Advanced Precalculus Summer 2018 Assignment Due Date: Friday, August 17, 2018 Mrs. Bermudez:

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1 Bayside Academy Advanced Precalculus Summer 08 Assignment page Advanced Precalculus Summer 08 Assignment Due Date: Friday, August 7, 08 Mrs. Bermudez: This summer packet for students entering Advanced Precalculus is intended to reinforce topics and content students learned in Advanced Algebra and preview concepts in Precalculus. It will benefit you greatly net year to be comfortable with the skills and concepts in this packet before we begin the school year. How will the summer work be graded? The summer packet is epected to be completed by the first day of school. To give you a chance to seek etra help and answer questions, review packets will be collected for a 0-point grade the first full Friday of school (August 7), and a 0-point assessment on the review material will be given the same day. While not all problems have work, for those that do, you must show all work on separate paper! The answers to some problems are at the end of the packet for you to check, or even to work backwards to help you relearn the material. The Role of the Calculator The calculator will be used etensively in class as a tool to investigate regressions, statistics, graphs, and functions, even more so than in Advanced Algebra. Thus, we will use a calculator for many applications that typically cannot be done by hand. Otherwise, to keep your understanding of number operations and graphing skills sharp, using a calculator when it is not needed is discouraged. You also will learn quickly that the more advanced and abstract the algebra is, the less useful and more impractical using a calculator is. However, your calculator can be a useful tool to check your work and understanding of the skills on this packet, so feel free to check your work with your graphing calculator (or Desmos or Geogebra). Please keep in mind the assessment on Friday, August 7, will be non-calculator. Suggested Timeline Try to do a few problems from each section each week. Don t overload yourself by trying to complete them all in one sitting the day before school, but also don t stress so much that you don t enjoy your summer. If you get stuck, check the solutions and try to work your way backwards, or check out some tutorials on Khan Academy. A Personal Note I am looking forward to working with each of you net year. Now that you have completed Advanced Algebra, you will be able to understand and appreciate the more comple applications of mathematics, and we will be able to delve into topics in basic physics, statistics and calculus. Not only will you epand your mathematical knowledge, but hopefully your curiosity and enjoyment of mathematics. If at any point throughout the summer you have any questions or concerns about the summer work, please do not hesitate to me at sbermudez@baysideacademy.org. Have a great summer and I ll see you in August! Mrs. Bermudez

2 Bayside Academy Advanced Precalculus Summer 08 Assignment page. Write the equation of the line, in slope-intercept form, passing through the points (4, ) and (7, -).. Write the equation of the line with -intercept of and y-intercept of.. Find the equation for the line perpendicular to 5 7 y and passing through (6, 5). Graph each function, inequality, or system on the aes provided. Be as detailed as possible, including at least key points on each graph (or for linear functions) and any asymptotes. Then, state the domain and range for each graph (in interval or inequality notation). You may change the scaling as necessary y4 y 5. 4y 7. y 0.5

3 Bayside Academy Advanced Precalculus Summer 08 Assignment page 8., g ( ), 0. y 9. y. g ( ) ( )

4 Bayside Academy Advanced Precalculus Summer 08 Assignment page 4. h( ) 4. 4, p 6, ( ),. y y ( )

5 Bayside Academy Advanced Precalculus Summer 08 Assignment page m( ) 0 9 (use you calculator to find the minimum!) 8. ( ) ( y ) 9 7. q( ) ( 5) ( 6) 4 9. y

6 Bayside Academy Advanced Precalculus Summer 08 Assignment page 6, r ( ) 0. ( ),. k( ) log. y. f( ) Factor each of the following completely b 0b z 4z 8. 9c 0c5. 6 7y k k n 4. mn mt sn st

7 Bayside Academy Advanced Precalculus Summer 08 Assignment page 7 For problems -65, simplify each. Leave each in eact, simplified form, and all rational epressions written as a single fraction with no negative eponents or radicals in the denominator z z z z m m 0 5a m m y y 5. m 5 m 5m 46. ( np ) ( np) r s 6. s 5r a 5a 6 a 7. a4 a 6d 9 6 d 6d 8. 5d 5d 7d m( a m) ( ) y z y y ( i) ( i)( i) 6. 6( 8 i) (5 7 i) b a a b 40. a b ab i 5i 4. a a4 a a a i z z For which values of is 5 undefined? Use the properties of logarithms to condense into a single logarithm ln ln 68. log ( ) log y

8 Bayside Academy Advanced Precalculus Summer 08 Assignment page 8 For problems 69-86, solve for the unknown variable. Give the eact value(s). 69. ( 7 ) 6( 7 ) log e ln ln log( 7) ( ) ( 9) ( 5) c c 86. c 4 c Fill in the unit circle below, in both degrees and radians, without using a calculator, and use it to evaluate problems sin 88. sin 89. cos sec 6 9. tan 9. cot csc( 00 )

9 Bayside Academy Advanced Precalculus Summer 08 Assignment page 9 Selected Answers 7. y 5 ( 6) y D: (, ) R: (,4] 7. 0 b ( b ) i log ( ) y m 5 m b a ab 7. 5, i 78. = m 6 5 log 7 84.