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.
|
|
- Lawrence Young
- 5 years ago
- Views:
Transcription
1 Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2017 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 summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus AB. All of the skills covered in this packet are skills from Algebra 2 and Pre-Calculus. If you need to use reference materials please do so. While graphing calculators will be used in class the majority of this packet should be done without one. If it says to you use one then please do otherwise please refrain. As you know AP Calculus AB is a fast paced course that is taught at the college level. There is a lot of material in the curriculum that must be covered before the AP exam in May. The better you know the prerequisite skills coming into the class the better the class will go for you. Spend some time with this packet and make sure you are clear on everything covered. If you have questions please contact me via and I will be glad to help. (If you take a picture of your work and the questions it usually makes things go faster) This assignment will be collected and graded as your first test. Be sure to show all appropriate work. In addition, there may be a quiz on this material during the first quarter. All questions must be complete with the correct work. I am very excited to see you all in August. Good Luck!!
2 I. Intercepts The x-intercept is where the graph crosses the x- axis. You can find the x-intercept by setting 0. Find the intercepts for each of the following The y-intercept is where the graph crosses the y- intercept. You can find the y-intercept by setting 0 Example: Find the intercepts for 3 4 Solution 2. 2 X-intercept Set Add 4 to both sides. 4 3 Take the square root of both sides Write as two equations Subtract 3 from both sides 5 1 Y-intercept Set 0 Add Square Add four to both sides 5
3 II. Complex Fractions When simplifying fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common denominator of all the denominators in the complex fraction. 1. Example
4 III. System of Equations Use substitution or elimination method to solve the system of equations. Find the point(s) of intersection of the graphs for the given equations. 1. 8, 47 Example: Elimination Method Add the two equations and you get , 4 Plug 3 and 5 into an original equation Points of intersection are 5,4, 5, 4, 3,0 Substitution , Solve one equation for a variable Plug into the other equation The rest is like the previous example IV. Functions Let Find each
5 To evaluate a function for a given value, simply plug the value into the function for x. read f of g of x. Means to plug the inside function (in this case in for x in the outside function (in this case, ) Example Given 2 1 and 4 find Find function f for the given V. Interval Notation Solve each equation. State your
6 Complete the table with the appropriate notation or graph answer in BOTH interval notation and graphically Solution 24 Interval Notation Graph 1, VI. Domain and Range Find the domain and range. The domain of a function is the set of x values for which the function is defined. The range of a function is the set of y values that a function can return. In Calculus we usually write domains and ranges in interval notation. Example: Find the domain and range for 3 Solution Since we can only take the square root of positive numbers 30 which means that 3. So we would say the domain is 3,. Note that we have used a [ to indicate that 2 is included. If 3 was not to be included we would have used a (. The smallest y value that the function can return is 0 so the range is 0, sin 3.
7 VII. Inverses Find the inverse of each function To find the inverse of a function, simply switch the x and the y and solve for the new y value. Rewrite as y Switch x and y Solve for your new y Rewrite in inverse notation 1 To prove that one function is an inverse of another function, you need to show that Prove that f and g are inverse of each other , 0 9
8 VIII. Symmetry x-axis substitute in y for y into the equation. If this yields an equivalent equation then the graph has x-axis symmetry. If this is the case, this is not a function as it would fail the vertical line test. Test for symmetry with respect to each axis and the origin y-axis substitute in x for x into the equation. If this yields an equivalent equation then the graph has y-axis symmetry. A function that has y-axis symmetry is called an even function. Origin Substitute in -x for x into the equation and substitute y for y into the equation. If this yields an equivalent equation then the graph has origin symmetry. If a function has origin symmetry it is called an odd function In order for a graph to represent a function it must be true that for every x value in the domain there is exactly one y value. To test to see if an equation is a function we can graph it and then do the vertical line test. Example 1 Is 2 a function? Solution: this is not a function because it does not pass the vertical line test. 3. Example 2: Test for symmetry with respect to each axis and the origin given the equation 4 0
