HOW TO NOT LOSE POINTS...
|
|
- Daniella Reeves
- 5 years ago
- Views:
Transcription
1 Math Analysis B Final Review
2 GROUP MATERIALS
3 INSTRUCTIONS 1) Ms. Lee picks a student randomly. 2) Selected student chooses a question. 3) Group discusses question and writes FINAL WORK & SOLUTION on whiteboard. 4) When Ms. Lee calls TIME, all groups raise their whiteboards. 5) Groups with the correct answer earn points.
4 HOW TO NOT LOSE POINTS... - Students take turns writing on the whiteboard. After each question, whiteboard must be rotated CLOCKWISE. - Follow instructions! - Ask for hints ONLY when your group absolutely needs one. Hints cost $50. - Don t write/draw anything unnecessary. Don t use the markers on anything other than the whiteboards.
5 JEOPARDY BOARD Exponential Functions Logarithmic Functions Log & Exp Expressions Transform ations Unit Circle $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500
6 Exponential Functions - $100 Repeated addition Repeated multiplication Click to see answer
7 Exponential Functions - $100 Repeated addition multiplication Repeated multiplication power Click to return to Jeopardy Board
8 Exponential Functions - $200 Which equation represents an exponential function? A. f(x) = 2(x-4) + 1 B. h(x) = 2^(x-4) + 1 C. t(x) = (x-4)^2 + 1 D. m(x) = e^(x-4) + 1 Click to see answer
9 Exponential Functions - $200 Which equation represents an exponential function? B. h(x) = 2^(x-4) + 1 D. m(x) = e^(x-4) + 1 Click to return to Jeopardy Board
10 Exponential Functions - $300 Which graph represents an exponential function? A. B. C. D. Click to see answer
11 Exponential Functions - $300 A. Which graph represents an exponential function? Click to return to Jeopardy Board
12 Exponential Functions - $400 Which table represents an exponential function? A. x y B x y - 1 1/ C. x y D. x y Click to see answer
13 Exponential Functions - $400 Which table represents an exponential function? B. x y - 1 1/ C. x y Click to return to Jeopardy Board
14 Exponential Functions - $500 Which of the following does not represent an exponential function? A. n(x) = 5-4^x B. b(x) = 5-4x C. D. x y Click to see answer
15 Exponential Functions - $500 Which of the following does not represent an exponential function? B. r(x) = 5-4x C. Click to return to Jeopardy Board
16 Logarithmic Functions - $100 What is the inverse function of logarithmic functions? Click to see answer
17 Logarithmic Functions - $100 What is the inverse function of logarithmic functions? Exponential functions Click to return to Jeopardy Board
18 Logarithmic Functions - $200 Which equation represents a logarithmic function? A. f(a) = 5 - ln(a+3) B. h(a) = 5 - sin (a+3) C. t(a) = 5 - log(a+3) D. m(a) = 5 - e^(a+3) Click to see answer
19 Logarithmic Functions - $200 Which equation represents a logarithmic function? A. f(a) = 5 - ln(a+3) C. t(a) = 5 - log(a+3) Click to return to Jeopardy Board
20 Logarithmic Functions - $300 Why are common logarithms and natural logarithms important? Click to see answer
21 Logarithmic Functions - $300 Common logs - base of 10 Natural logs - base of e *These are the only logs that are available on the calculator. Click to return to Jeopardy Board
22 Logarithmic Functions - $400 Which graph represents a logarithmic function? A. B. C. D. Click to see answer
23 Logarithmic Functions - $400 B. Which graph represents a logarithmic function? Click to return to Jeopardy Board
24 Logarithmic Functions - $500 Which of the following does not represent a logarithmic function? A. r(x) = -log5 (x+3) B. q(x) = -ln(x+3) C. D. x y Click to see answer
25 Logarithmic Functions - $500 Which of the following does not represent a logarithmic function? D. x y Click to return to Jeopardy Board
26 Log & Exp Expressions - $100 Which are equivalents of ln 1? A. log 1 B. 1 C. 0 D. 10 E. log41 Click to see answer
27 Log & Exp Expressions - $100 Which are equivalents of ln 1? A. log 1 C. 0 E. log41 Click to return to Jeopardy Board
28 Log & Exp Expressions - $200 Simplify each expression. a) ln e 4 b) 7 log Click to see answer
29 Log & Exp Expressions - $200 Simplify each expression. a) ln e = 4 4 log b) 7 = Click to return to Jeopardy Board
30 Log & Exp Expressions - $300 8 Simplify log 10 Click to see answer
