Pre-Calculus Honors - Spokane Public Schools

Pre-Calculus Honors Class Title: Pre-Calculus Honors Teacher Name: Mrs. Coles, Mrs. Knowles and Mr. Leifer Materials needed: calculator (optional) Summer Support Times: Summer Drop in Hours: Monday, August 26th 3:30-4:00 pm. Please check with the office for the room number of your pre-calculus honors teacher. In addition, answer keys will be posted on our classroom doors by Tuesday, August 27th. Additional Information: If you are taking this class, you are interested in learning advanced concepts in mathematics. This class will prepare you for AP Calculus. Pre-Calculus Honors is designed to strengthen students’ algebraic skills and provide students the opportunity to acquire skills working with trigonometry and advanced functions. Students are expected to have mastered algebra and geometry skills and to have thoroughly understood the concepts covered in prior courses. We have a summer assignment intended to help you brush up on these topics. There are two parts to your Pre-Calculus Summer Assignment. You will receive credit for both parts. Part 1 is a memorization list: You will have a quiz on the first day of school covering the memorization list in this packet. This quiz will go in the gradebook and there will be no retakes! Part 2 is the Summer Skills Packet: The Summer Skills Packet needs to be complete on the first day of school, Thursday, August 29, 2019. All work must be shown, and it must be neat and organized to receive full points. Feel free to email us if you have any questions. Have a great summer!! Mrs. Coles cherylc@spokaneschools.org Mrs. Knowles Mr. Leifer megank@spokaneschools.org lukel@spokaneschools.org

Pre Calculus Honors Summer Assignment Welcome to Pre Calculus Honors! If you are taking this class, you are interested in learning advanced concepts in mathematics and preparing yourself to be successful in AP Calculus. Pre Calculus Honors is designed to strengthen students’ algebraic skills and provide students the opportunity to acquire skills working with trigonometry and advanced functions. Students are expected to have mastered the skills of algebra and geometry and to have thoroughly understood the concepts covered in prior courses. There are certain skills that you have learned in your previous math courses that you need mastery of moving into Pre Calculus. We have a summer assignment that is intended to help you brush up on these topics. There are two parts to your Pre Calculus Summer Assignment. Part 1: Memorization and Part 2: Pre Calculus Honors Summer Skills Packet. You will receive credit for both parts. All work that is part of the Summer Skills Packet needs to be completed by the first day of school Thursday August 30th. We will be available for assistance on the summer assignment on the following day. Summer Drop In Hours: Monday August 27th 3pm to 4pm Mrs. Munsey N151 Mrs. Knowles N143 A key with answers will be posted on our classroom doors Monday August 27th All work must be NEAT, ORGANIZED, AND SHOWN to receive full points. Feel free to email us if you have any questions. Have a great summer!! Mrs. Munsey ashleem@spokaneschools.org Mrs. Knowles megank@spokaneschools.org Part 1: Memorization. You will have a quiz on the first day of school covering the memorization list in this packet. THIS QUIZ WILL GO IN THE GRADEBOOK AND THERE WILL BE NO RETAKES!!!! The ideas on this list pop up throughout the Pre Calculus course and it is expected that you know them. A practice quiz has been included in this packet. On the first day of class you will be quizzed on the following: Evaluating exact values of sine, cosine, and tangent Graph sine and cosine functions and identify amplitude and period from graphs or equations Write equations of a line given two points in both point slope form and slope intercept Be able to factor polynomials including quadratics and sum/differences of perfect squares Rewrite exponential properties in equivalent forms Recognize the graphs, equations and tables of values for all the functions on the list

Pre Calculus Summer Memorization List Trigonometric Exact Values/Unit Circle 1st Quadrant: Functions Sine 𝑓(𝑥) asin(𝑏𝑥) 𝑘 Amplitude: 𝑎 Cosine 𝑓(𝑥) acos(𝑏𝑥) 𝑘 Period: 𝑃 2𝜋 Vertical Shift: 𝑘 𝑏 Linear Functions/Concepts 𝑆𝑙𝑜𝑝𝑒: 𝑚 𝑦2 𝑦1 𝑥2 𝑥1 𝑃𝑜𝑖𝑛𝑡 𝑆𝑙𝑜𝑝𝑒 𝐹𝑜𝑟𝑚: 𝑦 𝑦1 𝑚(𝑥 𝑥1 ) 𝑆𝑙𝑜𝑝𝑒 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝐹𝑜𝑟𝑚: 𝑦 𝑚𝑥 𝑏 Quadratics 𝑢2 𝑣 2 (𝑢 𝑣)(𝑢 𝑣) 𝑢3 𝑣 3 (𝑢 𝑣)(𝑢2 𝑢𝑣 𝑣 2 ) 𝑢2 2𝑢𝑣 𝑣 2 (𝑢 𝑣)2 𝑢3 𝑣 3 (𝑢 𝑣)(𝑢2 𝑢𝑣 𝑣 2 ) 𝑢2 2𝑢𝑣 𝑣 2 (𝑢 𝑣)2 Properties of Exponents 𝑥 𝑚 𝑥 𝑛 𝑥 𝑚 𝑛 𝑥𝑚 𝑥 𝑚 𝑛 𝑥𝑛 (𝑥 𝑚 )𝑛 𝑥 𝑚𝑛 (𝑥𝑦)𝑚 𝑥 𝑚 𝑦 𝑚 𝑥 𝑚 𝑥𝑚 ( ) 𝑚 𝑦 𝑦 𝑥0 1 1 𝑥𝑚 𝑥 𝑚 1 𝑛 𝑥 𝑥 𝑛 1 𝑛 𝑛 1 𝑛 𝑥𝑦 𝑥 𝑦 𝑥 𝑛 𝑦 𝑛 𝑛 1 1 𝑥 𝑥 𝑛 𝑥𝑛 𝑦 𝑛 𝑦 𝑦 𝑛 𝑛 ( 𝑥 ) 𝑚 𝑛 𝑚 𝑥 𝑚 𝑥 𝑛

