I) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)

Size: px
Start display at page:

Download "I) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)"

Transcription

1 AP Calculus Summer Packet Answer Key Reminders:. This is not an assignment.. This will not be collected.. You WILL be assessed on these skills at various times throughout the course.. You are epected to be able to do all the questions in this packet without a calculator ecept for those in Section XXI. I) Simplifying fractions: ) y y y ) ) ) y y 5) h h h II) Factoring: 6) 8) 6 6 7) 9) ) ) 9 Prime (using only) ) 7 9 ) ) 5) III) Solving: 7 5

2 6) 5 0 8, 7) 9 5 8) 5 0, 9) 0 0, 0 0,5,6 ) 600 0) ) y z z y z ) 6 ) 9 5) 9 ( = is etraneous.) 6) ) 8) 8 7 9), 6 0 0) 0 ) 5 0 0, 5 IV) Are the following epressions equal to ln?

3 ) ln yes ) ln 8 ln no ) ln8 ln yes 5) ln ln yes 6) ln ln no 6) ln no V) Equations of lines: 7) Find the equation of the line that has a slope of 5 and passes through the y 5 or y 5 9 point (, -). 8) Find the equation of the line that passes through the points (, ) and (, -). y or y or y 9) Find the equation of the line that passes through the points (-, ) and is parallel to the line y y or y. 0) Find the equation of the line that has a slope of 0 and passes through the point (-5, ). y ) Find the equation of the line that passes through the origin and is perpendicular to the line y 7. y ) Find the equation of the line that has an undefined slope and passes through the point (, -5).

4 VI) Intercepts: ) Find the and y intercepts of y 9. -intercepts: (, 0) and (-, 0). y-intercepts: (0, ) and (0, -) ) Find the equation of the line that has an -intercept of 5 and a y- intercept of. y 0 or y 0 5 or y VII) Equations of graphs: 5) y 6) y 7) 8) y 9) y 6

5 VIII) Given the slope, sketch the following lines: [If you do not trust your sketches, see your instructor.] 50) Sketch a line with a slope of. 5) Sketch a line with a slope of. 5) Sketch a line with a slope of -. 5) Sketch a line with a slope of. IX) Sketch the following graphs: [You can check your answers with a graphing calculator, but please know that you are epected to know what these look like without the use of a graphing calculator.] 5) f ( ) 55) f ( ) 56) f ( ) 57) f ( ) 58) 59) y 60) f ( ) ln 6) f ( ) 6) f( ) 6) f( ) 6) f ( ) 65) f ( ) 66) 68) 70) f 67) f ( ) ( ) f 69) f ( ) / ( ) f ( ) / 7) f ( ) e 7) f( ) 7) y 5 X) Absolute value: 7), 0, 0 75),,

6 XI) Domain and range: 76) f ( ) D:, R : 77) f( ) D: 0, R: 0 78) f( ) D :, R :0 y 79) f ( ) e D:, R: 0 80) f ( ) D:, R: 0 8) f ( ) D:, R: 8) f ( ) ln D: 0, R: 8) D f ( ) :,,,, R: 0 8) f( ) 0 6 D: 6, R: 0 XII) Inverses: 85) f ( ) f ( ) 86) f ( ) f ( ) 87) f( ) f ( ) 88) f ( ) ln f ( ) e XIII) Compositions of functions if: f ( ), g( ), and j( ) f 90) j 89) () 9 f 9) f j 6 9) g g f h h h h 9) 9) f h f h h h

7 XIV) Simultaneous equations: 95a) y 8 y 5 95b) y 9 7 y9 (, ) (-0, 89) and (, ) 96a) The length, l, of a certain rectangle is twice the width, w. Write an equation for the perimeter the rectangle as a function of the width, w. P=6w 96b) If the area of the rectangle described above is 50 square feet, find the length and the width of the rectangle. W = 5 feet and l = 0 feet XV) Intersection of curves: 97) Find the point of intersection between the lines y and y 5. (, ) 98) Find the point of intersection between the lines y 7 and the curve y 5. Also sketch the area between the graphs. (-, 5) and (, 8) XVI) What do the following mean? [If you do not trust your answers, see your instructor.] 99) a graph is in the first quadrant f 5 00) 0) an epression is a function 0) a zero of a function is 0) y is directly proportional to (give an eample) 0) the coefficient of the third term is 5 (give an eample) 05) a function has only one root 06) a function is a polynomial 07) two triangles are similar 08) a function is even 09) a function is odd