9 Solution: x-axis since there is no way to make this look like the original it is not symmetric to the x axis y-axis since there is no way to make this look like the original it is not symmetric to the y axis Origin since this does look like the original it is symmetric to the origin IX. Vertical Asymptotes To find the vertical asymptotes, set the denominator equal to zero to find the x-value for which the function is undefined. That will be the vertical asymptote. Determine the vertical asymptotes for the function (it will be a line)
10 X. Holes (Points of Discontinuity) Given a rational function if a number causes the denominator and the numerator to be 0 then both the numerator and denominator can be factored and the common zero can be cancelled out. This means there is a hole in the function at this point. For each function list find the holes 1. Example 1 Find the hole in the following function 2 2 Solution: When 2 is substituted into the function the denominator and numerator both are 0. Factoring and cancelling but 2 this restriction is from the original function before canceling. The graph of the function witll look identical to except for the hole at 2 2. XI. Horizontal Asymptotes Case 1: Degree of the numerator is less than the degree of the denominator. The asymptote is 0 Case 2: Degree of the numerator is the same as the degree of the denominator. The asymptote is the ratio of the lead coefficients. Case 3: Degree of the numerator is greater than the degree of the denominator. There is no horizontal asymptote. The function increases without bound. (If the degree of the numerator is exactly 1 more than the degree of the denominator, then there is a slant asymptote, which is determined with long division.) Determine the horizontal asymptotes using the three cases
11 XII. Solving for indicated variables for x XIII. Absolute Value and Piecewise Functions In order to remove the absolute value sign from a function you must: 1. Find the zeros of the expression inside of the absolute value. 2. Make a sign chart of the expression inside the absolute value 3. Rewrite the equation without the absolute value as a piecewise function. For each interval where the expression is positive we can write that interval by just dropping the absolute value. For each interval that is negative we must take the opposite sign. Write the following absolute value expressions as piecewise expressions (by remove the absolute value): Example 1 Rewrite the following equation without using absolute value symbols. 2 4 Solution:
12 Find where the expression is 0 for the part in the absolute value Put in any value less than -2 into 2x+4 and you get a negative. Put in any value more than -2 and you get a positive. Write as a piecewise function. Be sure to change the sign of each term for any part of the graph that was negative on the sign chart. XIV Exponents Write without fractional exponents A fractional exponent means you are taking a root. For example is the same as 1. 2 Example 1: Write without fractional exponent: Solution: Notice that the index is the denominator and the power is the numerator Negative exponents mean that you need to take the reciprocal. For example means and means 2. Example 2: Write with positive exponents: Solution: Example 3: Write with positive exponents and 6. 8
13 without fractional exponents: Solution: Write with positive exponents: 7. 2 When factoring always factor out the lowest exponent for each term. Example 4: Solution: Factor then simplify When dividing two terms with the same base, we subtract the exponents. If the difference is negative then the term goes in the denominator if the difference is positive then the term goes in the numerator Example 5: Simplify Solution: first you must distribute the exponent.. Then since we have two terms with x as the base we can subtract the exponents. Thus Example 6: Factor and simplify Solution: The common terms are x and (x-3). The lowest exponent for x is 1. The lowest exponents for (x-3) is. So factor out 3 and obtain This will simplify to Leaving a final solution of
14 XV. Natural Logarithms Express as a single logarithm: Recall that ln and are inverse to each other. 1. 3ln2ln4ln Properties of Natural Log: ln lnln Example 1: ln2 ln5 ln 10 ln lnln Solve for x 2. 3ln 1 Example 2: ln 6 ln 2 ln 3 ln ln Example 3: ln 4ln 3ln 2 ln 2 ln ln, ln 1, ln 1 0, 1 Example 4: Use the properties of natural logs to solve for x ln 5 ln ln 5 ln7 ln11ln2 5ln7ln11ln2 ln 5 ln 7 ln 11 ln 2 ln 11 ln 2 ln 5 ln
15 XVI. Radians and Degree Measure Convert to degrees Use degrees Use radians to get rid of radians and convert to to get rid of degrees and convert to radians Convert to radians XVII. Trig. Equations and special values You are expected to know the special values for trigonometric functions. Fill in the table to the right and study it. (Please) You can determine sine or cosine of a quadrantal angle by using the unit circle. The x-coordinate is the cosine and the y-coordinate is the sine of the angle. Example: sin 90 1 cos sin cos sin cos
16 XVIII. Trig. Identities You should study the following trig identities and memorize them before school starts (we use them a lot) Find all the solutions to the equations. You should not need a caluclator. (hint one of these has NO solution) 1. sin 2. 2cos cos 4cos1 4. 2sin 3sin cos 1cos0
