PreCalculus Summer Packet

Transcription

1 PreCalculus Summer Packet Entering into PreCalculus means entering into your first year of college preparatory mathematics. There is a major shift in epectation for students to be able to recall many skills at a moment s notice. Certain concepts that have been taught to you over the previous years are assumed to be mastered. If you do not have these skills, you will find that you will consistently get problems incorrect net year as you make mistakes. It is frustrating for students who spend much of their homework time relearning algebra concepts in addition to learning how to tie the concepts together. This summer packet is intended for you to brush up and possibly relearn these topics. On the following pages, you have assorted problems related to specific topics. Each problem should be done in the space provided. Rather than give you a tetbook to remind you of the formulas and techniques necessary to solve the problem, there are a few websites listed that have full instructions on the techniques. If and when you are unsure of how to attempt these problems, use these websites. Don t fake your way through these problems. You are only setting yourself up for a future struggle. Realize also that many concepts are interrelated. This will be the focus throughout net year as we eamine the mathematical relationships between topics numerically, algebraically and graphically. While you may be strong in one of these approaches, you must learn to view each topic from the other two approaches as well to achieve full understanding. Success on your tests and quizzes throughout the year will depend on you being able to do so. You need to get off to a good start so spend some quality time on this packet this summer. Tear off this first page and return the remaining sheets stapled together. Be sure your name appears on the first sheet. Work needs to be shown when needed. Also, do not rely on the calculator to work through the majority of these problems. You will be tested without the calculator, so practice without the calculator. This packet is to be completed by the first day back in school in the fall. You will be tested over this material on the second day of class. You will also be epected to efficiently work through the problems under a time constraint. Many students are not prepared for this epectation and find they do not have the time to check their answers like they are used to. Prepare accordingly. It is a mistake to decide to do this now. Let it go until mid-summer. We want these techniques to be relatively fresh in your mind in the fall. But, do not wait to do them at the very last minute. These take time. If you do a few concepts a day, the whole packet will take you about a week to complete. We hope you take this seriously as we sincerely wish for you to be successful throughout this net year. Your preparation over the summer will be rewarded in unepected ways during the year. Good Luck! Note: Should you have any questions regarding this packet over the summer, Mr. Perdun and Mr. Beck will be available to answer your question via . When you ask your question, please let them know what steps you have taken on your own so they may give you better guidance to solve that problem. Their addresses are pbeck@ccs.k.in.us and dperdun@ccs.k.in.us.

2 Use to search for skill-related videos on any of these topics. Use to find specific math related topics with accompanying videos. Use to see step by step answers for specific questions you may have. Topics Eponents. Basic Rules. Fractional Eponents. Simplifying Radicals Factoring. Factoring by GCF. Factoring quadratic epressions. Special Factoring formulas 7. Factoring through synthetic division Equations/Inequalities 8. Solving linear equations. 9. Solving quadratic equations by factoring 0. Solving quadratic equations by quadratic formula. Solving radical equations. Solving rational equations. Solving logarithmic equations Functions. Function notation. Function names. Function Operations. Graphing 7. Function transformations 8. Graphing Parent Functions by T-chart using smart points 9. Basic Graphing using smart points General Topics 0. Distance and Midpoint formulas. Intercepts. Equations of lines. Pythagorean Theorem. Common Algebraic Errors

3 : Eponent Rules Simplify the following. ( ). Name. ( y) y. y. y 9 y 7y. y : Fractional Eponents Evaluate the following without a calculator ( ) : Simplifying Radicals Simplify and rationalize the following

4 : Factoring by GCF Factor the following completely. 9. 9y 8 y. 8 y y : Factoring Quadratic Epressions Factor the following completely : Special Factoring Factor the following completely. 0. a ab b ( a b) a b ( a b)( a ab b ) a ab b ( a b) a b ( a b)( a ab b ) 9 y a b a b a b ( )( ) y y. 7y

5 7: Factoring through Synthetic Division Use synthetic division to factor as indicated.. ( )( ). 7 ( )( ). ( )( ). ( )( ) 8: Solving Linear Equations Solve the following for the unknown variable.... ( 8) ( 7) 9: Solving Quadratic Equations by Factoring Factor to solve for

6 0: Solving Quadratic Equations using the Quadratic Formula For each equation, solve for the indicated epression.. 0 for. 0 for. 0 for : Solving Radical Equations Solve the following for : Solving Rational Equations Solve the following for : Solving Logarithmic Equations Solve the following for. log 7. log 9. log ( )

7 : Function Notation Given f ( ), answer the following questions.. Find f (0). Find f( ) 0. Find f 7 Given f ( ), answer the following questions.. Find the zeros of f( ). Solve f( ). Find 8 9 f 8 : Function Names Match the following equations to their description.. f ( ) A. Linear Function. f ( ) B. Quadratic Function. f( ) C. Absolute Value Function. f ( ) ( ) ( ) D. Cubic Function. f ( ) ( ) E. Cube Root Function. f ( ) ( ) F. Square Root Function 7. f ( ) ( ) G. Rational Function 8. f ( ) H. Polynomial Function

8 : Function Operations Perform the following function operations if f ( ) and g( ). f g( ). ( ) g f. ( f g)( ). f f ( ). g g( ). Find g g( ) 0 7: Function Transformation Use the graph of y f ( ) at the right to sketch the following transformations y f ( ). y f ( ). y f ( ) y f ( ). y f( ). y f ( )

9 8: Graphing Parent Functions using T-Charts Graph the following using a T-Chart with smart values. State the Domain and Range of each function.. f( ). f ( ). f ( ) D: R: D: R: D: R:. f( ). f ( ). f( ) D: R: D: R: D: R: 7. f( ) 8. f( ) 9. f ( ) log D: R: D: R: D: R:

10 9: Basic Graphing Choosing Smart Points Fill in the T-chart using at least smart -values (that enable you to find eact points). f ( ). 7 f ( ). f ( ) 0: Distance and Midpoint Formulas Find the distance between the two points. Then find the midpoint between the two points. 7. (,); (, )., ;,., ;, : Intercepts Use the following equations to find the and y intercept(s). y 9. 9 y. y : Equations of Lines Find the equation of the line that has the given characteristics. Leave your answer in the form indicated.. slope ; y int :. Parallel to y through. Perpendicular to 7y (Standard Form), through, (Slope-intercept form) (Point-Slope Form)

11 : Pythagorean Theorem Use the diagram at the right to answer the following questions. Be sure to simplify. c b. Find b if a =, c =. Find c if a =, b=. If a = c, and b = 0, find a a : Algebraic Errors to Avoid