8 XVII) What are the following formulas? 0) Quadratic formula b b ac a ) Pythagorean Theorem a b c ) the hypotenuse of a isosceles right triangle with a leg of length. ) the hypotenuse of a right triangle with shortest leg having a length of. ) the volume of a sphere V r 5) the volume of a cylinder V r h 6) the volume of a cone V r h 7) the volume of a bo with a square base V h 8) the surface area of a sphere SA r 9) the surface area of a cylinder with no top SA r rh 0) the area of a triangle A bh ) the area of a trapezoid A hb b ) the cross section through the center of a sphere A r ) the volume of a prism that has an equilateral triangle with side of length and height of length y [Ambiguous question -- don t worry about this one.] ) area of an equilateral triangle in terms of the length of a side s XVIII) Solve using similar triangles: s A 5) A si foot man is standing 0 feet away from a 0 foot lamppost. What is the length of his shadow? 0/7 feet 6) Water is dripping out of a conical figure that has a diameter of 8 inches and a height of inches. When the depth of the water is 8 inches, what is the radius of the water? 8/ inches XIX) Find the equations of the horizontal and vertical asymptotes of each function: 7) y 8) y H. A.: y 0, V. A.: H. A.: y, V. A.:

9 XX) Eponent Rules: Which of the following are true? 9) 0 True 0) True 0) y y NO!!! ) No ) 5 y y True ) 5 No 8 ) 6) 5w 5 t 5 t True 5) 5 9 w True 7) No No false. 8) True 8) Technically, this is because we do not know if is positive or negative. Just be careful. 9) 5 5 NO!!! 0) No ) y y NO!!! ) True ) e ln True ) ln e True ) e ln ln5 True 5) ln ln 5 No 6) Epand using the properties of logarithms: ln ln 7 ln 0 ln ) Condense into a single logarithmic epression using the properties of 7 logarithms: 7 ln ln 5 5 ln 5 5

10 XXI) Using the graphing calculator: 8) Graph y 0. on the -y plane on the right: 9) Find the roots of the equation above (not shown in the graph -- danger of graphing calculator ), -.0,.9 50) Find the point of intersection for the graphs y and y. (.087, 8.7) 5) Find the maimum value for the graph f ( ) ) For the function in #5, find the intervals on which f( ) is increasing. (-, 0.60 ) XXII) What are the following trigonometric identities? 5) 55) 57) 59) sc e cos 5) sin tan cs o 56) cos sin 58) cot csc cc s sin cos cot sn i sec tan XXIII) Evaluate the following epressions: 60) sin 6 6) cos 6 6) 7 tan 6 6) cos 0 6) cos 65) 5 csc 6

11 66) sec 67) cot 0 68) sin 6 69) tan undefined 70) sin 6 5 7) cot 7) sin 7) cot 7) sec 75) tan 76) csc undefined 77) sec XXIV) Sketch one period of the following trigonometric graphs: [Check with your instructor if you do not know how to graph these by hand.] 78) y sin 79) y cos 80) y tan 8) y sec 8) y csc 8) y cot XXV) Solve the following trigonometric equations for the given domain: 8) sin cos on 0, 5,

Welcome to AP Calculus!

Welcome to AP Calculus! Welcome to AP Calculus! This packet is meant to help you review some of the mathematics that lead up to calculus. Of course, all mathematics up until this point has simply been a build-up to calculus,

More information

Summer Review Packet AP Calculus

Summer Review Packet AP Calculus Summer Review Packet AP Calculus ************************************************************************ Directions for this packet: On a separate sheet of paper, show your work for each problem in this

More information

AP Calc Summer Packet #1 Non-Calculator

AP Calc Summer Packet #1 Non-Calculator This packet is a review of the prerequisite concepts for AP Calculus. It is to be done NEATLY and on a SEPARATE sheet of paper. All problems are to be done WITHOUT a graphing calculator. Points will be

More information

Calculus Summer TUTORIAL

Calculus Summer TUTORIAL Calculus Summer TUTORIAL The purpose of this tutorial is to have you practice the mathematical skills necessary to be successful in Calculus. All of the skills covered in this tutorial are from Pre-Calculus,

More information

CALCULUS AB/BC SUMMER REVIEW PACKET (Answers)

CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) Name CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) I. Simplify. Identify the zeros, vertical asymptotes, horizontal asymptotes, holes and sketch each rational function. Show the work that leads to your