17 XIX. Graphing Trig Functions Graph two complete periods of the function. sin and cos have a period of 2 and an amplitude of 1. Use the parent graphs above to help you sketch a graph of the function below. For sin, A = amplitude, = period, phase shift (positive C/B shift left, negative C/B shift right) and K = vertical shift
18 XX. Inverse Trig Functions Inverse Trig Functions can be written in one of two ways: arcsin sin For each of the following, express the value for y in radians 1. arcsin Inverse trig functions are defined only in the quadrants as indicated below due to their restricted domains. 2. arccos1 Example 1: Express the value of y in radians arctan 1 3 Solution: Draw a reference triangle This means the reverence angle is 30 or. So so it falls in the 3. tan 1 interval from Thus Example 2: Find the value without a calculator cos 5 6 Solution For each of the following give the value without a calculator. 4. tan arccos Draw the reference triangle in the correct quadrant fits. Find the missing side using the Pythagorean
19 Theorem. Find the ratio of the cosine of the reference triangle. cos secsin 6. sin arctan 7. sin sin XXI. Transformations of a Graph Graph the parent function of each set using your calculator. Draw a quick sketch on your paper of each additional equation in the family. Check your sketch with the graphing calculator. 1. Parent Function a. 5 b. 3 c. 10 d. 8 e. 4 f g. h. 3 6 i. 4 8 j Parent Function sin (set mode to radians) a. sin 2 b. sin 2 c. 2sin d. 2sin Parent Function cos a. cos3 b. cos c. 2cos2 d. 2cos1
20 4. Parent Function a. 2 b. c. 5 d. 3 e. 4 f Parent Function a. 2 b. c. 6 d. e. f. 2 g Parent Function ln a. ln 3 b. ln3 c. ln 2 d. ln e. ln f. ln24 7. Parent Function a. b. c. 3 d. e. 8. Parent Function a. 5 b. 2 c. 3 d. e Resize your window to 0,1 0,1 Graph all of the following functions in the same window. List the functions from the highest graph to the lowest graph. How do they compare for values of 1? a. b. c. d. e. f.
21 10. Given Use your calculator to find all roots to the nearest Given 3 6 Use your calculator to find all the roots to the nearest Find the points of intersection. a. 3 2, 42 b. 5 2, 32 (If you found any errors in the packet please let me know so I can correct it. Thanks!)
Walt Whitman High School SUMMER REVIEW PACKET. For students entering AP CALCULUS BC
Walt Whitman High School SUMMER REVIEW PACKET For students entering AP CALCULUS BC Name: 1. This packet is to be handed in to your Calculus teacher on the first day of the school year.. All work must be
More informationAP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
More informationAP Calculus AB Summer Review Packet
AP Calculus AB Summer Review Packet Mr. Burrows Mrs. Deatherage 1. This packet is to be handed in to your Calculus teacher on the first day of the school year. 2. All work must be shown on separate paper
More informationAP Calculus Summer Review Packet School Year. Name
AP Calculus Summer Review Packet 016-017 School Year Name Objectives for AP/CP Calculus Summer Packet 016-017 I. Solving Equations & Inequalities (Problems # 1-6) Using the properties of equality Solving
More informationIntegrated Algebra 2 and Trigonometry. Quarter 1
Quarter 1 I: Functions: Composition I.1 (A.42) Composition of linear functions f(g(x)). f(x) + g(x). I.2 (A.42) Composition of linear and quadratic functions II: Functions: Quadratic II.1 Parabola The
More informationPre-Calculus Summer Assignment
Name: Pre-Calculus Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Pre-Calculus.
More informationTrigonometry Summer Assignment
Name: Trigonometry Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Trigonometry.
More informationSummer Review for Students Entering Pre-Calculus with Trigonometry. TI-84 Plus Graphing Calculator is required for this course.
Summer Review for Students Entering Pre-Calculus with Trigonometry 1. Using Function Notation and Identifying Domain and Range 2. Multiplying Polynomials and Solving Quadratics 3. Solving with Trig Ratios
More informationSouth County Secondary School AP Calculus BC
South County Secondary School AP Calculus BC Summer Assignment For students entering Calculus BC in the Fall of 8 This packet will be collected for a grade at your first class. The material covered in
More informationCW High School. Advanced Math A. 1.1 I can make connections between the algebraic equation or description for a function, its name, and its graph.
1. Functions and Math Models (10.00%) 1.1 I can make connections between the algebraic equation or description for a function, its name, and its graph. 4 Pro cient I can make connections between the algebraic
More informationDear Accelerated Pre-Calculus Student:
Dear Accelerated Pre-Calculus Student: We are very excited that you have decided to take this course in the upcoming school year! This is a fast-paced, college-preparatory mathematics course that will
More informationSummer Review for Students Entering Pre-Calculus with Trigonometry. TI-84 Plus Graphing Calculator is required for this course.