31 Log & Exp Expressions - $300 Simplify log /8 Click to return to Jeopardy Board
32 Log & Exp Expressions - $400 When the bases in an exponential equation are the same, you can solve the equation by Click to see answer
33 Log & Exp Expressions - $400 When the bases in an exponential equation are the same, you can solve the equation by Writing a separate equation for the exponents and solving the equation. Click to return to Jeopardy Board
34 Log & Exp Expressions - $500 When the bases in an exponential equation cannot be manipulated to be the same, you can solve the equation by... Click to see answer
35 Log & Exp Expressions - $500 When the bases in an exponential equation cannot be manipulated to be the same, you can solve the equation by... Rewriting the exponential equation as a logarithmic equaiton. Click to return to Jeopardy Board
36 Transformations - $100 How do you identify a translation in an equation? Click to see answer
37 Transformations - $100 How do you identify a translation in an equation? addition/subtraction of a number Click to return to Jeopardy Board
38 Transformations - $200 How do you identify a stretch/shrink in an equation? Click to see answer
39 Transformations - $200 How do you identify a stretch/shrink in an equation? multiplication/division of a number Click to return to Jeopardy Board
40 Transformations - $300 How do you identify a reflection in an equation? Click to see answer
41 Transformations - $300 How do you identify a reflection in an equation? Taking the opposite or Making it negative Click to return to Jeopardy Board
42 Transformations - $400 How do you distinguish a vertical translation/stretch/shrink from a horizontal translation/stretch/shrink? Click to see answer
43 Transformations - $400 How do you distinguish a vertical translation/stretch/shrink from a horizontal translation/stretch/shrink? vertical +/-/ / to whole function horizontal +/-/ / to input only Click to return to Jeopardy Board
44 Transformations - $500 Describe how to transform f (x) = log x to obtain m(x) = -4 - log (3x - ½). Click to see answer
45 Transformations - $500 Describe how to transform f(x) = log x to obtain m(x) = -4 - log (3x - ½). m(x) = -4 - log (3(x - ⅙)) Translate right ⅙ units Horizontally shrink by ⅓ Reflect across the x-axis Translate down 4 units Click to return to Jeopardy Board
46 Trigonometry - $100 What is the unit circle created with a hypotenuse of Click to see answer
47 Trigonometry - $100 The unit circle is created with right triangles with a hypotenuse of 1. The hypotenuses are represented by the radii of the unit circle. Click to return to Jeopardy Board
48 Trigonometry - $200 Identify the quadrant of the terminal side and reference angle of 31 /3. Click to see answer
49 Trigonometry - $200 Identify the quadrant of the terminal side and reference angle of 31 /3. terminal side is in QI reference angle is /3 Click to return to Jeopardy Board
50 Trigonometry - $300 Which of the following trig functions have a domain of all real numbers? Click to see answer
51 Trigonometry - $300 Which of the following trig functions have a domain of all real numbers? SINE & COSINE (sinusoid functions) Click to return to Jeopardy Board
52 Trigonometry - $400 Which key feature does each transformation affect? Transformation V Translation H Translation V Stretch/Shrink H Stretch/Shrink Key Feature Domain Range Zeros Asymptotes Amplitude Period Click to see answer
53 Trigonometry - $400 Which key feature does each transformation affect? Transformation V Translation H Translation V Stretch/Shrink H Stretch/Shrink Key Feature Range, Zeros Domain, Zeros, Asymptotes Range, Amplitude Domain, Zeros, Asymptotes, Period Click to return to Jeopardy Board
54 Trigonometry - $500 Evaluate the following trigonometric values WITHOUT the unit circle. a) sin 3 /2 = -1 b) cos /2 = 0 c) tan /4 = 1 d) cot - /4 = -1 e) sec /2 = undefined Click to see answer
55 Trigonometry - $500 Evaluate the following trigonometric values WITHOUT the unit circle. a) sin /2 b) cos /2 c) tan /4 d) cot - /4 e) sec /2 Click to return to Jeopardy Board
Math 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts
