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. The following pages include assorted problems related to specific topics. Each problem should be completed in the space provided. If and when you are unsure of how to attempt these problems, use the websites provided to view full instructions regarding the necessary concepts. Don t fake your way through these problems. If you do you will be setting yourself to struggle net year. Realize that many concepts are interrelated. This will be the case 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 your ability to do so. Also, do not rely on the calculator for the majority of the problems. Most of the Pre- Calculus tests include a non-calculator portion, so practice without the calculator. This packet must be completed by the first day of class in the fall. To receive full credit you must SHOW ALL WORK whenever it is deemed important by your teacher (which is nearly always). You will be tested over this material the second day of class. Pace yourself to complete this assignment throughout the summer. It would be a mistake to finish it all in the first few weeks of summer. It would be equally ill-advised to attempt to complete it the day before school begins. These techniques to be relatively fresh in your mind in the fall, but the packet will take time to complete well. If you do a couple of concepts a day, the whole packet will take you about a couple of weeks to complete. You might also consider working with a partner or small group as fequently we are "better together". Please take this assignment seriously and do your best work. I sincerely want you to be successful net year. If that is your desire too, make your preparation over the summer your first step toward attaining that goal. Have a mathtastic summer! See you net fall! Mrs. Anderson

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. Unit Circle 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 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