More information

Summer Review Packet. for students entering. AP Calculus BC

Summer Review Packet. for students entering. AP Calculus BC Summer Review Packet for students entering AP Calculus BC The problems in this packet are designed to help you review topics that are important to your success in AP Calculus. Please attempt the problems

More information

AP Calculus I Summer Packet

AP Calculus I Summer Packet AP Calculus I Summer Packet This will be your first grade of AP Calculus and due on the first day of class. Please turn in ALL of your work and the attached completed answer sheet. I. Intercepts The -intercept

More information

Summer Review Packet. for students entering. IB Math SL

Summer Review Packet. for students entering. IB Math SL Summer Review Packet for students entering IB Math SL The problems in this packet are designed to help you review topics that are important to your success in IB Math SL. Please attempt the problems on

More information

By Alex O Brien, updated on 6/24/2014

By Alex O Brien, updated on 6/24/2014 HEBRON HIGH SCHOOL AP CALCULUS SUMMER ASSIGNMENT AP Calculus AB/BC Mathematics fun for all! By Ale O Brien, updated on 6/4/04 The purpose of this assignment is to make certain that you have much of the

More information

Directions: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.

Directions: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice. AP Calculus AB SUMMER ASSIGNMENT Multiple Choice Section Directions: Please read questions carefully It is recommended that you do the Short Answer Section prior to doing the Multiple Choice Show all work

More information

A: Super-Basic Algebra Skills. A1. True or false. If false, change what is underlined to make the statement true. a.

A: Super-Basic Algebra Skills. A1. True or false. If false, change what is underlined to make the statement true. a. A: Super-Basic Algebra Skills A1. True or false. If false, change what is underlined to make the statement true. 1 T F 1 b. T F c. ( + ) = + 9 T F 1 1 T F e. ( + 1) = 16( + ) T F f. 5 T F g. If ( + )(

More information

Advanced Calculus Summer Packet

Advanced Calculus Summer Packet Advanced Calculus Summer Packet PLEASE DO ALL YOUR WORK ON LOOSELEAF PAPER! KEEP ALL WORK ORGANIZED This packet includes a sampling of problems that students entering Advanced Calculus should be able to

More information

AP Calculus AB Summer Assignment

AP Calculus AB Summer Assignment Name: AP Calculus AB Summer Assignment Due Date: The beginning of class on the last class day of the first week of school. The purpose of this assignment is to have you practice the mathematical skills

More information

Calculus Summer Packet

Calculus Summer Packet Calculus Summer Packet Congratulations on reaching this level of mathematics in high school. I know some or all of you are bummed out about having to do a summer math packet; but keep this in mind: we

More information

Honors Pre-Calculus Summer Work

Honors Pre-Calculus Summer Work Honors Pre-Calculus Summer Work Attached you will find a variety of review work based on the prerequisites needed for the Honors Pre-Calculus curriculum. The problems assigned should be the minimum you

More information

CALCULUS AB/BC SUMMER REVIEW PACKET

CALCULUS AB/BC SUMMER REVIEW PACKET Name CALCULUS AB/BC SUMMER REVIEW PACKET Welcome to AP Calculus! Calculus is a branch of advanced mathematics that deals with problems that cannot be solved with ordinary algebra such as rate problems

More information

AP Calculus AB Summer Review Packet

AP Calculus AB Summer Review Packet AP Calculus AB Summer Review Packet 016-017 Mr. Le jtle1@gmail.com Leuzinger High School Rm. G-0 The following packet is designed to help you review topics that are important to your SUCCESS in AP Calculus.

More information

AP CALCULUS AB - SUMMER ASSIGNMENT 2018

AP CALCULUS AB - SUMMER ASSIGNMENT 2018 Name AP CALCULUS AB - SUMMER ASSIGNMENT 08 This packet is designed to help you review and build upon some of the important mathematical concepts and skills that you have learned in your previous mathematics

More information

Calculus Summer Work

Calculus Summer Work Calculus Summer Work About This Packet ( and this class) Welcome! This packet includes a sampling of problems that students entering AP Calculus should be able to answer. The questions are organized by

More information

AP Calculus AB Information and Summer Assignment

AP Calculus AB Information and Summer Assignment AP Calculus AB Information and Summer Assignment General Information: Competency in Algebra and Trigonometry is absolutely essential. The calculator will not always be available for you to use. Knowing

More information

AP Calculus BC Summer Review

AP Calculus BC Summer Review AP Calculus BC 07-08 Summer Review Due September, 07 Name: All students entering AP Calculus BC are epected to be proficient in Pre-Calculus skills. To enhance your chances for success in this class, it

