AP CALCULUS AB Study Guide for Midterm Exam 2017

Size: px
Start display at page:

Download "AP CALCULUS AB Study Guide for Midterm Exam 2017"

Transcription

1 AP CALCULUS AB Study Guide for Midterm Exam 2017 CHAPTER 1: PRECALCULUS REVIEW 1.1 Real Numbers, Functions and Graphs - Write absolute value as a piece-wise function - Write and interpret open and closed intervals - Find the distance between two point - Find the root(s) of an equation - Use the equation of a circle - Apply the vertical line test to see if a graph is a function - Know the difference between even and odd functions - Apply transformations to equations to get other equations 1.2 Linear and Quadratic Functions - State a linear equation in slope-intercept form - Write an equation is standard form, slope-intercept form point-slope form - Find parallel and perpendicular equations of a given equation - Find the roots of a quadratic equation either by factoring or the quadratic formula - Apply the process of completing the square, when needed 1.3 The Basic Classes of Functions - Find the degree and leading coefficient of a polynomial function - Know the domain and range and graphs of: rational function, algebraic function, exponential function, and composite functions 1.4 Trigonometric Functions - Convert an angle from radians to degrees, and vice versa - Find the length of an arc on a circle of radius r - Work with radians more than degrees - Know the 6 basic trigonometry functions and their definitions - Know the basic properties of sine and cosine: periodicity, parity, and basic identities - Know the sine and cosine of the basic functions: 0, /2, /3, /4, and their multiples in the four quadrants 1.5 Inverse Functions - Know if a function is one-to-one or not - Find the inverse of f(x) if it exists - Recognize that f(x) is one-to-one if and only if every horizontal line intersects the graph of f(x) in at most one point - The graph of a function s inverse reflects the graph of f(x) through the line y = x. - Find the domain and the range of the main inverse functions

2 1.6 Exponential and Logarithmic Functions - Identify and know the domain of the exponential and logarithmic functions - Apply the logarithm laws (4) - Know the domain and range and identify the sinh x and cosh x (hyperbolic functions) and their inverses 1.7 Technology: Calculators and Computers - Set the viewing window correctly for the equation that needs to be graphed - Work in radians and not degrees for trig functions - Find how many roots and where they are - Describe the set of all solutions; know when there are no solutions - Identify asymptotes if working with a rational function CHAPTER 2: LIMITS 2.1 Limits, Rates of Change and Tangent Lines - Identify that the average rate of change is the same as the slope of the secant line - Instantaneous rate of change is the limit of the average rates of change, which is the same thing as the slope of the tangent line - find the velocity of an object in linear motion (same as the rate of change of position) - See that the average rate of change over every interval and the instantaneous rate of change at every point are equal to the slope m 2.2 Limits: A Numerical and Graphical Approach - Find the value of the limit using a table or a graph - Determine the value of a limit using the limit definition - Determine the one-sided limits of specific functions numerically and graphically - Apply the concept that the limit may exist even if f(c) is not defined - Identify the asymptote as the vertical line in the case of a one-sided or two-sided infinite limit 2.3 Basic Limit Laws - Evaluate the limit using the basic limit laws 2.4 Limits and Continuity - Identify a discontinuity, and know the three common discontinuities ( removable, jump and infinite) - Apply the definition of one-sided continuity - Define and apply the concept of continuity - Apply the laws of continuity: polynomials, rational functions, nth-root and algebraic functions, trig functions and their inverses, exponential and logarithmic functions

3 - Substitution method: If f(x) is known to be continuous at x = c, then the value of the limit of f(x) is f(c) 2.5 Evaluating Limits Algebraically - Use substitution when function is continuous - Recognize when a limit is in indeterminate form, and see if it can be transformed into a new expression that you can find the limit of 2.6 Trigonometric Limits - Recognize when the Squeeze theorem need to be applied 2.7 Limits at Infinity - Calculate the limits at infinity, especially involving rational functions and specific limits - Find the horizontal asymptotes of a rational function 2.8 Intermediate Value Theorem - Show that an equation has at least one solution, according to the Intermediate Value Theorem - Show the existence of zeros CHAPTER 3 DIFFERENTIATION 3.1 Definition of the Derivative - Calculate f (a) using the limit definition - Recognize when the definition of derivative is presented and when a shortcut can be used - Apply the equation of the tangent line in point-slope form 3.2 The Derivative as a Function - Write and recognize different notations for derivative - Use the power rule for derivatives - Compute the derivative and find an equation of the tangent line to the graph at a specific point - Find the derivatives of exponential and logarithmic functions - Remember that differentiability implies continuity, not vice versa 3.3 Product and Quotient Rules - Distinguish and apply the product rule and the quotient rule to problems