1. Using Function Notation and Identifying Domain and Range 2. Multiplying Polynomials and Solving Quadratics 3. Solving with Trig Ratios and Pythagorean Theorem 4. Multiplying and Dividing Rational Expressions
More information8.6 Other Trigonometric Functions
8.6 Other Trigonometric Functions I have already discussed all the trigonometric functions and their relationship to the sine and cosine functions and the x and y coordinates on the unit circle, but let
More informationAP Calculus BC Summer Assignment
AP Calculus BC Summer Assignment Name Due Date: First Day of School Welcome to AP Calculus BC! This is an exciting, challenging, fast paced course that is taught at the college level. We have a lot of
More informationGanado Unified School District Pre-Calculus 11 th /12 th Grade
Ganado Unified School District Pre-Calculus 11 th /12 th Grade PACING Guide SY 2016-2017 Timeline & Resources Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to highlight
More information1. The Pythagorean Theorem
. The Pythagorean Theorem The Pythagorean theorem states that in any right triangle, the sum of the squares of the side lengths is the square of the hypotenuse length. c 2 = a 2 b 2 This theorem can be
More informationAlgebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions
Slide 1 / 162 Algebra II Slide 2 / 162 Trigonometric Functions 2015-12-17 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 162 Radians & Degrees & Co-terminal angles Arc
More informationMastery. PRECALCULUS Student Learning Targets
PRECALCULUS Student Learning Targets Big Idea: Sequences and Series 1. I can describe a sequence as a function where the domain is the set of natural numbers. Connections (Pictures, Vocabulary, Definitions,
More informationGanado Unified School District Trigonometry/Pre-Calculus 12 th Grade
Ganado Unified School District Trigonometry/Pre-Calculus 12 th Grade PACING Guide SY 2014-2015 Timeline & Resources Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to
More informationFinal Exam: Precalculus
Final Exam: Precalculus Apr. 17, 2018 ANSWERS Without Notes or Calculators Version A 1. Consider the unit circle: a. Angle in degrees: What is the angle in radians? What are the coordinates? b. Coordinates:
More informationPRESCOTT UNIFIED SCHOOL DISTRICT District Instructional Guide Revised 6/3/15
PRESCOTT UNIFIED SCHOOL DISTRICT District Instructional Guide Revised 6/3/15 Grade Level: PHS Subject: Precalculus Quarter/Semester: 1/1 Core Text: Precalculus with 1 st week Chapter P - Prerequisites
More informationGanado Unified School District #20 (Pre-Calculus 11th/12th Grade)
Ganado Unified School District #20 (Pre-Calculus 11th/12th Grade) PACING Guide SY 2018-2019 Timeline & Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to highlight a quantity
More informationHiram High School Accelerated Pre-Calculus Summer Assignment
Hiram High School Accelerated Pre-Calculus Summer Assignment This is a fast-paced, college-preparatory course that will prepare you to be successful in college math and in AP Calculus. This is a rigorous
More informationFOR ALL STUDENTS TAKING PRE CALCULUS
FOR ALL STUDENTS TAKING PRE CALCULUS 2016 2017 SUMMER REVIEW PACKET Due 1st Day of School Name Pre Calculus Summer Assignment Information Welcome to Pre Calculus! This summer review assignment is designed
More informationPre Calculus Worksheet: Fundamental Identities Day 1
Pre Calculus Worksheet: Fundamental Identities Day 1 Use the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before. Strategy
More informationAlgebra II Trigonometric Functions
Slide 1 / 162 Slide 2 / 162 Algebra II Trigonometric Functions 2015-12-17 www.njctl.org Slide 3 / 162 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc
More informationA lg e b ra II. Trig o n o m e tric F u n c tio
1 A lg e b ra II Trig o n o m e tric F u n c tio 2015-12-17 www.njctl.org 2 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc Length & Area of a Sector
More informationUnit 1 and Unit 2 Concept Overview
Unit 1 and Unit 2 Concept Overview Unit 1 Do you recognize your basic parent functions? Transformations a. Inside Parameters i. Horizontal ii. Shift (do the opposite of what feels right) 1. f(x+h)=left
More informationSNAP Centre Workshop. Introduction to Trigonometry
SNAP Centre Workshop Introduction to Trigonometry 62 Right Triangle Review A right triangle is any triangle that contains a 90 degree angle. There are six pieces of information we can know about a given
More informationTrigonometry Curriculum Guide Scranton School District Scranton, PA
Trigonometry Scranton School District Scranton, PA Trigonometry Prerequisite: Algebra II, Geometry, Algebra I Intended Audience: This course is designed for the student who has successfully completed Algebra
More informationUnit 3, Lesson 1.3 Special Angles in the Unit Circle
Unit, Lesson Special Angles in the Unit Circle Special angles exist within the unit circle For these special angles, it is possible to calculate the exact coordinates for the point where the terminal side
More informationGraphing Trigonometric Functions: Day 1
Graphing Trigonometric Functions: Day 1 Pre-Calculus 1. Graph the six parent trigonometric functions.. Apply scale changes to the six parent trigonometric functions. Complete the worksheet Exploration:
More informationb) develop mathematical thinking and problem solving ability.