More information

AP Calculus AB Mrs. Mills Carlmont High School

AP Calculus AB Mrs. Mills Carlmont High School AP Calculus AB 015-016 Mrs. Mills Carlmont High School AP CALCULUS AB SUMMER ASSIGNMENT NAME: READ THE FOLLOWING DIRECTIONS CAREFULLY! Read through the notes & eamples for each page and then solve all

More information

West Essex Regional School District. AP Calculus AB. Summer Packet

West Essex Regional School District. AP Calculus AB. Summer Packet West Esse Regional School District AP Calculus AB Summer Packet 05-06 Calculus AB Calculus AB covers the equivalent of a one semester college calculus course. Our focus will be on differential and integral

More information

AP Calculus AB SUMMER ASSIGNMENT. Dear future Calculus AB student

AP Calculus AB SUMMER ASSIGNMENT. Dear future Calculus AB student AP Calculus AB SUMMER ASSIGNMENT Dear future Calculus AB student We are ecited to work with you net year in Calculus AB. In order to help you be prepared for this class, please complete the summer assignment.

More information

AP Calculus (BC) Summer Assignment (169 points)

AP Calculus (BC) Summer Assignment (169 points) AP Calculus (BC) Summer Assignment (69 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion

More information

Summer Review Packet for Students Entering AP Calculus BC. Complex Fractions

Summer Review Packet for Students Entering AP Calculus BC. Complex Fractions Summer Review Packet for Students Entering AP Calculus BC Comple Fractions When simplifying comple fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common

More information

AP Calculus Summer Assignment

AP Calculus Summer Assignment AP Calculus Summer Assignment 07-08 Welcome to AP Calculus. This summer assignment will help you review some Algebraic and Trigonometric topics that you will need for some problems in Calculus. This summer

More information

Albertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school.

Albertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school. Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2015 DUE DATE: The beginning of class on the last class day of the first week of school. This assignment is to be done at you leisure during the

More information

The American School of Marrakesh. AP Calculus AB Summer Preparation Packet

The American School of Marrakesh. AP Calculus AB Summer Preparation Packet The American School of Marrakesh AP Calculus AB Summer Preparation Packet Summer 2016 SKILLS NEEDED FOR CALCULUS I. Algebra: *A. Exponents (operations with integer, fractional, and negative exponents)

More information

Accuplacer College Level Math Study Guide

Accuplacer College Level Math Study Guide Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these

More information

Welcome to AP Calculus AB!

Welcome to AP Calculus AB! Welcome to AP Calculus AB! This packet includes a sampling of problems that students entering AP Calculus should be able to answer. The questions are organized by topic: A Super-Basic Algebra Skills T

More information

Calculus AB. Mathematics fun for all!

Calculus AB. Mathematics fun for all! HEBRON HIGH SCHOOL AP CALCULUS SUMMER MATHEMATICS REVIEW PACKET AP Calculus AB/BC Mathematics fun for all! The purpose of this assignment is to make certain that you have much of the mathematical skills

More information

Name Date. Show all work! Exact answers only unless the problem asks for an approximation.

Name Date. Show all work! Exact answers only unless the problem asks for an approximation. Advanced Calculus & AP Calculus AB Summer Assignment Name Date Show all work! Eact answers only unless the problem asks for an approimation. These are important topics from previous courses that you must

More information

Welcome to Advanced Placement Calculus!! Summer Math

Welcome to Advanced Placement Calculus!! Summer Math Welcome to Advanced Placement Calculus!! Summer Math - 017 As Advanced placement students, your first assignment for the 017-018 school year is to come to class the very first day in top mathematical form.

More information

!"#$%&'(&)*$%&+",#$$-$%&+./#-+ (&)*$%&+%"-$+0!#1%&

!#$%&'(&)*$%&+,#$$-$%&+./#-+ (&)*$%&+%-$+0!#1%& !"#$%&'(&)*$%&",#$$-$%&./#- (&)*$%&%"-$0!#1%&23 44444444444444444444444444444444444444444444444444444444444444444444 &53.67689:5;978?58"@A9;8=B!=89C7DE,6=8FG=CD=CF(76F9C7D!)#!/($"%*$H!I"%"&1/%/.!"JK$&3

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=

More information

A.P. Calculus Summer Assignment

A.P. Calculus Summer Assignment A.P. Calculus Summer Assignment This assignment is due the first day of class at the beginning of the class. It will be graded and counts as your first test grade. This packet contains eight sections and