Introduction Math 121: Calculus 1 - Fall 201/2014 Review of Precalculus Concepts Welcome to Math 121 - Calculus 1, Fall 201/2014! This problems in this packet are designed to help you review the topics
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationMath 121: Calculus 1 - Fall 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Fall 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Fall 01/01! This problems in this packet are designed to help you review the topics from Algebra
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
More informationHello Future Calculus Level One Student,
Hello Future Calculus Level One Student, This assignment must be completed and handed in on the first day of class. This assignment will serve as the main review for a test on this material. The test will
More informationAs we know, the three basic trigonometric functions are as follows: Figure 1
Trigonometry Basic Functions As we know, the three basic trigonometric functions are as follows: sin θ = cos θ = opposite hypotenuse adjacent hypotenuse tan θ = opposite adjacent Where θ represents an
More informationMath 121: Calculus 1 - Winter 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Winter 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Winter 01/01! This problems in this packet are designed to help you review the topics from
More informationFind all solutions cos 6. Find all solutions. 7sin 3t Find all solutions on the interval [0, 2 ) sin t 15cos t sin.
7.1 Solving Trigonometric Equations with Identities In this section, we explore the techniques needed to solve more complex trig equations: By Factoring Using the Quadratic Formula Utilizing Trig Identities
More informationWhat students need to know for CALCULUS (Regular, AB and BC) Students expecting to take Calculus should demonstrate the ability to:
What students need to know for CALCULUS (Regular, AB and BC) Students expecting to take Calculus should demonstrate the ability to: General: keep an organized notebook take good notes complete homework
More informationTrigonometric Functions. Section 1.6
Trigonometric Functions Section 1.6 Quick Review Radian Measure The radian measure of the angle ACB at the center of the unit circle equals the length of the arc that ACB cuts from the unit circle. Radian
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More information4 The Trigonometric Functions
Mathematics Learning Centre, University of Sydney 8 The Trigonometric Functions The definitions in the previous section apply to between 0 and, since the angles in a right angle triangle can never be greater
More informationMath 120: Precalculus Autumn 2017 A List of Topics for the Final
Math 120: Precalculus Autumn 2017 A List of Topics for the Final Here s a fairly comprehensive list of things you should be comfortable doing for the final. Really Old Stuff 1. Unit conversion and rates
More informationPre-Calc Trigonometry
Slide 1 / 207 Slide 2 / 207 Pre-Calc Trigonometry 2015-03-24 www.njctl.org Slide 3 / 207 Table of Contents Unit Circle Graphing Law of Sines Law of Cosines Pythagorean Identities Angle Sum/Difference Double
More informationCalculus Summer Math Practice. 1. Find inverse functions Describe in words how you use algebra to determine the inverse function.
1 Calculus 2017-2018: Summer Study Guide Mr. Kevin Braun (kbraun@bdcs.org) Bishop Dunne Catholic School Calculus Summer Math Practice Please see the math department document for instructions on setting
More informationExam Review 2 nd Semester 6-1 Operations on Functions
NAME DATE PERIOD Exam Review 2 nd Semester 6-1 Operations on Functions Find (f + g)(x), (f g)(x), (f g)(x), and (x) for each f(x) and g(x). 1. f(x) = 8x 3; g(x) = 4x + 5 2. f(x) = + x 6; g(x) = x 2 If
More informationA. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.
Algebra - Problem Drill 19: Basic Trigonometry - Right Triangle No. 1 of 10 1. Which of the following points lies on the unit circle? (A) 1, 1 (B) 1, (C) (D) (E), 3, 3, For a point to lie on the unit circle,
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. (a) 5
More informationUniversity Calculus I. Worksheet # 8 Mar b. sin tan e. sin 2 sin 1 5. b. tan. c. sec sin 1 ( x )) cos 1 ( x )) f. csc. c.
