Final Exam: Precalculus
|
|
|
- Grant Page
- 5 years ago
- Views:
Transcription
1 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: What is the angle in degrees? What is the angle in radians? 2. Evaluate / simplify each expression: a. b. Version B 1. Consider the unit circle: a. Angle in degrees: What is the angle in radians? What are the coordinates? b. Coordinates: What is the angle in degrees? What is the angle in radians?
2 2. Evaluate / simplify each expression: a. b. Regular Problems Version A 3. Graph the function. Show at least two complete cycles. 4. Solve the equation : CORRECTION: a. using the co sine inverse function (calculator answer) b. for or
3 c. for all where or is any integer 5. Simplify this rational expression: 6. Simplify and state the excluded values:
4 7. Make a table and graph for the function. Bonus: What is the inverse of this function? Answer with table, graph, and equation. 8. Simplify and rewrite this logarithmic expression more than one way: Note: Simply writing a calculator answer is not enough.
5 9. Evaluate / simplify each logarithm expression. Justify your answer by rewriting the equation into exponential form. a. because b. because 10. Solve for : 11. If, show that.
6 Version B Regular Problems 2. Graph the function. Show at least two complete cycles. 3. Solve the equation : CORRECTION: a. using the cosine inverse function (calculator answer) b. for or c. for all where or is any integer
7 4. Simplify this rational expression: 5. Simplify and state the excluded values:
8 6. Make a table and graph for the function. Bonus: What is the inverse of this function? Answer with table, graph, and equation. 7. Simplify and rewrite this logarithmic expression more than one way: Note: Simply writing a calculator answer is not enough.
9 8. Evaluate / simplify each logarithm expression. Justify your answer by rewriting the equation into exponential form. a. because b. because 9. Solve for : 10. If, show that. Conceptual Questions Note: The numbering here follows Version A which is the correct numbering. 12. Explain the meaning and purpose of each of the following concepts in your own words: a. the unit circle The unit circle is a tool to help us remember the trigonometric ratios and evaluate trig functions for all the special angles related to the and triangles. It is called the unit circle because the radius of the circle (the hypotenuse of each triangle) is one.
10 b. factors / factoring Factors are the numbers that multiply to make another number (the product). Factoring is the procedure of breaking up a product into its factors. In algebra, factoring is important for simplifying rational expressions as well as solving certain polynomial equations. c. excluded value An excluded value is a certain number (value) that a variable cannot assume because it would make the overall expression undefined. It is important to state excluded values when cancelling a variable factor out of a denominator since dividing by zero is undefined. d. logarithm A logarithm is the exponent needed on a given base in order to make the given result. A logarithmic function and exponential function of the same base are inverse to each other. 13. Each of the following contains a mistake. Describe the error. a. Graphing : All the transformations are correct, but the graph is showing the sine function, which starts in the middle, rather than the cosine function, which starts at the top. b. Simplifying a rational expression: The error is cancelling out the when it is being added, not multiplied. You can only use division to cancel multiplication, not addition. c. Simplifying a logarithmic expression: To use the properties of logarithms such as the quotient property, the base of the logarithms must be equal.
GREENWOOD 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
PRECALCULUS 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
Curriculum 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
CURRICULUM MAP. Course / Subject: Precalculus Grade: 11/12 Teacher: Kelly, Kirk, McCollick, Palkovics, Roderick Month: September (19 days)
Month: September (19 days) - Change from radian to degree measure, & vice versa - Find angles that are coterminal with a given angle - Find reference angle for a given angle Angles & Their Measure (Section
AP 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
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 Factor each expression. 2. y 3 y 3 y 6 x 4 4. y 2 1 y 5 y 3 5.
Multiplying and Dividing Rational Expressions
Page 1 of 14 Multiplying and Dividing Rational Expressions Attendance Problems. Simplify each expression. Assume all variables are nonzero. x 6 y 2 1. x 5 x 2 2. y 3 y 3 3. 4. x 2 y 5 Factor each expression.
Math 083 Final Exam Practice
Math 083 Final Exam Practice Name: 1. Simplify the expression. Remember, negative exponents give reciprocals.. Combine the expressions. 3. Write the expression in simplified form. (Assume the variables
(Type your answer in radians. Round to the nearest hundredth as needed.)
1. Find the exact value of the following expression within the interval (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Type N
Algebra 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.