More information

Incoming Magnet Precalculus / Functions Summer Review Assignment

Incoming Magnet Precalculus / Functions Summer Review Assignment Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were

More information

1. 4 2y 1 2 = x = x 1 2 x + 1 = x x + 1 = x = 6. w = 2. 5 x

1. 4 2y 1 2 = x = x 1 2 x + 1 = x x + 1 = x = 6. w = 2. 5 x .... VII x + x + = x x x 8 x x = x + a = a + x x = x + x x Solve the absolute value equations.. z = 8. x + 7 =. x =. x =. y = 7 + y VIII Solve the exponential equations.. 0 x = 000. 0 x+ = 00. x+ = 8.

More information

AP Calculus Summer is Long Enough Worksheet

AP Calculus Summer is Long Enough Worksheet AP Calculus Summer is Long Enough Worksheet There are certain skills that have been taught to you over the previous years that are essential towards your success in AP Calculus. If you do not have these

More information

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc

More information

AP Calculus AB Summer Math Packet

AP Calculus AB Summer Math Packet Name Date Section AP Calculus AB Summer Math Packet This assignment is to be done at you leisure during the summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus

More information

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department Updated 6/014 The problems in this packet are designed to help you review topics from previous math courses that are important to your success in Calculus with Applications. It is important that you take

More information

AP Calculus AB Summer Assignment

AP Calculus AB Summer Assignment AP Calculus AB 07-08 Summer Assignment Welcome to AP Calculus AB! You are epected to complete the attached homework assignment during the summer. This is because of class time constraints and the amount

More information

Math 121: Calculus 1 - Winter 2012/2013 Review of Precalculus Concepts

Math 121: Calculus 1 - Winter 2012/2013 Review of Precalculus Concepts Introduction Math 11: Calculus 1 - Winter 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Winter 01/01! This problems in this packet are designed to help you review the topics from

More information

Math 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts

Math 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts Introduction Math 121: Calculus 1 - Fall 201/2014 Review of Precalculus Concepts Welcome to Math 121 - Calculus 1, Fall 201/2014! This problems in this packet are designed to help you review the topics

More information

Summer AP Assignment Coversheet Falls Church High School

Summer AP Assignment Coversheet Falls Church High School Summer AP Assignment Coversheet Falls Church High School Course: AP Calculus AB Teacher Name/s: Veronica Moldoveanu, Ethan Batterman Assignment Title: AP Calculus AB Summer Packet Assignment Summary/Purpose:

More information

Avon High School Name AP Calculus AB Summer Review Packet Score Period

Avon High School Name AP Calculus AB Summer Review Packet Score Period Avon High School Name AP Calculus AB Summer Review Packet Score Period f 4, find:.) If a.) f 4 f 4 b.) Topic A: Functions f c.) f h f h 4 V r r a.) V 4.) If, find: b.) V r V r c.) V r V r.) If f and g

More information

Calculus Summer Packet

Calculus Summer Packet Calculus Summer Packet There are certain skills that have been taught to you over the previous years that are essential towards your success in Calculus. This summer packet is intended for you to retain/review/relearn

More information

Troy High School AP Calculus Summer Packet

Troy High School AP Calculus Summer Packet Troy High School AP Calculus Summer Packet As instructors of AP Calculus, we have etremely high epectations of students taking our courses. We epect a certain level of independence to be demonstrated by

More information

Math 121: Calculus 1 - Fall 2012/2013 Review of Precalculus Concepts

Math 121: Calculus 1 - Fall 2012/2013 Review of Precalculus Concepts Introduction Math 11: Calculus 1 - Fall 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Fall 01/01! This problems in this packet are designed to help you review the topics from Algebra

More information

AP Calculus (BC) Summer Assignment (104 points)

AP Calculus (BC) Summer Assignment (104 points) AP Calculus (BC) Summer Assignment (0 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion

More information

A.P. Calculus Summer Packet

A.P. Calculus Summer Packet A.P. Calculus Summer Packet Going into AP calculus, there are certain skills that have been taught to you over the previous years that we assume you have. If you do not have these skills, you will find

More information

Summer Packet Greetings Future AP Calculus Scholar,

Summer Packet Greetings Future AP Calculus Scholar, Summer Packet 2017 Greetings Future AP Calculus Scholar, I am excited about the work that we will do together during the 2016-17 school year. I do not yet know what your math capability is, but I can assure