4 3.4 Rates of Change - Connect the instantaneous rate of change as the derivative - Solve linear motion problems, to find distance, velocity and acceleration - Solve marginal cost and gravity problems 3.5 Higher Derivatives - Calculate higher derivatives 3.6 Trigonometric Functions - Calculate the derivatives of the six trigonometric functions 3.7 The Chain Rule - Identify when the chain rule needs to be used - Find the derivative using the appropriate rule or combination of rules - Use the chain rule to find derivatives 3.8 Derivatives of Inverse Functions - Find the derivative of the inverse of functions - Compute the derivative at a point dedicated without a calculator 3.9 Derivatives of General Exponential and Logarithmic Functions - Apply and solve derivative formulas for e x, ln x, b x and log xb - Find the derivatives of hyperbolic functions and inverse hyperbolic functions 3.10 Implicit Differentiation - Use implicit differentiation to compute the derivative when x and y are related by an equation - Remember to include the factor dy/dx when differentiating expressions involving y with respect to x 3.11 Related Rates - Calculate an unknown rate of change in terms of other rates of change that are known, including the sliding ladder problem, or filling a rectangular tank or conical tank, tracking a rocket, finding the change in volume of a sphere, the Pythagorean Theorem, similar triangles, etc. - Draw a diagram if possible - Find an equation that relates the known and unknown derivatives

5 CHAPTER 4 APPLICATIONS OF THE DERIVATIVE 4.1 Linear Approximation and Applications - Use linear approximation to estimate a small change 4.2 Extreme Values - Find the minimum and/or the maximum value of a function - Find the local extrema and critical points - Find the extrema on a closed interval (include the endpoints when calculating) - Recognize Rolle s Theorem and when it can be used 4.3 The Mean Value Theorem - Verify the Mean Value Theorem with a function and endpointe - Find intervals where a function is increasing and decreasing - Analyze and test critical points - Apply and analyze the First Derivative Test 4.4 The Shape of a Graph - Test for Concavity at the points of inflection - Find the points of inflections and intervals of concavity - Know what to do where the second derivative does not exist - Apply and analyze the Second Derivative Test - Find the intervals on which the function is concave up or down, the points of inflection, the critical points and the local minima and maxima - Sketch the graph of a function knowing the critical and inflection points 4.5 L Hopital s Rule - Know when to apply the rule - Know when the rule needs to be applied more than once - Evaluate limits using L Hopital s Rule 4.6 Graph Sketching and Asymptotes - Focus on transition points to sketch a graph by determining the signs of f and f, noting transition points and sign combinations, drawing arcs of appropriate shape and asymptotic behavior 4.7 Applied Optimization - Choose variables and write the objective function and then apply techniques to solve: find the critical points, evaluate the function at the critical points and the endpoints; state the largest and smallest values as the extreme values of f(x) on [a,b]

Review Guideline for Final

Review Guideline for Final Review Guideline for Final Here is the outline of the required skills for the final exam. Please read it carefully and find some corresponding homework problems in the corresponding sections to practice.

More information

Harbor Creek School District

Harbor Creek School District Unit 1 Days 1-9 Evaluate one-sided two-sided limits, given the graph of a function. Limits, Evaluate limits using tables calculators. Continuity Evaluate limits using direct substitution. Differentiability

More information

AP Calculus BC Scope & Sequence

AP Calculus BC Scope & Sequence AP Calculus BC Scope & Sequence Grading Period Unit Title Learning Targets Throughout the School Year First Grading Period *Apply mathematics to problems in everyday life *Use a problem-solving model that

More information

Pre-Calculus EOC Review 2016

Pre-Calculus EOC Review 2016 Pre-Calculus EOC Review 2016 Name The Exam 50 questions, multiple choice, paper and pencil. I. Limits 8 questions a. (1) decide if a function is continuous at a point b. (1) understand continuity in terms

More information

AP Calculus BC Syllabus

AP Calculus BC Syllabus AP Calculus BC Syllabus Course Overview and Philosophy This course is designed to be the equivalent of a college-level course in single variable calculus. The primary textbook is Calculus, 7 th edition,

More information

Due Date: Thursday, March 22, 2018

Due Date: Thursday, March 22, 2018 The Notebook Project AP Calculus AB This project is designed to improve study skills and organizational skills for a successful career in mathematics. You are to turn a composition notebook into a Go To

