without use of a calculator

Transcription

1 Summer 017 Dear Incoming Student, Congratulations on accepting the challenge of taking International Baccalaureate Mathematics Standard Level (IB Math SL). I have prepared this packet to give you additional information about the course and to help you prepare to be successful in IB Math SL. IB Math SL is a rigorous two-year course that covers topics in Algebra, Functions, Trigonometry, Vectors, Statistics and Probability, and Calculus. In May of your senior year, you will take an IB Math SL exam certifying that you have mastered the content of a college-level curriculum. IB Math SL is a demanding course. You should be proud of the work you have done to prepare yourself thus far. My goal is to help you grow as a mathematician as much as possible over the next two years, but I can only be a guide. It is up to you to put forth the consistent effort necessary to succeed in this course. I have developed a summer assignment to help you refresh some skills necessary for success in this course. Please complete the entire packet, showing all of your work carefully, without use of a calculator. Everything in this packet should be review for you, and I expect it to take a total of approximately three hours of work. If much of the material is new to you, or if it takes significantly longer than three hours, please contact me to discuss whether your placement in IB Math SL is appropriate. Your summer assignment is due on the first day of class. It will be collected and graded. You must show all work to receive credit. We will take a quiz on the material included in this packet during our second week of class. Please make sure that you have mastered the material in this packet to ensure your success on our first quiz. I look forward to getting to know you and working closely with you over the next two years. Please feel free to me at any time with questions. I am here to support you. Have a relaxing, enjoyable summer. I look forward to studying mathematics with you next year! IB Formula Book Sincerely, Mrs. Saffo saffol@fultonschools.org

2 IB Math Standard Level Summer Assignment 017 QUADRATICS Section A: Factor each quadratic. If the quadratic cannot be factored, write prime Section B: Solve each equation. Some may factor, while others may require use of the quadratic formula = = = = = = 0

3 IB Math Standard Level Summer Assignment 016 FUNCTIONS Section A: Graph each function, clearly showing its key features (maxima, minima, and intercepts). Identify its domain and range. (Remember: No calculator!) 1. ( ) = 5. ( ) = ( ) = ( ) = ( ) = ( ) = 4

4 IB Math Standard Level Summer Assignment 017 Section B: Find the inverse of each function. 1. ( ) = + 1. ( ) = 3 3. ( ) = 5 4. ( ) = If the point (, 7) is on the graph of ( ), what point must be on the graph of 1 ( )? 6. Explain, in complete sentences, the relationship between a function and its inverse. Section C: Let ( ) = 1; ( ) = 3 and h( ) = 5. Find each composite function. 1. ( )( ). (h )( ) 3. ( h)(4) 4. ( )( 1)

5 IB Math Standard Level Summer Assignment 016 Section D: Use the information below to answer the questions about transformations of functions. 1. For each pair of functions ( ) and ( ), describe the transformations that would transform ( ) into ( ). a) ( ) = ; ( ) = ( 5) + b) ( ) = ; ( ) = 3 10 c) ( ) = ; ( ) = 5( ) 1

6 IB Math Standard Level Summer Assignment 017 EXPONENTIAL AND LOGARITHMIC EQUATIONS Section A: Solve each equation for. In some equations you will get a numeric answer, and in some your answer will be an equation. As long as y is isolated on one side of the equal sign, you have completed the problem. (Remember: No calculator!) 1. =. 5 = 3. 4 = 7 4. log = 8 5. log + log ( + 1) = = 6 7. ln( 5) = 8. ln( ) = 4

7 IB Math Standard Level Summer Assignment 016 TRIGONOMETRIC FUNCTIONS Section A: Find the exact value of each. There is a blank unit circle at the end of your packet which you may fill in to help you. (Remember: No calculator!) 1. sin 60. cos 5 3. sin π 4. tan cos ( π ) 6. sin ( π ) cos ( 5π ) 8. tan sin ( 4π ) tan sin cos ( 7π ) 6

8 IB Math Standard Level Summer Assignment 017 Section B: Graph each trigonometric equation on the domain 0 π. (Remember: No calculator!) 1. ( ) = sin. ( ) = cos Section C: Solve each trigonometric equation for 0 π. 1. sin = 1. cos = sin = 3 4. tan = 1 *Recall: sin = (sin )

9 IB Math Standard Level Summer Assignment 016 Below is a blank unit circle. You may fill in the unit circle to help complete the Trigonometric Functions section in your packet. It is not necessary to complete the entire unit circle. It is just here to help you if needed. Congratulations! You have completed your IB Math SL summer assignment. If you have any questions or concerns, please write them below and I will address them during the first week of class. If you have a question that you would like answered before the first week of class, please me at saffol@fultonschools.org