More information

IB Mathematics HL 1/AP Calculus AB Summer Packet

IB Mathematics HL 1/AP Calculus AB Summer Packet IB Mathematics HL /AP Calculus AB Summer Packet There are certain skills that have been taught to you over the previous years that are essential towards your success in IB HL /AP Calculus. If you do not

More information

Summer Mathematics Prep

Summer Mathematics Prep Summer Mathematics Prep Entering Calculus Chesterfield County Public Schools Department of Mathematics SOLUTIONS Domain and Range Domain: All Real Numbers Range: {y: y } Domain: { : } Range:{ y : y 0}

More information

Summer AP Assignment Coversheet Falls Church High School

Summer AP Assignment Coversheet Falls Church High School Summer AP Assignment Coversheet Falls Church High School Course: AP Calculus AB Teacher Name/s: Veronica Moldoveanu, Ethan Batterman Assignment Title: AP Calculus AB Summer Packet Assignment Summary/Purpose:

More information

Southington High School 720 Pleasant Street Southington, CT 06489

Southington High School 720 Pleasant Street Southington, CT 06489 BLUE KNIGHTS Southington High School 720 Pleasant Street Southington, CT 06489 Phone: (860) 628-3229 Fax: (860) 628-3397 Home Page: www.southingtonschools.org Principal Brian Stranieri Assistant Principals

More information

With topics from Algebra and Pre-Calculus to

With topics from Algebra and Pre-Calculus to With topics from Algebra and Pre-Calculus to get you ready to the AP! (Key contains solved problems) Note: The purpose of this packet is to give you a review of basic skills. You are asked not to use the

More information

sin x (B) sin x 1 (C) sin x + 1

sin x (B) sin x 1 (C) sin x + 1 ANSWER KEY Packet # AP Calculus AB Eam Multiple Choice Questions Answers are on the last page. NO CALCULATOR MAY BE USED IN THIS PART OF THE EXAMINATION. On the AP Eam, you will have minutes to answer

More information

AP CALCULUS AB,...) of Topical Understandings ~

AP CALCULUS AB,...) of Topical Understandings ~ Name: Precalculus Teacher: AP CALCULUS AB ~ (Σer) ( Force Distance) and ( L, L,...) of Topical Understandings ~ As instructors of AP Calculus, we have etremely high epectations of students taking our courses.

More information

Section Page(s) Problems to Complete Points Section 1 Exercises Section 2 Exercises Section 3 Exercises

Section Page(s) Problems to Complete Points Section 1 Exercises Section 2 Exercises Section 3 Exercises To help you prepare for AP Calculus AB, you are required to complete this assignment. These problems will allow you to review and master the prerequisite skills necessary for this rigorous course so that

More information

AP Calculus AB Summer Packet (Due the 2nd day of class school year)

AP Calculus AB Summer Packet (Due the 2nd day of class school year) AP Calculus AB Summer Packet (Due the 2nd day of class 2007-2008 school year) Name: **Round answers to the nearest.001 ecept where eact answers are required.** **Selected answers are on the back. The graphs

More information

( ) 2 + 2x 3! ( x x ) 2

( ) 2 + 2x 3! ( x x ) 2 Review for The Final Math 195 1. Rewrite as a single simplified fraction: 1. Rewrite as a single simplified fraction:. + 1 + + 1! 3. Rewrite as a single simplified fraction:! 4! 4 + 3 3 + + 5! 3 3! 4!

More information

SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET

SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET 017-018 Name: 1. This packet is to be handed in on Monday August 8, 017.. All work must be shown on separate paper attached to the packet. 3.

More information

2018 Summer Assignment AP Calculus BC. Due Dates: Part 1 is due no later than Aug. 1 Part 2 is due no later than Aug. 15

2018 Summer Assignment AP Calculus BC. Due Dates: Part 1 is due no later than Aug. 1 Part 2 is due no later than Aug. 15 08 Summer Assignment AP Calculus BC Due Dates: Part is due no later than Aug. Part is due no later than Aug. 5 The assignment must be postmarked or hand delivered to the school (preferably to me Part :

More information

Numbers Content Points. Reference sheet (1 pt. each) 1-7 Linear Equations (1 pt. each) / Factoring (2 pt. each) /28

Numbers Content Points. Reference sheet (1 pt. each) 1-7 Linear Equations (1 pt. each) / Factoring (2 pt. each) /28 Summer Packet 2015 Your summer packet will be a major test grade for the first nine weeks. It is due the first day of school. You must show all necessary solutions. You will be tested on ALL material;