Submission for Pre-Calculus MATH 20095 1. Course s instructional goals and objectives: The purpose of this course is to a) develop conceptual understanding and fluency with algebraic and transcendental
More informationWelcome. Please Sign-In
Welcome Please Sign-In Day 1 Session 1 Self-Evaluation Topics to be covered: Equations Systems of Equations Solving Inequalities Absolute Value Equations Equations Equations An equation says two things
More informationGREENWOOD PUBLIC SCHOOL DISTRICT Algebra III Pacing Guide FIRST NINE WEEKS
GREENWOOD PUBLIC SCHOOL DISTRICT Algebra III FIRST NINE WEEKS Framework/ 1 Aug. 6 10 5 1 Sequences Express sequences and series using recursive and explicit formulas. 2 Aug. 13 17 5 1 Sequences Express
More informationUse the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before.
Pre Calculus Worksheet: Fundamental Identities Day 1 Use the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before. Strategy
More informationHonors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1
Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1
More informationSecondary Math 3- Honors. 7-4 Inverse Trigonometric Functions
Secondary Math 3- Honors 7-4 Inverse Trigonometric Functions Warm Up Fill in the Unit What You Will Learn How to restrict the domain of trigonometric functions so that the inverse can be constructed. How
More informationCurriculum Map: Mathematics
Curriculum Map: Mathematics Course: Honors Advanced Precalculus and Trigonometry Grade(s): 11-12 Unit 1: Functions and Their Graphs This chapter will develop a more complete, thorough understanding of
More informationSection 7.6 Graphs of the Sine and Cosine Functions
Section 7.6 Graphs of the Sine and Cosine Functions We are going to learn how to graph the sine and cosine functions on the xy-plane. Just like with any other function, it is easy to do by plotting points.
More informationThis assignment is due the first day of school. Name:
This assignment will help you to prepare for Geometry A by reviewing some of the topics you learned in Algebra 1. This assignment is due the first day of school. You will receive homework grades for completion
More informationSection Rational Functions and Inequalities. A rational function is a quotient of two polynomials. That is, is a rational function if
Section 6.1 --- Rational Functions and Inequalities A rational function is a quotient of two polynomials. That is, is a rational function if =, where and are polynomials and is not the zero polynomial.
More informationGraphing Trig Functions - Sine & Cosine
Graphing Trig Functions - Sine & Cosine Up to this point, we have learned how the trigonometric ratios have been defined in right triangles using SOHCAHTOA as a memory aid. We then used that information
More informationEnd Behavior and Symmetry
Algebra 2 Interval Notation Name: Date: Block: X Characteristics of Polynomial Functions Lesson Opener: Graph the function using transformations then identify key characteristics listed below. 1. y x 2
More informationMath 121. Graphing Rational Functions Fall 2016
Math 121. Graphing Rational Functions Fall 2016 1. Let x2 85 x 2 70. (a) State the domain of f, and simplify f if possible. (b) Find equations for the vertical asymptotes for the graph of f. (c) For each
More informationROCKWOOD CURRICULUM WRITING PROCESS OVERVIEW
ROCKWOOD CURRICULUM WRITING PROCESS OVERVIEW Course Content Area Last Update for this Course Trigonometry Mathematics February 2009 Results of Program Evaluation Program Evaluation Recommendations Continue
More informationEnochs Pre-AP SM3 Summer Assignment
Enochs Pre-AP SM Summer Assignment 07-8 In 07-8 school year, Pre-AP SM classes will be taught by Mrs Dodds & Mrs Rubalcava Both teachers require the same Summer Assignment However, in order to acquire
More informationMath 144 Activity #2 Right Triangle Trig and the Unit Circle
1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the
More informationName: Teacher: Pd: Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION)
Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION) In this unit, we will Learn the properties of sine and cosine curves: amplitude, frequency, period, and midline. Determine what the parameters a, b,
More informationUsing Fundamental Identities. Fundamental Trigonometric Identities. Reciprocal Identities. sin u 1 csc u. sec u. sin u Quotient Identities
3330_050.qxd /5/05 9:5 AM Page 374 374 Chapter 5 Analytic Trigonometry 5. Using Fundamental Identities What you should learn Recognize and write the fundamental trigonometric identities. Use the fundamental
