 4. 5.
D. Factoring Polynomials I. Using the Greatest Common Factor (GCF) to factor - Always determine whether there is a GCF before starting any other factoring pattern Ex. 1 * in this example the GCF is * divide each term by = GCF remaining trinomial * Now, we must determine if the remaining polynomial in the parentheses is factorable. Can this trinomial be factored into two binomials? In order to determine this you can make a list of all the factors of 30. 30 30 1 30-1 -30 2 15-2 -15 3 10-3 -10 5 6-5 -6 Since the factors -5-6 = 30 AND -5 + -6 = -11, we will choose these factors to help us create the binomial factors. II. Difference of Two Perfect Squares Pattern - This pattern will ONLY work with a subtraction sign and 2 perfect squares. Ex. 1 terms * some students call this the square root pattern since you take the square root of both III. Solving An Equation by Factoring - If given an equation, set the equation equal to zero. Then you can solve by factoring if you set each factor equal to zero and solve the factor equations for the variable.
PRACTICE SET 4 Factor each expression 1. 2. 3. 9x 2 36 4. x 4 81 5. E. Radicals and the Quadratic Formula I. The Quaadratic Formula - Need standard form: - The quadratic formula is used to solve quadratic equations where factoring is not an option. The quadratic formula will leave your answer in radical form and you MUST simplify the radical whenever possible. The Quadratic Formula: x = 2 b ± b 4ac 2a, where a =/ 0 Ex. 1 Solve: You may leave your answer in this. However, you should recognize that this represents two different solutions: 5 + 73 5 73 x = 4, and x = 4
Ex. 2 Solve: Note: You must simplify the square root of 112. PRACTICE SET 5 For each of these last problems, show how to solve the given equation using EACH of the methods given. 1. 2x 2 7x 4 = 0 Solve by: a. graphing b. the quadratic formula c. factoring 2. b 2 4b = 12 Solve by: a. factoring b. the quadratic formula c. graphing 3. x 2 36 = 0 Solve by: a. factoring b. graphing c. the square root method 4. 9x 2 = 4 Solve by: a. factoring b. the square root method c. the quadratic formula 5. 2x 2 22 = 7x Solve by the method of your choice.