More information

MATH 1040 Objectives List

MATH 1040 Objectives List MATH 1040 Objectives List Textbook: Calculus, Early Transcendentals, 7th edition, James Stewart Students should expect test questions that require synthesis of these objectives. Unit 1 WebAssign problems

More information

CHAPTER 1 Prerequisites for Calculus 2. CHAPTER 2 Limits and Continuity 58

CHAPTER 1 Prerequisites for Calculus 2. CHAPTER 2 Limits and Continuity 58 CHAPTER 1 Prerequisites for Calculus 2 1.1 Lines 3 Increments Slope of a Line Parallel and Perpendicular Lines Equations of Lines Applications 1.2 Functions and Graphs 12 Functions Domains and Ranges Viewing

More information

Mathematics Scope & Sequence Calculus AB

Mathematics Scope & Sequence Calculus AB Mathematics Scope & Sequence 2015-16 Calculus AB Revised: March 2015 First Six Weeks (29 ) Limits and Continuity Limits of (including onesided limits) An intuitive understanding of the limiting process

More information

Math 4C Fall 2008 Final Exam Study Guide Format 12 questions, some multi-part. Questions will be similar to sample problems in this study guide,

Math 4C Fall 2008 Final Exam Study Guide Format 12 questions, some multi-part. Questions will be similar to sample problems in this study guide, Math 4C Fall 2008 Final Exam Study Guide Format 12 questions, some multi-part. Questions will be similar to sample problems in this study guide, homework problems, lecture examples or examples from the

More information

CW High School. Calculus/AP Calculus A

CW High School. Calculus/AP Calculus A 1. Algebra Essentials (25.00%) 1.1 I can apply the point-slope, slope-intercept, and general equations of lines to graph and write equations for linear functions. 4 Pro cient I can apply the point-slope,

More information

AP Calculus AB Syllabus

AP Calculus AB Syllabus AP Calculus AB Syllabus Course Overview and Philosophy This course is designed to be the equivalent of a college-level course in single variable calculus. The primary textbook is Calculus of a Single Variable,

More information

Region 16 Board of Education. Precalculus Curriculum

Region 16 Board of Education. Precalculus Curriculum Region 16 Board of Education Precalculus Curriculum 2008 1 Course Description This course offers students an opportunity to explore a variety of concepts designed to prepare them to go on to study calculus.

More information

MATHEMATICS AP Calculus (BC) Standard: Number, Number Sense and Operations

MATHEMATICS AP Calculus (BC) Standard: Number, Number Sense and Operations Standard: Number, Number Sense and Operations Computation and A. Develop an understanding of limits and continuity. 1. Recognize the types of nonexistence of limits and why they Estimation are nonexistent.

More information

AP Calculus BC. Course Description:

AP Calculus BC. Course Description: AP Calculus BC Course Description: The two fundamental problems of Calculus include: 1) finding the slope of the tangent to a curve, determined by the derivative, and 2) finding the area of a region under

More information

MATHEMATICAL ANALYSIS CURRICULUM GUIDE

MATHEMATICAL ANALYSIS CURRICULUM GUIDE MATHEMATICAL ANALYSIS CURRICULUM GUIDE Loudoun County Public Schools 2010-2011 Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet. INTRODUCTION

More information

Essential Understandings. Essential Questions. Essential Knowledge. Vocabulary. Essential Skills. 1 of 5

Essential Understandings. Essential Questions. Essential Knowledge. Vocabulary. Essential Skills. 1 of 5 Understandings Questions Knowledge Vocabulary Skills The concept of a derivative is introduced using limits & continuity. Students find derivative shortcuts for the basic functions. Students explore where

More information

Objectives List. Important Students should expect test questions that require a synthesis of these objectives.

Objectives List. Important Students should expect test questions that require a synthesis of these objectives. MATH 1040 - of One Variable, Part I Textbook 1: : Algebra and Trigonometry for ET. 4 th edition by Brent, Muller Textbook 2:. Early Transcendentals, 3 rd edition by Briggs, Cochran, Gillett, Schulz s List

More information

Wed. Sept 28th: 1.3 New Functions from Old Functions: o vertical and horizontal shifts o vertical and horizontal stretching and reflecting o

Wed. Sept 28th: 1.3 New Functions from Old Functions: o vertical and horizontal shifts o vertical and horizontal stretching and reflecting o Homework: Appendix A: 1, 2, 3, 5, 6, 7, 8, 11, 13-33(odd), 34, 37, 38, 44, 45, 49, 51, 56. Appendix B: 3, 6, 7, 9, 11, 14, 16-21, 24, 29, 33, 36, 37, 42. Appendix D: 1, 2, 4, 9, 11-20, 23, 26, 28, 29,

