Franklin High School AB Calculus Prerequisite Work

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1 Franklin High School AB Calculus Prerequisite Work Below you will find an assignment set based on the prerequisites needed for the AB Calculus curriculum taught at Franklin High School. The problems assigned should be the minimum you do to be successful in your net course. It is epected that you: 1. Go to the Franklin Community Library and check out your book ASAP.. Complete the problems below on other paper, with all work shown. 3. Be prepared for an assessment on the material below within the first week of class. Required Work: 1. Are you ready for Calculus Packet. This includes 36 questions and a logarithmic review. Please include all work and justifications. Some answers have been included. The rest will be provided the first week of school. Calculus Term 1 Standards Overview Complete the Calculus Sample Mastery Quiz problems. These problems overview the types of problems you will see on the standard quizzes during the first semester of Calculus. The answers will be provided the first week of school. For those of you who wish to review/etend the work you have done in algebra and Honors Pre-Calculus the following work is recommended Recommended Work: 1. Review Problems from Appendices D.1, D., D.3 and F Below you will find the math work from our Larson tetbook appendices. The Problems come from CD- Rom included with our student tetbook: Student CD-Rom (Calculus Learning Tools). Appendi D.1: Real Numbers and the Real Line: Workout all eamples on your paper. Eercise: (Pages D8-D9) -1 even, 15- all, 6-58 evens Appendi D.: The Cartesian Plane: Workout all eamples on your paper. Eercise: (Pages D15-D16) -1 even, 0-50 evens Appendi D.3: Review of Trigonometric Functions: Workout all eamples on your paper. Eercise: (Pages D5-D7) -18 even, 19- all,7-0 all, -6 evens Appendi F: Comple Numbers: Workout all eamples on your paper. Eercise: (Pages F10-F11) -76 multiples of

2 . Book work From Chapter P (Preparation for Calculus) Below you will find the bookwork from our Larson, Calculus book. It is recommended that you outline the sections below, work out all eamples, and complete the work from the first three sections (P1-P3.) Section (P1) Graphs and Models: Workout all eamples on your paper. Eercise: (Page 8-9) 1-1 all, even, EOE, 59-6 all, 6-7 EOE, all. Section (P) Linear Models and Rates of Change: Workout all eamples on your paper. Eercise: (Page 16-18) -7 evens Section (P3) Functions and Graphs: d. Workout all eamples on your paper. Eercise: (Page 7-9) 1-38 all, (18-0 graph function), 7,8,5-6,71,7 all 3. Calculus Book Overview : It is recommended you look through Chapters 1-3 of the Larson Calculus book. These chapters cover the topics to be completed during the first semester of class.. Calculus CD-Rom Overview : It is recommended you look through the resources that are available on the CD-Rom and online for you to access. Calculus SAMPLE MASTERY QUIZ The graded mastery quiz will only include one of each type of question, additional problems were provided to give a sense of the variations each question might contain. 1. Find the domain of the given function. a. f f 1 1. Solve the following using the rational roots theorem. a. f Sketch by hand a variety of transformations involving eponential, logarithmic, and/or trigonometric functions.

3 b) y a) y 3 y tan log 1 c) ysin d). Solving a variety of trigonometric equations algebraically. a) sin 3 b) 3 tan 1 c) cos 5cos ( Alg. St. 3) Factor and simplify the following epression completely a) Writing the following finite and infinite sums in sigma notation, then find the sum using the sum formulas. a) ,935 b) c) d) Find the limit of a function as cusing substitution and/or simplification a) lim b) lim c) lim 0 d) lim 0 8. Find the limit of a function involving infinity. 1 a) lim lim +3 b) lim c) lim d) e) lim tan f) lim lim log 1 3e g) lim log5 1 h) 9. Find the derivative of the following functions by definition. 1 a) y3 5 b) y c) y d) y Find the equation of the tangent line to y 3 5 at 3.

4 11. Sketching bounded regions by rotating them around various lines. a) The region: y, y = 0, =, revolved around the -ais b) The region: y, y = 0, =, revolved around the y-ais c) The region: y, y = 0, =, revolved around the -ais d) The region: y, y = 0, =, revolved around the y-ais e) The region: y, y = 0, =, revolved around the =5 1. Writing functions for a given situation in terms of a related variable. a) Write a function that epresses the area of a circle as a function of its circumference b) If the width of a rectangle is 5 inches longer than the length, write a function that epresses the perimeter of a rectangle in terms of it length. Write a function that epresses the perimeter of a rectangle in terms of it width. c) Water is being stored in a cylindrical tank that has a radius of 30 meters. Write an epression for the volume of water in the cylindrical tank as a function of the height of the water in the tank. 13. Using a graphing calculator to identify any of the following: ma/mins, zeros, and regions where the function is positive/negative, regions where the function increasing/decreasing. 3 f a) Find all relative ma/mins f()<0) (i.e. f and f 0 0 ) b) Find all zeros (i.e. f()=0) c) Find all regions where f() is pos/neg (i.e. f()>0 and d) Find all regions where f() is inc/dec 1. Using a Graphing Calculator to find where various functions intersect. f and g 3 b) a) f and g cos c) f and g Using a Graphing Calculator to find the derivative of the following at a given point 1 a. y at y at cos

5 Are you ready for Calculus Answer Sheet ( 3) 1. a. ( 1) 5 5 d a a a b 3 1 3a b 1 3 ab d. ab e. a b f. a b. a d a. log 5( 1) log a. 1 log a. bc a bc cy bz

6 V bc a b c d. e. f. 8. a. h A h r A P 1 nr y d y or 1 1 y ( ) y 8 1 9y a. ( )( ) ( )( 5)( 5) ( 3)( 6 9) d. ( i)( i)( 1)( 1) 10. a. 0,, 5 5,, a. 1. a ,,, ,, 6 6 k, k, 6 5 k 6 cos10 3

7 d. e. f. g. h. 5 sin 1 tan ( 1) 1 sin ( 1) 9 cos sin tan cos ( 1) 13. See Graphs 1. a or a a. 1 1 or ,, 3 3,1 17. a., 31,, 18. a. 3,5 6 or 5 or a. 73y 0 3 y1 0

8 y 3 0. a. sol : (, 1) See Graph 1. a. ( 1) ( y ) y1 Center : ( 3,). a. Radius : 10 3y a. int : (9,0) ( 5) ( y3) y a. D: (, ) (1, ) D: (, ) i. R: y D: (, ) (, ) ii. 5 5 R: y(, ) (, ) 6. D: (,0) (0, ) y 1 for 0 R : y 1 for 0 7. a. 1 ( h) 1 ( 1) h 8. See Graphs 9. See Graphs 30. a. y ( 1) See graphs

9 31. a. 3. a. y ( 1) ( 1) y ( 1) ( 1) y f ( ) 1 f ( ) 5 1 f 1 ( ) ( ) 1, See Graphs 3. a. tr ht h r rt h e. 35. a. r(3 ) 9 m d. 3.6 km e. 30 or a. sin( ) sin cos( ) cos cos( y) cos cos y sin sin y d. sin( y) sin cos y sin ycos a. cos( ) cos cos( ) sin sin( ) sin sin( ) cos(0) cos cos sin ( sin ) 1 cos sin cos cos( ) d. cos cos sin sin cos sin cos cos sin cos (1 cos ) cos 1 cos cos sin (1 sin ) (sin ) 1sin sin cos sin cos sin cos

10 f. g. cos cos 1 cos cos 1 cos 1 cos let 1 cos cos cos 1sin sin 1 cos 1 cos sin let 1 cos sin