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
PRESCOTT 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
Warm Up Simplify each expression. Assume all variables are nonzero.
Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 x 4 Factor each expression. 2. y 3 y 3 y 6 4. y 2 1 y 5 y 3 5. x 2 2x 8 (x 4)(x + 2) 6. x 2 5x x(x 5) 7. x
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 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
Working 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.
You 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
b) 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
Choose the correct answer below. 2. Convert the angle to a decimal in degrees.
1. Choose the figure that shows an angle of in standard position. Choose the correct answer below. 2. Convert the angle to a decimal in degrees. (Do not round until the final answer. Then round to two
Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using
Ch 13 - RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using trigonometric
Mathematics NC Math 3 Scope and Sequence 176 Instructional Days (Traditional) 88 Instructional Days (Block) 9 Units
Mathematics NC Math 3 Scope and Sequence 176 Instructional () 88 Instructional () 9 Units Unit 1: Functions and Their Inverses NC.M3.F-BF.4a Understand the inverse relationship between exponential and
AP 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
Montana Instructional Alignment HPS Critical Competencies Mathematics Honors Pre-Calculus
Content Standards Content Standard 1 - Number Sense and Operations Content Standard 2 - Data Analysis A student, applying reasoning and problem solving, will use number sense and operations to represent
Amphitheater 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
Trigonometry 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
2.2 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
Mastery. 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,
Algebra II Chapter 6: Rational Exponents and Radical Functions
Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions
Mathematics 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
Chapter 0: Algebra II Review
Chapter 0: Algebra II Review Topic 1: Simplifying Polynomials & Exponential Expressions p. 2 - Homework: Worksheet Topic 2: Radical Expressions p. 32 - Homework: p. 45 #33-74 Even Topic 3: Factoring All
AP 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
Welcome. 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
(-,+) (+,+) Plotting Points
Algebra Basics +y (-,+) (+,+) -x +x (-,-) (+,-) Plotting Points -y Commutative Property of Addition/Multiplication * You can commute or move the terms * This only applies to addition and multiplication
Pre-Algebra to Pre-Calculus
Pre-Algebra to Pre-Calculus 11,000 free-response questions for middle and high school math This document shows the table of contents and number of questions in EducAide s database module called Pre-Alg
1. 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
Integrated 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
Section 7.5 Inverse Trigonometric Functions II
Section 7.5 Inverse Trigonometric Functions II Note: A calculator is helpful on some exercises. Bring one to class for this lecture. OBJECTIVE 1: Evaluating composite Functions involving Inverse Trigonometric
Unit 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
Mathematics. Smyth County Schools Curriculum Map Grade:11-12 Subject:Math Analysis MA.1, MA.6, MA.8, MA.9 MA.1, MA.2, MA.3.
MA.1, MA.2, MA.3 Grade:11-12 Subject:Math Analysis 1st Quarter 2nd Quarter MA.1, MA.6, MA.8, MA.9 Standards Content Functions: Polynomial, linear, Radical, Rational, Irrational, One to One, Continuous
Limits. 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()
Voluntary State Curriculum Algebra II
Algebra II Goal 1: Integration into Broader Knowledge The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.
CW 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
by Kevin M. Chevalier
Precalculus Review Handout.4 Trigonometric Functions: Identities, Graphs, and Equations, Part I by Kevin M. Chevalier Angles, Degree and Radian Measures An angle is composed of: an initial ray (side) -
5.2 Verifying Trigonometric Identities
360 Chapter 5 Analytic Trigonometry 5. Verifying Trigonometric Identities Introduction In this section, you will study techniques for verifying trigonometric identities. In the next section, you will study
Circular Trigonometry Notes April 24/25
Circular Trigonometry Notes April 24/25 First, let s review a little right triangle trigonometry: Imagine a right triangle with one side on the x-axis and one vertex at (0,0). We can write the sin(θ) and
: Find the values of the six trigonometric functions for θ. Special Right Triangles:
ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using
Look 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
Unit 2 Intro to Angles and Trigonometry
HARTFIELD PRECALCULUS UNIT 2 NOTES PAGE 1 Unit 2 Intro to Angles and Trigonometry This is a BASIC CALCULATORS ONLY unit. (2) Definition of an Angle (3) Angle Measurements & Notation (4) Conversions of
This unit is built upon your knowledge and understanding of the right triangle trigonometric ratios. A memory aid that is often used was SOHCAHTOA.