Basic Parent Functions and Key Values x -2 -1 0 1 2 f(x) 2 1 0 1 2 x -2 -1 0 1 2 f(x) -8 -1 0 1 8 x -2 -1 0 1 2 f(x) -1/2 -1 Undefined 1 1/2 x 0 1 f(x) 1 e Absolute Value 𝑓(𝑥 ) 𝑥 Cubic 𝑓(𝑥 ) 𝑥 3 Rational/Reciprocal 1 𝑓(𝑥 ) 𝑥 Exponential (Base e) 𝑥 ( ) 𝑓 𝑥 𝑒 𝑒 2.718 x 1 e f(x) 0 1 Natural Logarithmic 𝑓(𝑥 ) 𝑙𝑛𝑥 𝑒 2.718 x -2 -1 0 1 2 f(x) -2 -1 0 1 2 x -2 -1 0 1 2 f(x) 4 1 0 1 4 x -1 0 1 4 9 f(x) Undefined 0 1 2 3 x -8 -1 0 1 8 f(x) -2 -1 0 1 2 Linear 𝑓(𝑥 ) 𝑥 Quadratic 𝑓(𝑥 ) 𝑥 2 Square Root 𝑓(𝑥 ) 𝑥 Cube Root 3 𝑓(𝑥 ) 𝑥

Pre Calc. Honors Summer Assignment PRACTICE QUIZ Name: Section 1 Trigonometric Exact Values/Unit Circle 1st Quadrant Fill in each of the following. 1. 2. Radians Sinθ Cosθ Tanθ ( , ) 0 𝝅 𝟔 𝝅 𝟒 𝝅 𝟑 𝝅 𝟐 ( , ) Section 2 Functions 𝒇(𝒙) 𝒂𝒔𝒊𝒏𝒃𝒙 𝒌 1. Graph the basic cosine function. 3. Amplitude 2. Graph the basic sine Function 4. Period: 5. Vertical Shifts Section 3 Linear Functions 1. Fill in each formula. 𝑆𝑙𝑜𝑝𝑒: 𝑚 𝑃𝑜𝑖𝑛𝑡 𝑆𝑙𝑜𝑝𝑒 𝐹𝑜𝑟𝑚: 𝑆𝑙𝑜𝑝𝑒 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝐹𝑜𝑟𝑚: 2. Given two points write the equation of the line that passed through the two points in both point slope and slope intercept form. (-3,-3) (1,3)

Section 4 Quadratic Functions 1. Fill in the factored form for each quadratic. 𝑥 2 49 𝑥 2 12𝑥 36 𝑎2 18𝑎 81 16𝑥 2 8𝑥 1 25𝑥 2 9 2. Factor each quadratic. 𝑥 2 13𝑥 48 7𝑥 2 41𝑥 30 Section 5 Exponent Properties Matching 1. 2. 1 𝑥𝑚 𝑥𝑛 1 A. 𝑥 𝑛 𝑦 𝑛 𝑥 𝑚 𝑥 𝑛 1 1 B. 𝑥 𝑛 𝑦 𝑛 3. (𝑥 𝑚 )𝑛 C. 𝑥 𝑚 𝑦 𝑚 4. (𝑥𝑦)𝑚 D. 𝑥 𝑚 𝑥𝑚 𝑦𝑚 5. (𝑦) E. 1 6. 𝑥 0 F. 𝑥 𝑛 𝑚 G. 𝑥 𝑚 𝑛 7. 𝑥 𝑚 𝑛 8. 𝑥 H. 1 𝑥𝑚 𝑛 9. 𝑛 𝑥𝑦 𝑥 𝑛 𝑦 𝑛 𝑥 𝑛 𝑦 𝑛 10. 𝑛 𝑥 𝑦 𝑚 11.( 𝑥 ) 𝑛 𝑥 𝑚 I. 𝑥 1 𝑛 J. 𝑥 𝑚 𝑛 K. 𝑥 𝑚𝑛

Section 6 Parent Functions: Complete all missing parts of the following table. Functions should be the basic parent functions and the graphs should be as accurate as possible. Column A (Table) Column B (Function) x -2 -1 0 1 2 f(x) x -2 -1 0 1 2 f(x) x -2 -1 0 1 2 f(x) x 0 1 f(x) Cubic 𝑓 (𝑥 ) Absolute Value 𝑓 (𝑥 ) Rational/Reciprocal 𝑓(𝑥 ) Exponential (Base e) 𝑓 (𝑥 ) 𝑒 x 1 e f(x) x -2 -1 0 1 2 f(x) x -1 0 1 4 9 f(x) x -8 -1 0 1 8 f(x) x -2 -1 0 1 2 f(x) Natural Logarithmic 𝑓 (𝑥 ) Linear 𝑓 (𝑥 ) Square Root 𝑓(𝑥 ) Cube Root 𝑓(𝑥 ) Quadratic 𝑓 (𝑥 ) Column C (Graph)

There are certain skills that you have learned in your previous math courses that you need mastery of moving into Pre Calculus. We have a summer assignment that is intended to help you brush up on these topics. There are two parts to your Pre Calculus Summer Assignment. Part 1: Memorization and Part 2: Pre Calculus Honors Summer Skills Packet.