More informationLook up partial Decomposition to use for problems #65-67 Do Not solve problems #78,79
Franklin Township Summer Assignment 2017 AP calculus AB Summer assignment Students should use the Mathematics summer assignment to identify subject areas that need attention in preparation for the study
More informationSantiago AP Calculus AB/BC Summer Assignment 2018 AB: complete problems 1 64, BC: complete problems 1 73
Santiago AP Calculus AB/BC Summer Assignment 2018 AB: complete problems 1 64, BC: complete problems 1 73 AP Calculus is a rigorous college level math course. It will be necessary to do some preparatory
More information2-3 Graphing Rational Functions
2-3 Graphing Rational Functions Factor What are the end behaviors of the Graph? Sketch a graph How to identify the intercepts, asymptotes and end behavior of a rational function. How to sketch the graph
More informationAP Calculus AB. Table of Contents. Slide 1 / 180. Slide 2 / 180. Slide 3 / 180. Review Unit
Slide 1 / 180 Slide 2 / 180 P alculus Review Unit 2015-10-20 www.njctl.org Table of ontents lick on the topic to go to that section Slide 3 / 180 Slopes Equations of Lines Functions Graphing Functions
More informationCollege Pre Calculus A Period. Weekly Review Sheet # 1 Assigned: Monday, 9/9/2013 Due: Friday, 9/13/2013
College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 9/9/013 Due: Friday, 9/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE
More informationTEKS Clarification Document. Mathematics Precalculus
TEKS Clarification Document Mathematics Precalculus 2012 2013 111.31. Implementation of Texas Essential Knowledge and Skills for Mathematics, Grades 9-12. Source: The provisions of this 111.31 adopted
More informationALGEBRA II A CURRICULUM OUTLINE
ALGEBRA II A CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Linear Equations and Inequalities 2. Polynomial Expressions and Equations 3. Rational Expressions and Equations 4. Radical Expressions and Equations
More informationThe following information is for reviewing the material since Exam 3:
Outcomes List for Math 121 Calculus I Fall 2010-2011 General Information: The purpose of this Outcomes List is to give you a concrete summary of the material you should know, and the skills you should
More informationto and go find the only place where the tangent of that
Study Guide for PART II of the Spring 14 MAT187 Final Exam. NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 5 multiple choice questions. You will
More informationTrigonometry. 9.1 Radian and Degree Measure
Trigonometry 9.1 Radian and Degree Measure Angle Measures I am aware of three ways to measure angles: degrees, radians, and gradians. In all cases, an angle in standard position has its vertex at the origin,
More information1.1 Pearson Modeling and Equation Solving
Date:. Pearson Modeling and Equation Solving Syllabus Objective:. The student will solve problems using the algebra of functions. Modeling a Function: Numerical (data table) Algebraic (equation) Graphical
More informationPRECALCULUS MR. MILLER
PRECALCULUS MR. MILLER I. COURSE DESCRIPTION This course requires students to use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study
More information,?...?, the? or? s are for any holes or vertical asymptotes.
Name: Period: Pre-Cal AB: Unit 14: Rational Functions Monday Tuesday Block Friday 16 17 18/19 0 end of 9 weeks Graphing Rational Graphing Rational Partial Fractions QUIZ 3 Conic Sections (ON Friday s Quiz)
More informationCourse Number 432/433 Title Algebra II (A & B) H Grade # of Days 120
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
More information1. (10 pts.) Find and simplify the difference quotient, h 0for the given function
MATH 1113/ FALL 016 FINAL EXAM Section: Grade: Name: Instructor: f ( x h) f ( x) 1. (10 pts.) Find and simplify the difference quotient, h 0for the given function h f ( x) x 5. (10 pts.) The graph of the
More informationSUM AND DIFFERENCES. Section 5.3 Precalculus PreAP/Dual, Revised 2017
SUM AND DIFFERENCES Section 5. Precalculus PreAP/Dual, Revised 2017 Viet.dang@humbleisd.net 8/1/2018 12:41 AM 5.4: Sum and Differences of Trig Functions 1 IDENTITY Question 1: What is Cosine 45? Question
More informationMath 3 Coordinate Geometry Part 2 Graphing Solutions
Math 3 Coordinate Geometry Part 2 Graphing Solutions 1 SOLVING SYSTEMS OF EQUATIONS GRAPHICALLY The solution of two linear equations is the point where the two lines intersect. For example, in the graph