More information

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points)

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points) BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: United and Continuous! ( points) For #- below, find the its, if they eist.(#- are pt each) ) 7 ) 9 9 ) 5 ) 8 For #5-7, eplain why

More information

AP Calculus AB/BC ilearnmath.net

AP Calculus AB/BC ilearnmath.net CALCULUS AB AP CHAPTER 1 TEST Don t write on the test materials. Put all answers on a separate sheet of paper. Numbers 1-8: Calculator, 5 minutes. Choose the letter that best completes the statement or

More information

A.P. Calculus Summer Packet

A.P. Calculus Summer Packet A.P. Calculus Summer Packet Going into AP calculus, there are certain skills that have been taught to you over the previous years that we assume you have. If you do not have these skills, you will find

More information

Math 005A Prerequisite Material Answer Key

Math 005A Prerequisite Material Answer Key Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)

More information

Math 170 Calculus I Final Exam Review Solutions

Math 170 Calculus I Final Exam Review Solutions Math 70 Calculus I Final Eam Review Solutions. Find the following its: (a (b (c (d 3 = + = 6 + 5 = 3 + 0 3 4 = sin( (e 0 cos( = (f 0 ln(sin( ln(tan( = ln( (g (h 0 + cot( ln( = sin(π/ = π. Find any values

More information

To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers

To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers Going into AP Calculus, there are certain skills that you have been taught to you over the previous years that we assume you

More information

Summer Review for Students Entering AP Calculus AB

Summer Review for Students Entering AP Calculus AB Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation

More information

AP CALCULUS BC SUMMER ASSIGNMENT

AP CALCULUS BC SUMMER ASSIGNMENT AP CALCULUS BC SUMMER ASSIGNMENT Dear BC Calculus Student, Congratulations on your wisdom in taking the BC course! We know you will find it rewarding and a great way to spend your junior/senior year. This

More information

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents Level D Review Packet - MMT This packet briefly reviews the topics covered on the Level D Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below,

More information

AP CALCULUS AB SUMMER ASSIGNMENT

AP CALCULUS AB SUMMER ASSIGNMENT AP CALCULUS AB SUMMER ASSIGNMENT 06-07 Attached is your summer assignment for AP Calculus (AB). It will probably take you - hours to complete depending on how well you know your material. I would not do

More information

xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7

xvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7 About the Author v Preface to the Instructor xvi WileyPLUS xxii Acknowledgments xxiii Preface to the Student xxvi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real

More information

C. Finding roots of trinomials: 1st Example: x 2 5x = 14 x 2 5x 14 = 0 (x 7)(x + 2) = 0 Answer: x = 7 or x = -2

C. Finding roots of trinomials: 1st Example: x 2 5x = 14 x 2 5x 14 = 0 (x 7)(x + 2) = 0 Answer: x = 7 or x = -2 AP Calculus Students: Welcome to AP Calculus. Class begins in approimately - months. In this packet, you will find numerous topics that were covered in your Algebra and Pre-Calculus courses. These are

More information

AP Calculus Summer Packet

AP Calculus Summer Packet AP Calculus Summer Packet Writing The Equation Of A Line Example: Find the equation of a line that passes through ( 1, 2) and (5, 7). ü Things to remember: Slope formula, point-slope form, slopeintercept

More information

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3 . Find an equation for the line that contains the points (, -) and (6, 9).. Find the value of y for which the line through A and B has the given slope m: A(-, ), B(4, y), m.. Find an equation for the line

More information

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if . Which of the following defines a function f for which f ( ) = f( )? a. f ( ) = + 4 b. f ( ) = sin( ) f ( ) = cos( ) f ( ) = e f ( ) = log. ln(4 ) < 0 if and only if a. < b. < < < < > >. If f ( ) = (

More information

MAT063 and MAT065 FINAL EXAM REVIEW FORM 1R x

MAT063 and MAT065 FINAL EXAM REVIEW FORM 1R x Page NEW YORK CITY COLLEGE OF TECHNOLOGY of the City University of New York R DEPARTMENT OF MATHEMATICS Revised Spring 0 W. Colucci, D. DeSantis, and P. Deraney. Updated Fall 0 S. Singh MAT06 and MAT06

More information

6.5 Trigonometric Equations

6.5 Trigonometric Equations 6. Trigonometric Equations In this section, we discuss conditional trigonometric equations, that is, equations involving trigonometric functions that are satisfied only by some values of the variable (or