Angular Rotations This unit is built upon your knowledge and understanding of the right triangle trigonometric ratios. A memory aid that is often used was SOHCAHTOA. sin x = opposite hypotenuse cosx =
A-C Valley Junior-Senior High School
Course of Study A-C Valley Junior-Senior High School Page 1 of 12 Applied Trigonometry (NAME OF COURSE) GRADE LEVEL(S): 11 Educational Curriculum Level Person(s) Revising Curriculum (List Names) 1. Junior-Senior
Math 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
Section 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b.
Section 2.3 Rational Numbers A rational number is a number that may be written in the form a b for any integer a and any nonzero integer b. Why is division by zero undefined? For example, we know that
ALGEBRA 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
Graphing 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
Ganado 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
Trigonometry To learn more about all our offerings Visit Knewton.com
Trigonometry 978-1-63545-099-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Jay Abramson, Arizona State University
College Technical Math 2
WTCS Repository 10-804-116 College Technical Math 2 Course Outcome Summary Course Information Description Topics include: vectors; trigonometric functions and their graphs; identities; exponential and
Ganado 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
Triangle Trigonometry
Honors Finite/Brief: Trigonometry review notes packet Triangle Trigonometry Right Triangles All triangles (including non-right triangles) Law of Sines: a b c sin A sin B sin C Law of Cosines: a b c bccos
AP 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
Math 144 Activity #3 Coterminal Angles and Reference Angles
144 p 1 Math 144 Activity #3 Coterminal Angles and Reference Angles For this activity we will be referring to the unit circle. Using the unit circle below, explain how you can find the sine of any given
Ganado 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
Rules of Exponents Part 1[Algebra 1](In Class Version).notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION.
.notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION.](/thumbs/95/124127108.jpg "Rules of Exponents Part 1[Algebra 1](In Class Version).notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION.")
WARM UP Simplify using order of operations. Aug 22 3:22 PM 1 Aug 22 4:09 PM 2 WARM UP a) The equation 3(4x) = (4x)3 illustrates which property? b) Which property of real numbers is illustrated by the equation
Honors 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
Using 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
College Technical Mathematics 1
Lakeshore Technical College 10-804-115 College Technical Mathematics 1 Course Outcome Summary Course Information Alternate Title College Technical Math 1 Description Total Credits 5 Total Hours 108...prepares
RELEASED. NC Final Exam. NC Math 3. Released Items. Student Name:
Released Items Student Name: N Math 017 018 Public Schools of North arolina State oard of Education epartment of Public Instruction Raleigh, North arolina 7699-614 N Final Exam opyright 017 by the North
Willmar Public Schools Curriculum Map
Subject Area Mathematics Senior High Course Name Advanced Algebra 2B Date June 2010 Advanced Algebra 2B and Algebra 2B courses parallel each other in content and time. The Advanced Algebra 2B class is
Summer 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
Grade 6 Math Curriculum Sequence School Year
Grade 6 Math Curriculum Sequence School Year 2010-2011 QUARTER 1 (Aug 30 Nov 5) 45 days BENCHMARK A (same skills as June Benchmark in previous grade) UNIT 1: Fractions 1 Review Add and Subtract Fractions
Dover-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
Section 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.
Summer Assignment Glossary
Algebra 1.1 Summer Assignment Name: Date: Hour: Directions: Show all work for full credit using a pencil. Circle your final answer. This assignment is due the first day of school. Use the summer assignment
Pre-Calculus Advanced. Chapter 10 Part 2. Period 8
Pre-Calculus Advanced Chapter 10 Part 2 Period 8 Date Topic of Discussion Assignment Stamp Monday, 4/9 Tuesday, 4/10 Wed 4/11 ½ Day Thu 4/12 Fri 4/13 10.4 Hyperbolas SAT More 10.4 Hyperbolas 10.5 General
CW Middle School. Math RtI 7 A. 4 Pro cient I can add and subtract positive fractions with unlike denominators and simplify the result.