More information

Single Variable Calculus, Early Transcendentals

Single Variable Calculus, Early Transcendentals Single Variable Calculus, Early Transcendentals 978-1-63545-100-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax

More information

PreCalculus. Curriculum (447 topics additional topics)

PreCalculus. Curriculum (447 topics additional topics) PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Topic Subtopics Essential Knowledge (EK)

Topic Subtopics Essential Knowledge (EK) Unit/ Unit 1 Limits [BEAN] 1.1 Limits Graphically Define a limit (y value a function approaches) One sided limits. Easy if it s continuous. Tricky if there s a discontinuity. EK 1.1A1: Given a function,

More information

Curriculum Catalog

Curriculum Catalog 2017-2018 Curriculum Catalog - for use with AP courses 2017 Glynlyon, Inc. Table of Contents CALCULUS COURSE OVERVIEW... 1 UNIT 1: GRAPHS AND LIMITS... 1 UNIT 2: DERIVATIVES... 2 UNIT 3: RELATED RATES...

More information

PreCalculus Honors Curriculum Pacing Guide First Half of Semester

PreCalculus Honors Curriculum Pacing Guide First Half of Semester Unit 1 Introduction to Trigonometry (9 days) First Half of PC.FT.1 PC.FT.2 PC.FT.2a PC.FT.2b PC.FT.3 PC.FT.4 PC.FT.8 PC.GCI.5 Understand that the radian measure of an angle is the length of the arc on

More information

Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam

Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam This outcomes list summarizes what skills and knowledge you should have reviewed and/or acquired during this entire quarter in Math 121, and what

More information

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT A P C a l c u l u s ( A B ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS Limits and Continuity Derivatives

More information

AP Calculus BC Syllabus Course Overview

AP Calculus BC Syllabus Course Overview AP Calculus BC Syllabus Course Overview Textbook Anton, Bivens, and Davis. Calculus: Early Transcendentals, Combined version with Wiley PLUS. 9 th edition. Hoboken, NJ: John Wiley & Sons, Inc. 2009. Course

More information

President. Trustees Marion Blane Steve Enella John Ferrara Wendy Gargiulo Janet Goller Gina Piskin. Kate Freeman, Business

President. Trustees Marion Blane Steve Enella John Ferrara Wendy Gargiulo Janet Goller Gina Piskin. Kate Freeman, Business Dr. Nancy Kaplan President Nina Lanci Vice President Trustees Marion Blane Steve Enella John Ferrara Wendy Gargiulo Janet Goller Gina Piskin John DeTommaso Superintendent of Schools Dr. Mara Bollettieri

More information

Calculus I

Calculus I Calculus I 978-1-63545-038-5 To learn more about all our offerings Visit Knewton.com/highered Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts Institute

More information

Standards for AP Calculus AB

Standards for AP Calculus AB I. Functions, Graphs and Limits Standards for AP Calculus AB A. Analysis of graphs. With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the

More information

Polynomials and Rational Functions. Quadratic Equations and Inequalities. Remainder and Factor Theorems. Rational Root Theorem

Polynomials and Rational Functions. Quadratic Equations and Inequalities. Remainder and Factor Theorems. Rational Root Theorem Pre-Calculus Pre-AP Scope and Sequence - Year at a Glance Pre-Calculus Pre-AP - First Semester Pre-calculus with Limits; Larson/Hostetler Three Weeks 1 st 3 weeks 2 nd 3 weeks 3 rd 3 weeks 4 th 3 weeks

More information

Algebra II Learning Targets

Algebra II Learning Targets Chapter 0 Preparing for Advanced Algebra LT 0.1 Representing Functions Identify the domain and range of functions LT 0.2 FOIL Use the FOIL method to multiply binomials LT 0.3 Factoring Polynomials Use

More information

Greenwich Public Schools Mathematics Curriculum Objectives. Calculus

Greenwich Public Schools Mathematics Curriculum Objectives. Calculus Mathematics Curriculum Objectives Calculus June 30, 2006 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify

More information

Correlation with College Board Advanced Placement Course Descriptions

Correlation with College Board Advanced Placement Course Descriptions Correlation with College Board Advanced Placement Course Descriptions The following tables show which sections of Calculus: Concepts and Applications cover each of the topics listed in the 2004 2005 Course

More information

BC Calculus Syllabus. Assessment Students are assessed in the following ways:

