AP Calculus AB Summer Assignment School Year

Transcription

1 AP Calculus AB Summer Assignment School Year Objective of the summer assignment: The AP Calculus summer assignment is designed to serve as a review for many of the prerequisite math skills required to be successful in the course. The goal is not only completion of the packet but also 100% mastery of the skills it contains. Resources/Materials necessary for the summer assignment: Notes from past math classes, other students, the internet, ing Mr. A Estimated length of time to complete: 6 hours Grade: 50 point homework assignment 5-7% of 1 st Quarter grade 5 point deduction for each day (not class) late. 3 point deduction for pages being out of order. (Look at the page numbers on the bottom.) Due Date: September 4/5, 018 Questions? Mr. Ascarrunz: jlascarrunz@fcps.edu Ms. Varanavage: javaranavage@fcps.edu

2 AP Calculus AB Mr. Ascarrunz Due date: First day of class Grading: This packet is a 100 point homework/classwork assignment that will be graded for accuracy. It will make up about 5-7% of your total first quarter grade (depending on other assignments). 5 point deduction for each day (not class) late. 3 point deduction for pages being out of order. (Look at the page numbers on the bottom.)

3 AP Calculus AB Summer Packet Your AP Calculus Eam is scheduled for Tuesday, May 14 th 019. Yes, that seems like a long ways off but May rolls around faster than you think. With so much calculus to learn prior to this date, we do not have the luury of spending the first quarter of the school year reviewing the prerequisite topics. This summer packet has been designed and provided to help you stay fresh on the essential knowledge to get us started quickly in September. The Summer Packet is comprised of a review of parent functions and a collection of mathematics problems for you to solve. You are epected to have completed the summer packet in its entirety by the first day of class. It will be collected and assigned a grade. Activities and assessments the first week of class will also require the completion of this packet. You are encouraged to search the web for assistance and collaborate with your future Calculus AB classmates. Remember, this packet is meant to help you refresh the topics and skills that you will need to call upon on a daily basis as we learn and perform calculus. It would be best to start this packet no earlier than August so the topics will be fresh in your mind when we start class in the fall. Do not wait until the night before school starts to complete; this packet takes time. Should you have any questions, please feel free to contact one of the AP Calculus AB teachers at the addresses below. Have fun and we ll see you in September. Mr. Ascarrunz JLAscarrunz@fcps.edu Name Page 1

4 Calculus AB Section 1 Parent Function Table Name Parent Function: A function that does not have any translations or stretches. While you may use your calculator to complete the table below, you will be responsible for knowing the characteristics of all of the parent functions included in this packet quickly and effortlessly during your year in calculus without the assistance of a graphing calculator. For each parent function: 1. Graph the function. State the domain and range 3. Determine if there is any symmetry (origin, -ais or y-ais) 4. Determine if the function is odd, even or neither 5. Write the equation of any asymptotes Function Type Equation Graph Characteristics of f() Constant f ( ) a (where a is a constant for eample: f ( ) 1 or y 1) Linear f ( ) Page

5 Function Type Equation Graph Characteristics of f() f Quadratic ( ) f Cubic ( ) 3 f ( ) Absolute Value ( ) f Or if 0 if < 0 Page 3

6 Function Type Equation Graph Characteristics of f() Greatest f ( ) Integer Square Root f ( ) f Cube Root ( ) 3 Page 4

7 Function Type Equation Graph Characteristics of f() Reciprocal f ( ) 1 Squared f 1 Reciprocal ( ) Eponential ( ) a f (where a is a constant for f 3 ) eample: ( ) Page 5

8 Function Type Equation Graph Characteristics of f() Natural Eponential ( ) e f (where e is the irrational number.7188.) ( ) log a f Logarithmic (where a is a constant for eample: f log ) ( ) 5 Natural f ( ) ln Logarithmic Page 6

9 Function Type Equation Graph Characteristics of f() Sine f ( ) sin Cosine f ( ) cos Tangent f ( ) tan Page 7

10 Function Type Equation Graph Characteristics of f() Cotangent f ( ) cot Secant f ( ) sec Cosecant f ( ) csc Page 8

11 Function Type Equation Graph Characteristics of f() Circle + y 1 Graphing Calculator NOT Permitted Section The Algebra of Functions Absolute Value as Piecewise Functions Write each absolute value function as a piecewise function. 1. y 4. y 9 Section 3 The Algebra of Functions Properties Match each epression on the right with each equivalent epression on the left. You may choose more than one that matches and you may use them more than once. 1. loga+ logb A. logb a B. log a b. 3. loga logb C. ( + a ) D. logab alogb E. ( + ) a F. ( + a) ( + a ) 4. ( + a ) G. undefined H. + 3a + 3a + a 5. log0 6. ( + ) a Continued on Net Page Page 9

12 Graphing Calculator NOT Permitted Calculus AB Section 4 The Algebra of Functions Solving Functions Solve each function using algebraic techniques such as but not ited to factoring, crossmultiplying and inverse operations without the use of a graphing calculator. You must show the algebraic steps that support the solution to each equation. You may NOT use a graphing calculator to solve sin for 0 < π Continued on Back Page 10

13 Graphing Calculator NOT Permitted Solve each equation using algebraic techniques NOT a graphing calculator 7. cos 1 for 0 < π 8. sin 1 0 for 0 < π 9. e 10. 5e ln( 5 ) 3 1. ( ) ln Page 11 Continue to net page

14 Graphing Calculator Permitted Calculus AB Section 5 The Algebra of Functions - Information from Graphs of Functions For each function, identify A) Domain, B) Range, C) -intercepts and D) y-intercepts. 1. f ( ) 1 A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?). f ( ) A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) 3. f ( ) 3 3 A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) Page 1 Continued on Back

15 Graphing Calculator Permitted 4. f ( ) 10 A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) 5. f ( ) ln( + ) A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) 6. f ( ) ln( ) A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) Continued on Net Page Page 13

16 Graphing Calculator Permitted 7. f ( ) e + 3 A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) 8. f ( ) e + 3 A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) f e 9. ( ) A) Domain (input of f()) B) Range (output of f()) C) -intercepts (what is the value of when y 0?) D) y-intercepts (what is the value of y when 0?) Continued on Net Page Page 14

17 Calculus AB Section 6 The Algebra of Functions Trigonometry Unit Circle Fill in the values on the Unit Circle below. Page 15 Continued on Net Page

18 Calculus AB Section 7 Limits and Continuity Evaluate each it without a calculator (3h + 1) 1 h h 0 7. sin t 1 t 3 t Page 16

19 Use functions f() and g() below to answer questions Graph f ( ) 1 on the grid below The graph of g( ) is given below. 9) ( ) f 15) g ( 3) 10) ( ) 0 + f 16) g ( 1) 11) f( ) 17) g ( ) + 1 1) f( ) 18) g ( ) 3 13) 4 f( ) 19) 5 g ( ) 14) ( ( ) ( )) 5 g f 0) ( g ( ) + ) 4 1. State the -values for which the it does not eist on g ( ).. State the -values for which f ( ) is discontinuous. 3. State the -values for which g ( ) is discontinuous. Page 17 The End