1. Foundations (14.29%) 1.1 I can add and subtract positive fractions with unlike denominators and simplify the result. 4 Pro cient I can add and subtract positive fractions with unlike denominators and
SNAP 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
Introduction to Applied and Pre-calculus Mathematics (2008) Correlation Chart - Grade 10 Introduction to Applied and Pre-Calculus Mathematics 2009
Use words and algebraic expressions to describe the data and interrelationships in a table with rows/columns that are not related recursively (not calculated from previous data) (Applied A-1) Use words
Unit Circle. Project Response Sheet
NAME: PROJECT ACTIVITY: Trigonometry TOPIC Unit Circle GOALS MATERIALS Explore Degree and Radian Measure Explore x- and y- coordinates on the Unit Circle Investigate Odd and Even functions Investigate
HOSTOS 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
Chapter 9: Right Triangle Trigonometry
Haberman MTH 11 Section I: The Trigonometric Functions Chapter 9: Right Triangle Trigonometry As we studied in Intro to the Trigonometric Functions: Part 1, if we put the same angle in the center of two
Rational Functions. By: Kaushik Sriram, Roshan Kuntamukkala, and Sheshanth Vijayakumar
Rational Functions By: Kaushik Sriram, Roshan Kuntamukkala, and Sheshanth Vijayakumar What are Rational Functions? Dictionary Definition: In mathematics, a rational function is any function which can be
Algebra II Chapter 8 Part 2: Rational Functions
Algebra II Chapter 8 Part 2: Rational Functions Chapter 8 Lesson 4 Multiply and Divide Rational Functions Vocabulary Words to Review: Reciprocal The rules of fractions DO NOT change! *When adding and subtracting,
Приложение 34 к приказу 949 от 29 сентября 2017 г. MOSCOW AVIATION INSTITUTE (NATIONAL RESEARCH UNIVERSITY)
Приложение 34 к приказу 949 от 29 сентября 2017 г. MOSCOW AVIATION INSTITUTE (NATIONAL RESEARCH UNIVERSITY) The Program for Entrance Exam in Mathematics MAI 2018 The first section lists the basic mathematical
A Planned Course Statement for. Trigonometry, CP. Course # 317 Grade(s) 12. Length of Period (mins.) 42 Total Clock Hours: 63
East Penn School District Secondary Curriculum A Planned Course Statement for Trigonometry, CP Course # 317 Grade(s) 12 Department: Mathematics ength of Period (mins.) 42 Total Clock Hours: 63 Periods
SUM 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
Math 144 Activity #4 Connecting the unit circle to the graphs of the trig functions
144 p 1 Math 144 Activity #4 Connecting the unit circle to the graphs of the trig functions Graphing the sine function We are going to begin this activity with graphing the sine function ( y = sin x).
The 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
Section 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.
TABLE 2: Mathematics College Readiness Standards for Score Range 13 15
TABLE 2: Mathematics College Readiness Standards for Score Range 13 15 Perform one-operation computation with whole numbers and decimals Solve problems in one or two steps using whole numbers Perform common
Pre-Calculus Summer Assignment
Pre-Calculus Summer Assignment Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q. 1. 2. Find a quadratic model for the set of values. 3. x 2 0 4 f(x)
1.6 Applying Trig Functions to Angles of Rotation
wwwck1org Chapter 1 Right Triangles and an Introduction to Trigonometry 16 Applying Trig Functions to Angles of Rotation Learning Objectives Find the values of the six trigonometric functions for angles
Design of the Power Standard Document
Design of the Power Standard Document There are five content strands in Mathematics: o Number, Operations, Algebra, Geometry/Measurement, Data/Statistics/Probability Power Standards were not identified
Summer 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
to 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
MAT 1033C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade)
MAT 0C -- Intermediate Algebra -- Lial Chapter 8 -- Roots and Radicals Practice for the Exam (Kincade) Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
Prentice Hall CME Project, Geometry 2009
Prentice Hall C O R R E L A T E D T O Draft for High School Math Math High School Math N.BC.1 Operate and solve problems involving rational exponents. N.BC.1.a Translate between writing numbers with rational
Pre-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.
Unit 7 Solving Right triangles math 2.notebook April 17, 2018
Warm Up Calculate the value of. Unit 7 Learning Intention: Given a right triangle, students will be able to write and use trigonometric ratios to solve right triangles. Success Criteria: 1. I will be able
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express
Verifying Trigonometric Identities
Verifying Trigonometric Identities What you should learn Verify trigonometric identities. Why you should learn it You can use trigonometric identities to rewrite trigonometric equations that model real-life
Name: 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