MATH 6 WINTER 06 University Calculus I Worksheet # 8 Mar. 06-0 The topic covered by this worksheet is: Derivative of Inverse Functions and the Inverse Trigonometric functions. SamplesolutionstoallproblemswillbeavailableonDL,
More informationAP Calculus AB Summer Preparation
AP Calculus AB Summer Preparation Name Topic #1: GRAPHING CALCULATOR SKILLS All students are required to have a graphing calculator (GC) for use with our course. Our course is taught with the Texas Instrument
More informationWelcome to AP Calculus!!!
Welcome to AP Calculus!!! In preparation for next year, you need to complete this summer packet. This packet reviews & expands upon the concepts you studied in Algebra II and Pre-calculus. Make sure you
More informationNAME: DATE: CLASS: AP CALCULUS AB SUMMER MATH 2018
NAME: DATE: CLASS: AP CALCULUS AB SUMMER MATH 2018 A] Refer to your pre-calculus notebook, the internet, or the sheets/links provided for assistance. B] Do not wait until the last minute to complete this
More information4.3 TRIGONOMETRY EXTENDED: THE CIRCULAR FUNCTIONS
4.3 TRIGONOMETRY EXTENDED: THE CIRCULAR FUNCTIONS MR. FORTIER 1. Trig Functions of Any Angle We now extend the definitions of the six basic trig functions beyond triangles so that we do not have to restrict
More informationPre Calc. Trigonometry.
1 Pre Calc Trigonometry 2015 03 24 www.njctl.org 2 Table of Contents Unit Circle Graphing Law of Sines Law of Cosines Pythagorean Identities Angle Sum/Difference Double Angle Half Angle Power Reducing
More informationAP Calculus Summer Assignment Summer 2017 Expectations for Summer Assignment on the first day of the school year.
Welcome to AP Calculus!!! For you to be successful in the fall when you come back to school you will need to complete this summer homework assignment. This will be worth grades when you get back to class
More informationInstructor: Kaddour Boukaabar Program: CMAP4 Parts A_B_C_D
Student: Date: Instructor: Kaddour Boukaabar Program: CMAP Parts A_B_C_D Assignment: Review For Math Assessment & Placement: Part D 1. Write as an exponential equation. log 100,000 = 10 10 = 100,000 10
More informationSummer Assignment MAT 414: Calculus
Summer Assignment MAT 414: Calculus Calculus - Math 414 Summer Assignment Due first day of school in September Name: 1. If f ( x) = x + 1, g( x) = 3x 5 and h( x) A. f ( a+ ) x+ 1, x 1 = then find: x+ 7,
More informationMATH 32 FALL 2012 FINAL EXAM - PRACTICE EXAM SOLUTIONS
MATH 3 FALL 0 FINAL EXAM - PRACTICE EXAM SOLUTIONS () You cut a slice from a circular pizza (centered at the origin) with radius 6 along radii at angles 4 and 3 with the positive horizontal axis. (a) (3
More informationCourse Outcome Summary
Course Information: Algebra 2 Description: Instruction Level: 10-12 Total Credits: 2.0 Prerequisites: Textbooks: Course Topics for this course include a review of Algebra 1 topics, solving equations, solving
More informationCalculus : Summer Study Guide Mr. Kevin Braun Bishop Dunne Catholic School. Calculus Summer Math Study Guide
1 Calculus 2018-2019: Summer Study Guide Mr. Kevin Braun (kbraun@bdcs.org) Bishop Dunne Catholic School Name: Calculus Summer Math Study Guide After you have practiced the skills on Khan Academy (list
More informationFind: sinθ. Name: Date:
Name: Date: 1. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ c a θ a a =
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationPre-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 informationCK- 12 Algebra II with Trigonometry Concepts 1
1.1 Pythagorean Theorem and its Converse 1. 194. 6. 5 4. c = 10 5. 4 10 6. 6 5 7. Yes 8. No 9. No 10. Yes 11. No 1. No 1 1 1. ( b+ a)( a+ b) ( a + ab+ b ) 1 1 1 14. ab + c ( ab + c ) 15. Students must
More informationLone Star College-CyFair Formula Sheet
Lone Star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a formula sheet or card to tests and instructors MUST
More informationA) 13 B) 9 C) 22 D) log 9
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. Participation in our review session will count as a quiz grade. Please bring any questions you have ready to ask!