More information

Calculus 1 (AP, Honors, Academic) Summer Assignment 2018

Calculus 1 (AP, Honors, Academic) Summer Assignment 2018 Calculus (AP, Honors, Academic) Summer Assignment 08 The summer assignments for Calculus will reinforce some necessary Algebra and Precalculus skills. In order to be successful in Calculus, you must have

More information

Topic 1: Fractional and Negative Exponents x x Topic 2: Domain. 2x 9 2x y x 2 5x y logg 2x 12

Topic 1: Fractional and Negative Exponents x x Topic 2: Domain. 2x 9 2x y x 2 5x y logg 2x 12 AP Calculus BC Summer Packet Name INSTRUCTIONS: Where applicable, put your solutions in interval notation. Do not use any calculator (ecept on Topics 5:#5 & :#6). Please do all work on separate paper and

More information

AP Calculus AB Summer Packet 2018

AP Calculus AB Summer Packet 2018 AP Calculus AB Summer Packet 2018 Dear Calculus Student: To be successful in AP Calculus AB, you must be proficient at solving and simplifying each type of problem in this packet. This is a review of Algebra

More information

AP CALCULUS BC Syllabus / Summer Assignment 2015

AP CALCULUS BC Syllabus / Summer Assignment 2015 AP CALCULUS BC Syllabus / Summer Assignment 015 Name Congratulations! You made it to BC Calculus! In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work

More information

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y. BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n + n ( 9 )( ) + + 6 + 9ab

More information

Summer Packet Pre-AP Algebra

Summer Packet Pre-AP Algebra Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must

More information

Answer Key 1973 BC 1969 BC 24. A 14. A 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 13. C 12. D 12. E 3. A 32. B 27. E 34. C 14. D 25. B 26.

Answer Key 1973 BC 1969 BC 24. A 14. A 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 13. C 12. D 12. E 3. A 32. B 27. E 34. C 14. D 25. B 26. Answer Key 969 BC 97 BC. C. E. B. D 5. E 6. B 7. D 8. C 9. D. A. B. E. C. D 5. B 6. B 7. B 8. E 9. C. A. B. E. D. C 5. A 6. C 7. C 8. D 9. C. D. C. B. A. D 5. A 6. B 7. D 8. A 9. D. E. D. B. E. E 5. E.

More information

AP CALCULUS Summer Assignment 2014

AP CALCULUS Summer Assignment 2014 Name AP CALCULUS Summer Assignment 014 Welcome to AP Calculus. In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work this summer. The following assignment

More information

QUESTIONS? NEED HELP? Ms. Markinson at Do not hesitate to ask for help!

QUESTIONS? NEED HELP?  Ms. Markinson at Do not hesitate to ask for help! East-West AP Calculus/ Markinson Name: Date: This packet includes a sampling of problems that students entering AP Calculus should be able to answer. In Calculus, it s rarely the calculus that you will

More information

AP Calculus I and Calculus I Summer 2013 Summer Assignment Review Packet ARE YOU READY FOR CALCULUS?

AP Calculus I and Calculus I Summer 2013 Summer Assignment Review Packet ARE YOU READY FOR CALCULUS? Name: AP Calculus I and Calculus I Summer 0 Summer Assignment Review Packet ARE YOU READY FOR CALCULUS? Calculus is a VERY RIGOROUS course and completing this packet with your best effort will help you

More information

Find: sinθ. Name: Date:

Find: sinθ. Name: Date: Name: Date: 1. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ c a θ a a =

More information

* A graphing calculator is highly recommended for this class!!!

* A graphing calculator is highly recommended for this class!!! AP Calculus AB Summer Packet 08-09 Ms. Febus - García marlene_febus@gwinnett.k.ga.us This packet includes a sampling of problems that students entering AP Calculus AB should be able to answer. The questions

More information

1. OBJECTIVE: Linear Equations

1. OBJECTIVE: Linear Equations CUNY YORK COLLEGE FINAL EXAM REVIEW MATH 120: Precalculus Use the following questions to review for your final examimation for Math 120. Your ability to answer these questions will reflect what you learned

More information

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. AP Calculus Summer Homework 2015-2016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points

More information

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

Advanced Precalculus Summer 2018 Assignment Due Date: Friday, August 17, 2018 Mrs. Bermudez: Bayside Academy Advanced Precalculus Summer 08 Assignment page Advanced Precalculus Summer 08 Assignment Due Date: Friday, August 7, 08 Mrs. Bermudez: sbermudez@baysideacademy.org This summer packet for

More information