BC Calculus Syllabus. Assessment Students are assessed in the following ways: BC Calculus Syllabus Assessment Students are assessed in the following ways: Unit tests Project Problem Sessions Weekly assignments done outside of class that consist of problems from released Quizzes

More information

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives Pre-Calculus MATH 119 Fall 2013 Learning Objectives Section 1.1 1. Use the Distance Formula 2. Use the Midpoint Formula 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables

More information

Math Review for AP Calculus

Math Review for AP Calculus Math Review for AP Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

Advanced Placement AB Calculus

Advanced Placement AB Calculus Advanced Placement AB Calculus Performance Objectives and Time Table Text: Calculus, 8 th edition, by Howard Anton, Irl Bivens, Stephen Davis. John Wiley & Sons, Inc. 005 FIRST NINE WEEKS SECOND NINE WEEKS

More information

Chetek-Weyerhaeuser High School

Chetek-Weyerhaeuser High School Chetek-Weyerhaeuser High School Advanced Math A Units and s Advanced Math A Unit 1 Functions and Math Models (7 days) 10% of grade s 1. I can make connections between the algebraic equation or description

More information

Advanced Placement Calculus AB. South Texas ISD. Scope and Sequence with Learning Objectives

Advanced Placement Calculus AB. South Texas ISD. Scope and Sequence with Learning Objectives Advanced Placement Calculus AB South Texas ISD Scope and Sequence with Learning Objectives Advanced Placement Calculus AB Scope and Sequence - Year at a Glance AP Calculus AB - First Semester Three Weeks

More information

B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC

B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC B L U E V A L L E Y D I S T R I C T C U R R I C U L U M & I N S T R U C T I O N Mathematics AP Calculus BC Weeks ORGANIZING THEME/TOPIC CONTENT CHAPTER REFERENCE FOCUS STANDARDS & SKILLS Analysis of graphs.

More information

Williamsville C.U.S.D. #15 Mathematics Curriculum

Williamsville C.U.S.D. #15 Mathematics Curriculum MATHEMATICS CURRICULUM AP CALCULUS 1 Program Title: A.P. Calculus Williamsville C.U.S.D. #15 Mathematics Curriculum Program Description: Program Content: AP Calculus is a full-year course. This course

More information

Topic Outline AP CALCULUS AB:

Topic Outline AP CALCULUS AB: Topic Outline AP CALCULUS AB: Unit 1: Basic tools and introduction to the derivative A. Limits and properties of limits Importance and novelty of limits Traditional definitions of the limit Graphical and

More information

Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10

Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10 Prep for Calculus This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (281 topics + 125 additional topics) Real

More information

Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015

Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015 Curriculum and Pacing Guide Mr. White AP Calculus AB Revised May 2015 Students who successfully complete this course will receive one credit AP Calculus AB and will take the AP Calculus AB Exam. 1. The

More information

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014)

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014) WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014) COURSE NAME: Pre-Calculus UNIT: Chapter 1 NO. OF DAYS: KEY LEARNING (S): UNIT ESSENTIAL QUESTIONS: What methods are used to solve equations

More information

Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.2 Solving Quadratic Equations

Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.2 Solving Quadratic Equations Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.1.1 Solve Simple Equations Involving Absolute Value 0.2 Solving Quadratic Equations 0.2.1 Use the

More information

Index. Excerpt from "Calculus" 2013 AoPS Inc. Copyrighted Material INDEX

Index. Excerpt from Calculus 2013 AoPS Inc.  Copyrighted Material INDEX Index #, 2 \, 5, 4 [, 4 - definition, 38 ;, 2 indeterminate form, 2 22, 24 indeterminate form, 22 23, see Euler s Constant 2, 2, see infinity, 33 \, 6, 3, 2 3-6-9 triangle, 2 4-dimensional sphere, 85 45-45-9

More information

Course Outline and Objectives. MA 1453 Precalculus with Graphing Calculators

Course Outline and Objectives. MA 1453 Precalculus with Graphing Calculators Effective Fall 2011 Course Outline and Objectives MA 1453 Precalculus with Graphing Calculators TEXT: Precalculus, 5 th Edition, by Faires and DeFranza ISBN 978-0-8400-6862-0 NOTE: A graphing calculator

More information

Review for Final. The final will be about 20% from chapter 2, 30% from chapter 3, and 50% from chapter 4. Below are the topics to study:

Review for Final. The final will be about 20% from chapter 2, 30% from chapter 3, and 50% from chapter 4. Below are the topics to study: Review for Final The final will be about 20% from chapter 2, 30% from chapter 3, and 50% from chapter 4. Below are the topics to study: Chapter 2 Find the exact answer to a limit question by using the