More informationMr. C s Math III Exam is Tue 1/14/14 in the Presentation Center please be there for 11:20 Check-In and Test Return. You may not leave early (sorry)
Mr. C s Math III Exam is Tue 1/14/14 in the Presentation Center please be there for 11:20 Check-In and Test Return Make Sure You Bring: Your Tests to return Calculator w/ good batteries Pencils/Erasers
More informationDefinitions Associated w/ Angles Notation Visualization Angle Two rays with a common endpoint ABC
Preface to Chapter 5 The following are some definitions that I think will help in the acquisition of the material in the first few chapters that we will be studying. I will not go over these in class and
More informationCCSSM Curriculum Analysis Project Tool 1 Interpreting Functions in Grades 9-12
Tool 1: Standards for Mathematical ent: Interpreting Functions CCSSM Curriculum Analysis Project Tool 1 Interpreting Functions in Grades 9-12 Name of Reviewer School/District Date Name of Curriculum Materials:
More informationPrecalculus Solutions Review for Test 6 LMCA Section
Precalculus Solutions Review for Test 6 LMCA Section 4.5-4.8 Memorize all of the formulas and identities. Here are some of the formulas for chapter 5. BasicTrig Functions opp y hyp r sin csc hyp r opp
More informationAP Calculus AB. Table of Contents. Slide 1 / 180. Slide 2 / 180. Slide 3 / 180. Review Unit
Slide 1 / 180 Slide 2 / 180 P alculus Review Unit 2015-10-20 www.njctl.org Table of ontents lick on the topic to go to that section Slide 3 / 180 Slopes Equations of Lines Functions Graphing Functions
More informationAmphitheater School District End Of Year Algebra II Performance Assessment Review
Amphitheater School District End Of Year Algebra II Performance Assessment Review This packet is intended to support student preparation and review for the Algebra II course concepts for the district common
More information1 Review of Functions Symmetry of Functions; Even and Odd Combinations of Functions... 42
Contents 0.1 Basic Facts...................................... 8 0.2 Factoring Formulas.................................. 9 1 Review of Functions 15 1.1 Functions.......................................
More informationGraphing Techniques. Domain (, ) Range (, ) Squaring Function f(x) = x 2 Domain (, ) Range [, ) f( x) = x 2
Graphing Techniques In this chapter, we will take our knowledge of graphs of basic functions and expand our ability to graph polynomial and rational functions using common sense, zeros, y-intercepts, stretching
More informationWorking with Rational Expressions
Working with Rational Expressions Return to Table of Contents 4 Goals and Objectives Students will simplify rational expressions, as well as be able to add, subtract, multiply, and divide rational expressions.
More informationFoundations of Math II
Foundations of Math II Unit 6b: Toolkit Functions Academics High School Mathematics 6.6 Warm Up: Review Graphing Linear, Exponential, and Quadratic Functions 2 6.6 Lesson Handout: Linear, Exponential,
More informationMathematics 12 Pre-Calculus WNCP
Mathematics 1 Pre-Calculus WNCP Page 1 Page Page 3-8 Page 9-1 General Information Record Chart Sample Guided Outlines Sample Unit Test Pages Textbook This course uses the textbook Pre-Calculus 1 ISBN 978007073870
More information1.) ( ) Step 1: Factor the numerator and the denominator. Find the domain. is in lowest terms.
GP3-HW11 College Algebra Sketch the graph of each rational function. 1.) Step 1: Factor the numerator and the denominator. Find the domain. { } Step 2: Rewrite in lowest terms. The rational function is
More informationMATH STUDENT BOOK. 12th Grade Unit 4
MATH STUDENT BOOK th Grade Unit Unit GRAPHING AND INVERSE FUNCTIONS MATH 0 GRAPHING AND INVERSE FUNCTIONS INTRODUCTION. GRAPHING 5 GRAPHING AND AMPLITUDE 5 PERIOD AND FREQUENCY VERTICAL AND HORIZONTAL
More informationHOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS. College Algebra with Trigonometric Functions
HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS Math 150 College Algebra with Trigonometric Functions CREDIT HOURS: 4.0 EQUATED HOURS: 4.0 CLASS HOURS: 4.0 PREREQUISITE: Passing Mat 15 or mat 20 or
More informationCLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?
CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..
More information9-1 GCSE Maths. GCSE Mathematics has a Foundation tier (Grades 1 5) and a Higher tier (Grades 4 9).
