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Equation Solving Name: ______ Pre-Calculus Summer Math Packet 2019 To better to prepare you for the challenges of Pre-Calculus next year, we have put together some worksheets for you to complete over the summer. The packet will be due the first day back to school in the fall. You will be assessed on the information from the packet during the first week of school. There are 6 sheets to be completed and about 10 weeks to do them in. We do not suggest that you try to do all of this in one sitting, nor should you try to complete it all the first week or last week of summer vacation! If you are taking Pre-Calculus Academic next year you DO NOT have to complete the problems in the Accelerated Section. These are all topics that have been taught in previous years and you should be familiar with them. The assignments stress some of the more important skills you have learned to date and the foundations for what we will be working on next year. A graphing calculator is required for Pre-Calc Accelerated and highly recommended for Pre-Calc Academic. If you cannot afford one you can loan one from the school. Any calculator in the TI-84 family is recommended. We hope you have a wonderful summer! See you in the fall!! Equation Solving Solve the following equations, check all answers to verify your solution. SHOW ALL WORK! 1 푥 7 1. -2(x + 4) – 3 = 7 2. 6(2x - 1) = 3(x - 3) + 7 3. + = 2 3 6 푥+3 푥 3푥+4 4. + = 6 5. + 푥 = 4 6. 0.4(x – 1) + 1 = 0.5x 4 3 2 7. A rectangular fence has a length of 10 feet. Its width is half its length. Find the perimeter of the fence and the area of the rectangle it encloses. Accelerated Questions: Solve the following equations expressing answers in exact form. 8. 퐴 = 푃 + 푃푟푡 푠표푙푣푒 푓표푟 푃. 9. 휋푥 + 3 = 4휋푥 solve for π Factoring Factor completely 1. 25푥2 − 16 2. 9푥2 − 6푥 + 1 3. 8x2 − 61x − 24 4. 18푥2 + 43푥 − 5 5. 4푥2 − 23푥 − 6 6. 푎2 − 푏2 Factor out the Greatest Common Factor (GCF) first, then factor the trinomial. 7. 6푥3 − 15푥2 + 9푥 8. 4푥4 + 20푥3 + 24푥2 Factor by Grouping 9. 3(푥 − 2) + 푥(푥 − 2) 10. 2푥3 − 5푥2 − 6푥 + 15 Accelerated Questions: Factor each polynomial. 11. 81푥4 − 16푦8 12. 푎3 + 푏3 13. 8푎푥 − 2푎푦 − 12푏푥 + 3푏푦 14. 8푥3 − 1 Linear Functions Calculate the slope of the line containing the points: 1. (4,1)푎푛푑 (2,3) 2. (−3,4)푎푛푑 (3, −4) 3. (2,7)푎푛푑 (2, −9) 4. (4, −3)푎푛푑 (−7, −3) Write an equation for the line with the given properties. Express answer in y = mx + b form: 5. containing the points (-2,4) and (2,12) 6. Vertical through the point (-3,6) 7. Horizontal through the point (4,-8) 8. Parallel to y=2x+7 and having the point (2,-4) 9. The line containing the points (a, 4) and (-3, 2) has a slope of 3. Find the value of a Accelerated Question: 10. Write an equation for the perpendicular bisector to the line segment having endpoints at (-1,4) and (3, -2). Express answer in standard form (Ax + By = C where A,B,C are integers, A>0) Quadratics Solve the following quadratic equations using the Quadratic Formula. Give exact, simplified answers. 1. 푥2 + 4푥 = 7 2. 푥2 + 3푥 − 7 = 0 Solve the following quadratic equations by Factoring 3. (2푥 − 1)(3푥 + 2) = 0 4. 푥2 − 7푥 + 12 = 0 5. 6x2 − 푥 − 12 = 0 Simplify the following complex expressions. Express answers in a + bi form. 57 −16 6. 푖 7. √−4 + √−9 8. √−4 ∙ √−9 9. √ √−1 4+5푖 10. 7(2 − 푖) − (3 + 8푖) 11. (2 + 3푖)(−4 + 푖) 12. 2−3푖 Accelerated Questions: Solve the following equations. 3푥 1 5 13. + = 14. √2푥 + 1 − 푥 = −1 푥+1 푥 2 15. 푥2 − 푥 + 5 = 0 Inequalities and Absolute Value Solve the following inequalities. 3 5 1 3 1. 푥 + > − 푥 2. |2푥 − 7| ≥ 5 2 3 2 4 Sketch the graph of: 3. 푦 ≥ 3푥 + 2 4. 푦 < 푥2 Accelerated Questions: Solve the following inequalities. 1 3 3 1 5. − |−1 − 푥| + > 6. 3(푥 − 5) − 5푥 < −7푥 + 4 < 푥 − 1 2 2 2 2 Exponents Simplify the following expressions using positive exponents: 5 6 −3 −4 2 −7 2 9푥5푦2푧 1. (3푥 푦 푧 )(2푥푦 푧) 2. (4푥 푦 푎) 3. 3푥−5푦푧−3 0 −2 5 −7 3 −2 3푥5+7푥 5. 3x (x y ) x6yab−2 4. ( ) 6. ( ) 5−7푥−3 ab6 Accelerated Questions: 7. At what rate (to the nearest hundredth of a percent) would an account have to pay in order to have $5000 grow to 푟 푛푡 $7000 if compounded weekly for six years? Use the compounding interest formula 퐴 = 푃 (1 + ) 푛 8. If you double a penny every nine days, how much will you have in 15 weeks? Use the formula 퐴 = 푃(2)푡/푑 .
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