More information

Dover-Sherborn High School Mathematics Curriculum Pre-Calculus Level 1/CP

Dover-Sherborn High School Mathematics Curriculum Pre-Calculus Level 1/CP Mathematics Curriculum A. DESCRIPTION This course is an extension of Algebra II with the emphasis in Trigonometry and introductory calculus topics. All major areas covered in Algebra II are reinforced

More information

College Algebra & Trig w Apps

College Algebra & Trig w Apps WTCS Repository 10-804-197 College Algebra & Trig w Apps Course Outcome Summary Course Information Description Total Credits 5.00 This course covers those skills needed for success in Calculus and many

More information

List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015)

List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015) List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT 155 1 Absolute Value Equations P 7 P 3 2 Absolute Value Inequalities P 9 P 4 3 Algebraic Expressions:

More information

Business Calculus

Business Calculus Business Calculus 978-1-63545-025-5 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Senior Contributing Authors: Gilbert

More information

Volusia County Mathematics Curriculum Map. Pre-Calculus. Course Number /IOD

Volusia County Mathematics Curriculum Map. Pre-Calculus. Course Number /IOD Volusia County Mathematics Curriculum Map Pre-Calculus Course Number 1202340/IOD Mathematics Department Volusia County Schools Revised June 9, 2012 Pre- Calculus Curriculum Map 120234/IOD COMPONENTS OF

More information

Cathedral Catholic High School Course Catalog

Cathedral Catholic High School Course Catalog Cathedral Catholic High School Course Catalog Course Title: Pre-Calculus Course Description: This course is designed to prepare students to begin their college studies in introductory Calculus. Students

More information

Pre-calculus 12 Curriculum Outcomes Framework (110 hours)

Pre-calculus 12 Curriculum Outcomes Framework (110 hours) Curriculum Outcomes Framework (110 hours) Trigonometry (T) (35 40 hours) General Curriculum Outcome: Students will be expected to develop trigonometric reasoning. T01 Students will be expected to T01.01

More information

Calculus Early Transcendentals

Calculus Early Transcendentals Calculus Early Transcendentals 978-1-63545-101-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts

More information

Math Prep for Statics

Math Prep for Statics Math Prep for Statics This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

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

Instructional Calendar Accelerated Integrated Precalculus. Chapter 1 Sections and 1.6. Section 1.4. Section 1.5

Instructional Calendar Accelerated Integrated Precalculus. Chapter 1 Sections and 1.6. Section 1.4. Section 1.5 1 st Semester 32. Compare and contrast properties of functions within and across a variety of functions. -Tabular, Graphical, and Algebraic Representations of Functions -Domain and Range of Functions -Increasing,

More information

Burlington County Institute of Technology Curriculum Document

Burlington County Institute of Technology Curriculum Document Burlington County Institute of Technology Curriculum Document Course Title: Calculus Curriculum Area: Mathematics Credits: 5 Credits per course Board Approved: June 2017 Prepared by: Jessica Rista, John

More information

Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007

Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007 Prentice Hall Calculus: Graphical, Numerical, and Algebraic AP* Student Edition 2007 C O R R E L A T E D T O AP Calculus AB Standards I Functions, Graphs, and Limits Analysis of graphs. With the aid of

More information

West Windsor-Plainsboro Regional School District Algebra and Trigonometry Grades 11-12

West Windsor-Plainsboro Regional School District Algebra and Trigonometry Grades 11-12 West Windsor-Plainsboro Regional School District Algebra and Trigonometry Grades 11-12 Unit 1: Linear Relationships & Functions Content Area: Mathematics Course & Grade Level: Algebra & Trigonometry, 11

More information

Calculus Honors Curriculum Guide Dunmore School District Dunmore, PA

Calculus Honors Curriculum Guide Dunmore School District Dunmore, PA Calculus Honors Dunmore School District Dunmore, PA Calculus Honors Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Major topics include: limits, derivatives, integrals. Instruction

More information

Mathematics 6 12 Section 26

Mathematics 6 12 Section 26 Mathematics 6 12 Section 26 1 Knowledge of algebra 1. Identify graphs of linear inequalities on a number line. 2. Identify graphs of linear equations and inequalities in the coordinate plane. 3. Identify

More information

I. Content Standard: Number, Number Sense and Operations Standard

I. Content Standard: Number, Number Sense and Operations Standard Course Description: Honors Precalculus is the study of advanced topics in functions, algebra, geometry, and data analysis including the conceptual underpinnings of Calculus. The course is an in-depth study