9-1 GCSE Maths GCSE Mathematics has a Foundation tier (Grades 1 5) and a Higher tier (Grades 4 9). In each tier, there are three exams taken at the end of Year 11. Any topic may be assessed on each of
More informationTABLE OF CONTENTS CHAPTER 1 LIMIT AND CONTINUITY... 26
TABLE OF CONTENTS CHAPTER LIMIT AND CONTINUITY... LECTURE 0- BASIC ALGEBRAIC EXPRESSIONS AND SOLVING EQUATIONS... LECTURE 0- INTRODUCTION TO FUNCTIONS... 9 LECTURE 0- EXPONENTIAL AND LOGARITHMIC FUNCTIONS...
More information2.2 Limit of a Function and Limit Laws
Limit of a Function and Limit Laws Section Notes Page Let s look at the graph y What is y()? That s right, its undefined, but what if we wanted to find the y value the graph is approaching as we get close
More informationRational functions, like rational numbers, will involve a fraction. We will discuss rational functions in the form:
Name: Date: Period: Chapter 2: Polynomial and Rational Functions Topic 6: Rational Functions & Their Graphs Rational functions, like rational numbers, will involve a fraction. We will discuss rational
More informationName: Rational Functions 2.1H. Set Topic: Simplifying rational expressions & operations on rational expressions
Name: Rational Functions 2.1H Ready, Set, Go! Ready Topic: Polynomial division Use division to determine if the given linear term is a factor of the polynomial. If it is a linear factor, then find the
More informationAlgebra 2 Semester 2 Final Exam Study Outline Semester 2 Final Exam Study Tips and Information
Algebra 2 Semester 2 Final Exam Study Outline 2013 Semester 2 Final Exam Study Tips and Information The final exam is CUMULATIVE and will include all concepts taught from Chapter 1 through Chapter 13.
More informationLesson #6: Basic Transformations with the Absolute Value Function
Lesson #6: Basic Transformations with the Absolute Value Function Recall: Piecewise Functions Graph:,, What parent function did this piecewise function create? The Absolute Value Function Algebra II with
More informationCalculus Chapter 1 Limits. Section 1.2 Limits
Calculus Chapter 1 Limits Section 1.2 Limits Limit Facts part 1 1. The answer to a limit is a y-value. 2. The limit tells you to look at a certain x value. 3. If the x value is defined (in the domain),
More information2-4 Graphing Rational Functions
2-4 Graphing Rational Functions Factor What are the zeros? What are the end behaviors? How to identify the intercepts, asymptotes, and end behavior of a rational function. How to sketch the graph of a
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA II. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA II 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Algebra II Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationLimits. f(x) and lim. g(x) g(x)
Limits Limit Laws Suppose c is constant, n is a positive integer, and f() and g() both eist. Then,. [f() + g()] = f() + g() 2. [f() g()] = f() g() [ ] 3. [c f()] = c f() [ ] [ ] 4. [f() g()] = f() g()
More informationName Summer Work Packet AP Calculus AB
Name Summer Work Packet AP Calculus AB Welcome to AP Calculus AB! Advanced Placement courses are designed to expose you to college level curriculum. This requires a great amount of planning from your teacher
More informationDover-Sherborn High School Mathematics Curriculum Pre-Calculus Level 2/CP
Mathematics Curriculum A. DESCRIPTION This is a precalculus course that expands the student s knowledge of some Algebra 2 topics and covers many of the topics found in a traditional college preparatory
More information1.1 calculator viewing window find roots in your calculator 1.2 functions find domain and range (from a graph) may need to review interval notation
1.1 calculator viewing window find roots in your calculator 1.2 functions find domain and range (from a graph) may need to review interval notation functions vertical line test function notation evaluate
More informationYou can graph the equation, then have the calculator find the solutions/roots/zeros/x intercepts.
To find zeros, if you have a quadratic, x 2, then you can use the quadratic formula. You can graph the equation, then have the calculator find the solutions/roots/zeros/x intercepts. Apr 22 10:39 AM Graphing
More informationImportant. Compact Trigonometry CSO Prioritized Curriculum. Essential. Page 1 of 6
Essential Important Compact Trigonometry CSO Prioritized Curriculum M.O.T.3.1 apply the right triangle definition of the six trigonometric functions of an angle to determine the values of the function
More informationTrigonometry and the Unit Circle. Chapter 4
Trigonometry and the Unit Circle Chapter 4 Topics Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Develop and apply the equation of the unit circle. Solve
More information2.3 Graph Sketching: Asymptotes and Rational Functions Math 125
.3 Graph Sketching: Asymptotes and Rational Functions Math 15.3 GRAPH SKETCHING: ASYMPTOTES AND RATIONAL FUNCTIONS All the functions from the previous section were continuous. In this section we will concern
More information