Rising Algebra 2/Trig Students! As a 7 th grader entering in to Algebra 2/Trig next year, it is very important that you have mastered the topics listed below. The majority of the topics were taught in Algebra 1, but it is important to remember some of the basic number sense you learned in elementary school. Fraction Operations add, subtract, multiply divide Solving proportions Solving multistep equations and inequalities Systems of Equations Factoring binomials and trinomials Solving quadratics Simplifying radicals and rationalizing the denominator Graphing Quadratic Equations Domain and Range of Graphs All of the topics listed above must be done without the use of a calculator. We will not use calculators in Algebra 2/Trig unless it is necessary (i.e. our statistics unit) Algebra 2/Trig is a highly accelerated, fast-paced high school level course. In order to cover the required curriculum, Ms. Lorenz will not have time to reteach Algebra 1 content. We recommend completing this packet, a few questions at a time, over the course of the summer. We prefer that you do not complete the problems right after school ends. Everything is still fresh in your mind! Take a few weeks off, start up the packet at the beginning or middle of July, and see what you remember! Ms. Lorenz will be posting answer keys to each section throughout the summer. She will also be providing you with tutorial videos and extra practice. Please use the resources she have given you as the opportunity to review the material and challenge yourself along the way! If you have any questions, please do not hesitate to reach out to Ms. Lorenz. I look forward to meeting you! Jayme.Lorenz@lcps.org (Directions for accessing the website can be found on the next page.)
1. 1. Go to the staff directory on the Mercer webpage and find Lorenz, J 2. On the left-hand side choose Uprising 8 th Graders (make sure it drops down Geometry and Algebra 2/Trig tabs) 3. Select the Algebra 2/Trig tab. When you select the class you will see options for the packet, answer keys, etc. 4. Check back often so you don t miss anything!
Fraction Operations When adding or subtracting fractions, you must first find a. When multiplying fractions, multiply. Use - - when dividing fractions! Complete the following fraction operations without a calculator. 1. 1 2 + 2 3 + 1 5 2. 1 6 2 3 4 5 3. 7 14 12 3 4. 5 2 3 5. 4 3 + 2 5 1 2 6. 7 6 3 4 8 5 7. 10 2 5 8. Thinking ahead 3 2x + 4 5 + 6 x
Solving Equations, Inequalities, and Proportions How do you solve a proportion? What do you do when you multiply or divide an inequality by a negative number? 1. 2 = 3 2 x 4 2. 7n 3(6 + 2n) = 3(n 8) 3. 6 + 4x = 1 3 (6x + 9) 4. 5 = 8 x 9 x+5 5. 167 < 6 + 7(2 7m) 6. 3(4x + 3) + 4(6x + 1) = 43 7. y+10 y 7 = 8 9 8. 1 3 x 7 3 = 12
Systems of Equations In Algebra 2/Trig, systems of equations will appear as soon as unit 3! You will not be permitted to use the calculator functions to solve the system for you. Math teachers at Mercer model the high school courses at John Champe High School. Algebra 2 (with or without Trig) classes at JCHS do not use calculators, so you will need to be able to solve a system by hand. Other than graphing, what are the two methods we use to solve a system of equations? 1. 2. Solve the following systems using the most appropriate (or preferred) method. Do not forget to find both variables and show all work! 1. 4x + 2y = 10 x y = 13 2. 5x + y = 8 3x + 2y = 10 3. y = 3x + 9 x + 3y = 17 4. One integer is three more than twice the second integer. The sum of the two integers is -9. Find the numbers. 5. At Great Wolf Lodge Ski Resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented? 6. x + 2y = 2 3x + 4y = 6 Thinking ahead! Give it a try y = x 2 + x 2 y = x + 1
Factoring and Solving Quadratics In Algebra 2/Trig, factoring will appear in many of our units! You will not be permitted to use the calculator functions to factor the polynomial for you. Math teachers at Mercer model the high school courses at John Champe High School. Algebra 2 (with or without Trig) classes at JCHS do not use calculators, so you will need to be able to solve quadratics by hand. Standard Form of a Quadratic: Quadratic Formula: When is it appropriate to use the square root method to solve a quadratic function? Solve each of the following quadratics using the most appropriate method. If the quadratic does not factor, you will be instructed to use the quadratic formula. Otherwise, please do not use it. 1. 2x 2 + 14 = 11x 2. 5x 2 20 = 0 3. x 2 15x = 56 4. (Quadratic Formula) 8x 2 5 = 4x 5. 1 2 x2 12 = 21 6. (x 9) 2 + 1 = 37
7. 8 3x = 5x 2 8. 4x 2 19x 5 = 0 9. 100x 2 25 = 0 10. 16x 2 = 64x Hint: You CANNOT divide by x!! 11. 2x 2 14x = 0 12. 4(x 3) 2 + 7 = 55 Thinking ahead (and putting it together!) It is important to know your fraction operations and how to factor so that when you are presented with a problem like the one below you are able to write the fraction in simplest form. x + 5 4x 16 2x2 32 x 2 25
Radicals In Algebra 2/Trig we will not only be simplifying square and cube roots, but 4 th, 5 th, 6 th (and so on!) roots as well. If there is a radical in the denominator of a fraction, we need to get rid of it by multiplying by a fraction of 1. This process is called rationalizing the denominator! Simplify each radical below. Having trouble? Use a factor tree to help you! 1. 180 2. 48 81 3. 18x2 6 3 4. 72 5. 3 2 6 3 6. 1715 Pay attention to cube root vs. square root! 7. 8 3 4 6 8. 3( 10 5 6) Hint: distribute!
Graphing Quadratic Equations y = x 2 + 6x 8 Does the parabola open up or down? Is the vertex a minimum point or a maximum point? Vertex a= b= c= Table of Values x Y Equation of Axis of Symmetry Roots y = 1 2 x2 + 2x + 3 Does the parabola open up or down? Is the vertex a minimum point or a maximum point? Vertex a= b= c= Table of Values x Y Equation of Axis of Symmetry Roots
Domain and Range x-values represent the of a function and y-values represent the of a function. Express your answers using set builder notation. For example {x x > 0} is read as: x such that x is greater than zero. 1. D: R: Is this a function? Yes or No 2. D: R: Is this a function? Yes or No 3. D: R: Is this a function? Yes or No