More information

MATH 100 and MATH 180 Learning Objectives Session 2010W Term 1 (Sep Dec 2010)

MATH 100 and MATH 180 Learning Objectives Session 2010W Term 1 (Sep Dec 2010) Course Prerequisites MATH 100 and MATH 180 Learning Objectives Session 2010W Term 1 (Sep Dec 2010) As a prerequisite to this course, students are required to have a reasonable mastery of precalculus mathematics

More information

AP Calculus BC. Course Overview. Course Outline and Pacing Guide

AP Calculus BC. Course Overview. Course Outline and Pacing Guide AP Calculus BC Course Overview AP Calculus BC is designed to follow the topic outline in the AP Calculus Course Description provided by the College Board. The primary objective of this course is to provide

More information

Curriculum Scope & Sequence

Curriculum Scope & Sequence Book: Sullivan Pre-Calculus Enhanced with Graphing Utilities Subject/Grade Level: MATHEMATICS/HIGH SCHOOL Curriculum Scope & Sequence Course: PRE-CALCULUS CP/HONORS ***The goals and standards addressed

More information

Topics Covered in Calculus BC

Topics Covered in Calculus BC Topics Covered in Calculus BC Calculus BC Correlation 5 A Functions, Graphs, and Limits 1. Analysis of graphs 2. Limits or functions (including one sides limits) a. An intuitive understanding of the limiting

More information

MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*

MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators* Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships.

More information

Learning Objectives for Math 165

Learning Objectives for Math 165 Learning Objectives for Math 165 Chapter 2 Limits Section 2.1: Average Rate of Change. State the definition of average rate of change Describe what the rate of change does and does not tell us in a given

More information

Pre-Calculus and Trigonometry Capacity Matrix

Pre-Calculus and Trigonometry Capacity Matrix Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational expressions Solve polynomial equations and equations involving rational expressions Review Chapter 1 and their

More information

Advanced Placement Calculus I - What Your Child Will Learn

Advanced Placement Calculus I - What Your Child Will Learn Advanced Placement Calculus I - What Your Child Will Learn I. Functions, Graphs, and Limits A. Analysis of graphs With the aid of technology, graphs of functions are often easy to produce. The emphasis

More information

I can translate between a number line graph, an inequality, and interval notation.

I can translate between a number line graph, an inequality, and interval notation. Unit 1: Absolute Value 2 I can translate between a number line graph, an inequality, and interval notation. 2 2 I can translate between absolute value expressions and English statements about numbers on

More information

Mathematics Precalculus: Academic Unit 1: Polynomial and Transcendental Functions

Mathematics Precalculus: Academic Unit 1: Polynomial and Transcendental Functions Understandings Questions Knowledge Functions can be used as models for real-life problems. Functions can be graphed, evaluated, transformed, analyzed, manipulated and combined using algebraic & graphical

More information

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required. Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;

More information

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT A P C a l c u l u s ( B C ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS Limits and Continuity Derivatives

More information

Advanced Placement Calculus Syllabus- BC

Advanced Placement Calculus Syllabus- BC Advanced Placement Calculus Syllabus- BC Prerequisites All students should have completed four years of secondary mathematics designed for accelerated students. These should consist of the accelerated

More information

Region 16 Board of Education AP Calculus Curriculum 2008

Region 16 Board of Education AP Calculus Curriculum 2008 Region 16 Board of Education AP Calculus Curriculum 2008 Course Description This course develops students understanding of the concepts of calculus and provides experience with its methods and applications.

More information

Saxon Calculus Scope and Sequence

Saxon Calculus Scope and Sequence hmhco.com Saxon Calculus Scope and Sequence Foundations Real Numbers Identify the subsets of the real numbers Identify the order properties of the real numbers Identify the properties of the real number

More information

PHASE 1 CURRICULUM MAP M. Fellmeth Course/Subject: Honors Precalculus Grade: 11 th Teacher: M. Hart

PHASE 1 CURRICULUM MAP M. Fellmeth Course/Subject: Honors Precalculus Grade: 11 th Teacher: M. Hart Month: September 1. How to describe angles using different units of measure and how to find the lengths associated with those angles. 2.3.11 A Select and use appropriate units and tools to measure to the

More information

Mathematics. AP Calculus. New Jersey Quality Single Accountability Continuum (NJQSAC) Course Title. Department:

Mathematics. AP Calculus. New Jersey Quality Single Accountability Continuum (NJQSAC) Course Title. Department: Date: September 1-15 September 16-30 What skills should students possess entering? What are the properties of linear, quadratic, exponential, parametric, and logarithmic equations? What is the difference

