Honors Algebra 2 Summer Assignment DUE: SEPTEMBER 20 th, 2018 As an incoming Honors Algebra 2 student, it is important that you are proficient in skills from previous math courses. This assignment contains examples of the skills you are expected to know, such as factoring quadratic expressions, solving quadratic equations using different methods (factoring, square roots, and quadratic formula), adding polynomial expressions, subtracting polynomial expressions, and multiplying quadratic expressions. **Completion of this packet will count towards your first assessment grade** **All students entering Honors Algebra 2 will be assessed on the skills reviewed in this assignment ** If you need assistance with any of these skills, we strongly recommend that you utilize the video resources that are provided. Enroll in the Google Classroom Franklin Township Math Summer Projects Grades 6-12 for easy access to hyperlinks using the code: 3ayq21k Or visit the Franklin Township Public Schools Mathematics page for more information: https://www.franklinboe.org/page/16759 SCORE CRITERIA SCORING RUBRIC 5 Student completed packet and showed effort throughout. 3 Student partially completed packet and showed little effort throughout. 0 Student did not complete packet or showed no effort throughout. 1
Systems of Equations Resource:http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/system-ofequations/solving-systems-equations/equations-solution-by-substitution http://www.virtualnerd.com/algebra-1/systems-equations-inequalities/elimination/elimination-bymultiplication/equations-solution-by-elimination-multiplication-alternative Solve each system of equations by substitution or elimination. 1) x = 3y 4 2x y = 7 2) x y = 6 x + y = 2 3) x 2y = 3 2x + 4y = 6 4) 3x 2y = 0 4x 3y = 15 Factoring: Greatest Common Factor Resource: https://www.youtube.com/watch?v=y1vd5wb0rnm Factor out the Greatest Common Factor from each of the following expressions 5) 8x 2 + 10x 6) 6n 2 30n + 42 7) 18p 3 63p 2 9p Factoring Quadratic Expressions When a = 1 Resource: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-byfactoring/v/example-1-solving-a-quadratic-equation-by-factoring Factor the following expressions. 8) x 2 + 14x + 45 9) x 2 11x + 24 10) x 2 + 6x 16 2
Factoring Quadratic Expressions When a > 1 Resources: http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/trinomial-factorization/leadingcoefficient-not-1/factor-by-a-c-method http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/trinomial-factorization/leadingcoefficient-not-1/trinomial-possible-factors Factor the following expressions COMPLETELY: 11) 2x 2 + 5x + 3 12) 4x 2 + 3x 7 13) 6x 2 11x + 4 14) 9x! y! 3x! y! 15xy 15) x + 4x! + 3x 16) 2x! y 4xy 30y 17) 8x! 162 18) c! 100 19) 2ak + k 6a 3 Solving Quadratic Equations by FACTORING: Resource: https://www.youtube.com/watch?v=sde-1lges0u Solve each of the following equations by FACTORING. 20) x 2 + 8x + 15 = 0 21) 3x 2 16x 7 = 5 22) 6x 2 13x + 3 = -3 3
Solving Quadratic Equations Using SQUARE ROOTS: Resource: https://learnzillion.com/lesson_plans/5135-solve-a-quadratic-equation-by-taking-a-square-root Solve each of the following equations using SQUARE ROOTS. 23) 4x 2 6 = 74 24) 4(x 1) 2 5 = 223 Solving Quadratic Equations Using the QUADRATIC FORMULA: Resource: https://www.youtube.com/watch?v=jswjmtfmdwg Solve the following equations using the QUADRATIC FORMULA: x =!!±!!!!!"!! 25) 4x 2 + 11x 20 = 0 26) x 2 3x = 3 27) 4x 2 1 = -8x Properties of Exponents Resource: https://www.mathsisfun.com/algebra/exponent-laws.html Simplify each of the following expressions using properties of exponents. 28) y! 3y! z 5yz! 29) 3x! 2x! 5x 30)!!"!!!!!"!"!!!!" 31)!"!!!!!!"!!!"!!" 32) 4! 33) 4x!y!! 4
Adding Polynomial Expressions Resource: http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/add/additionexample Add the following expressions. 34) (12y 2 + 17y 4) + (9y 2 13y + 3) = 35) (-7x 5 + 14 2x) + (10x 4 + 7x + 5x 5 ) Subtracting Polynomial Expressions Resource: http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/addsubtract/subtract/subtraction-example Subtract the following expressions. 36) (3x 2 8x + 5) (8x 2 2x + 1) 37) (3 6n 5 8n 4 ) - (-6n 4 3n 8n 5 ) Multiplying Polynomial Expressions Resource: https://www.khanacademy.org/math/algebra/introduction-to-polynomialexpressions/multiplying-polynomials-by-binomials/v/more-multiplying-polynomials Multiply each of the following expressions. 38) 6x 2 (4x 2 + 5x 6) 39) (4x + 5)(2x 1) 40) (3x + 2)(5x 2 8x + 2) 5
Apply Operations of Polynomials Resource: http://www.virtualnerd.com/algebra-1/exponents-exponential-functions/monomialspolynomials/polynomials/rectangle-area-from-monomial-polynomial-product Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and potatoes. His plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following: Write and simplify an expression that represents the length of the south side of the field. Write and simplify a polynomial expression that represents the perimeter of the pumpkin field. Write and simplify a polynomial expression that represents the area of the potato field. Write and simplify the polynomial expression that represents the area of the bean field if x = 3 and y = 7. What unit would the area of Bob s bean field have? 6
Application of Quadratic Functions Click on the Link to watch the video --> Punkin Chunkin How long does a Projectile Pumpkin stay in the air? Directions: Watch the video and follow along to solve Problem 1. It will tell us how long a Projectile Pumpkin will stay in the air. You may pause and re-watch the video as necessary. Problem 1: The graph of a Projectile Pumpkin may look like the graph below. The projectile s height over time can be described by the following quadratic equation where h = height and t = time. h = -16t 2 + 76t + 20 Based on the video and using the equation above, can you answer the following questions about the equation: What is the initial velocity (related to the acceleration of gravity) of the pumpkin? What is the initial upward velocity? What is the initial height? How long will the pumpkin stay in the air? To do this we must find the zero(s) or root(s) or solution(s) by FACTORING (Follow along with the video) Step 1 : Multiply by -1 Step 2: Divide by 4 Step 3: Ready to Factor ( t )( t ) = 0 Step 4: Set each Factor equal to zero and solve Step 5 : Using your answer from Step 4, Answer the Question How long does the pumpkin stay in the air before hitting the ground? 7
Now that you have finished the video and the related problem, see if you can use your skills to solve additional pumpkin related problems. Problem 2: What is the maximum height the pumpkin reaches? At what time does the pumpkin reach its maximum height? Problem 3: A pumpkin is launched from a catapult that is located at the top of a building that is 128 feet above the ground. The pumpkin s height can be calculated after t seconds by the following Equation: h = -16t 2 + 32t + 128 How long does the pumpkin stay in the air? Factor the quadratic equation and solve. 8