More information

STEM-Prep Pathway SLOs

STEM-Prep Pathway SLOs STEM-Prep Pathway SLOs Background: The STEM-Prep subgroup of the MMPT adopts a variation of the student learning outcomes for STEM from the courses Reasoning with Functions I and Reasoning with Functions

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 Summer Prep

AP Calculus Summer Prep AP Calculus Summer Prep Topics from Algebra and Pre-Calculus (Solutions are on the Answer Key on the Last Pages) The purpose of this packet is to give you a review of basic skills. You are asked to have

More information

Advanced Placement Calculus II- What Your Child Will Learn

Advanced Placement Calculus II- What Your Child Will Learn Advanced Placement Calculus II- What Your Child Will Learn Upon completion of AP Calculus II, students will be able to: I. Functions, Graphs, and Limits A. Analysis of graphs With the aid of technology,

More information

Curriculum Catalog

Curriculum Catalog 2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents PRE-CALCULUS COURSE OVERVIEW...1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT

More information

TEACHER CERTIFICATION EXAM 1.0 KNOWLEDGE OF ALGEBRA Identify graphs of linear inequalities on a number line...1

TEACHER CERTIFICATION EXAM 1.0 KNOWLEDGE OF ALGEBRA Identify graphs of linear inequalities on a number line...1 TABLE OF CONTENTS COMPETENCY/SKILL PG # 1.0 KNOWLEDGE OF ALGEBRA...1 1.1. Identify graphs of linear inequalities on a number line...1 1.2. Identify graphs of linear equations and inequalities in the coordinate

More information

*Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P.

*Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P. The Derivative & Tangent Line Problem *Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P. 1 The Derivative & Tangent Line Problem We can approximate using

More information

AP Calculus Curriculum Guide Dunmore School District Dunmore, PA

AP Calculus Curriculum Guide Dunmore School District Dunmore, PA AP Calculus Dunmore School District Dunmore, PA AP Calculus Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Advanced Placement Calculus is the highest level mathematics course offered

More information

Algebra 2 Khan Academy Video Correlations By SpringBoard Activity

Algebra 2 Khan Academy Video Correlations By SpringBoard Activity SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in

More information

Absolute and Local Extrema. Critical Points In the proof of Rolle s Theorem, we actually demonstrated the following

Absolute and Local Extrema. Critical Points In the proof of Rolle s Theorem, we actually demonstrated the following Absolute and Local Extrema Definition 1 (Absolute Maximum). A function f has an absolute maximum at c S if f(x) f(c) x S. We call f(c) the absolute maximum of f on S. Definition 2 (Local Maximum). A function

More information

COURSE: Essentials of Calculus GRADE: 12 PA ACADEMIC STANDARDS FOR MATHEMATICS:

COURSE: Essentials of Calculus GRADE: 12 PA ACADEMIC STANDARDS FOR MATHEMATICS: COURSE: Essentials of Calculus GRADE: 12 UNIT 1: Functions and Graphs TIME FRAME: 18 Days PA ACADEMIC STANDARDS FOR MATHEMATICS: M11.A.1 M11.A.1.1 M11.A.1.1.1 M11.A.1.1.2 M11.A.1.1.3 M11.A.2 M11.A.2.1

More information

Algebra 2 Khan Academy Video Correlations By SpringBoard Activity

Algebra 2 Khan Academy Video Correlations By SpringBoard Activity SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in

More information

Course Syllabus BHS Room 309 (360)

Course Syllabus BHS Room 309 (360) AP Calculus Mrs. Stansbery Course Syllabus BHS Room 309 (360) 473-0875 sandra.stansbery@bremertonschools.org Classroom Expectations 1. Come to class on time and prepared to learn. Take care of locker visits,

More information

I. AP Calculus AB Major Topic: Functions, Graphs, and Limits

I. AP Calculus AB Major Topic: Functions, Graphs, and Limits A.P. Calculus AB Course Description: AP Calculus AB is an extension of advanced mathematical concepts studied in Precalculus. Topics include continuity and limits, composite functions, and graphing. An

More information

Final Exam Study Guide

Final Exam Study Guide Final Exam Study Guide Final Exam Coverage: Sections 10.1-10.2, 10.4-10.5, 10.7, 11.2-11.4, 12.1-12.6, 13.1-13.2, 13.4-13.5, and 14.1 Sections/topics NOT on the exam: Sections 10.3 (Continuity, it definition

More information