More informationPRE-CALCULUS General Specific Math Skills
PRE-CALCULUS Welcome to Pre-Calculus! Pre-Calculus will be challenging but rewarding!! This full year course requires that everyone work hard and study for the entirety of the class. You will need a large
More informationAP Calculus Summer Assignment Summer 2017 Expectations for Summer Assignment on the first day of the school year.
Summer 07 Expectations for Summer Assignment This packet is to be submitted to your Calculus BC teacher on the first day of the school year. All work must be shown in the packet OR on separate paper attached
More informationChapter 2. First-Order Differential Equations
Chapter 2 First-Order Differential Equations i Let M(x, y) + N(x, y) = 0 Some equations can be written in the form A(x) + B(y) = 0 DEFINITION 2.2. (Separable Equation) A first-order differential equation
More informationSummer Review for Students Entering AP Calculus AB
Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation
More informationMath 370 Exam 2 Review Name
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. 10 of these questions will count as a quiz in Learning Catalytics. Round 1 will be individual. Round 2 will be in
More informationCoach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers
Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers CLASSIFICATIONS OF NUMBERS NATURAL NUMBERS = N = {1,2,3,4,...}
More informationInformation Page. Desmos Graphing Calculator IXL Username: Password: gothunder
i Information Page Class Website: http://padlet.com/william_kaden/algebra2stem Has PDFs of assignments. Additionally they can sometimes be found on Skyward. Desmos Graphing Calculator http://www.desmos.com/
More informationTopics from Algebra and Pre-Calculus. (Key contains solved problems)
Topics from Algebra and Pre-Calculus (Key contains solved problems) Note: The purpose of this packet is to give you a review of basic skills. You are asked not to use the calculator, except on p. (8) and
More informationSET 1. (1) Solve for x: (a) e 2x = 5 3x
() Solve for x: (a) e x = 5 3x SET We take natural log on both sides: ln(e x ) = ln(5 3x ) x = 3 x ln(5) Now we take log base on both sides: log ( x ) = log (3 x ln 5) x = log (3 x ) + log (ln(5)) x x
More informationUsing this definition, it is possible to define an angle of any (positive or negative) measurement by recognizing how its terminal side is obtained.
Angle in Standard Position With the Cartesian plane, we define an angle in Standard Position if it has its vertex on the origin and one of its sides ( called the initial side ) is always on the positive
More information1. OBJECTIVE: Linear Equations
CUNY YORK COLLEGE FINAL EXAM REVIEW MATH 120: Precalculus Use the following questions to review for your final examimation for Math 120. Your ability to answer these questions will reflect what you learned
More informationREVIEW: MORE FUNCTIONS AP CALCULUS :: MR. VELAZQUEZ
REVIEW: MORE FUNCTIONS AP CALCULUS :: MR. VELAZQUEZ INVERSE FUNCTIONS Two functions are inverses if they undo each other. In other words, composing one function in the other will result in simply x (the
More informationSummer Work Packet for MPH Math Classes
Summer Work Packet for MPH Math Classes Students going into AP Calculus AB Sept. 018 Name: This packet is designed to help students stay current with their math skills. Each math class expects a certain
More informationsin cos 1 1 tan sec 1 cot csc Pre-Calculus Mathematics Trigonometric Identities and Equations
Pre-Calculus Mathematics 12 6.1 Trigonometric Identities and Equations Goal: 1. Identify the Fundamental Trigonometric Identities 2. Simplify a Trigonometric Expression 3. Determine the restrictions on
More informationSection 6.2 Notes Page Trigonometric Functions; Unit Circle Approach
Section Notes Page Trigonometric Functions; Unit Circle Approach A unit circle is a circle centered at the origin with a radius of Its equation is x y = as shown in the drawing below Here the letter t
More informationCHAPTERS 5-7 TRIG. FORMULAS PACKET
CHAPTERS 5-7 TRIG. FORMULAS PACKET PRE-CALCULUS SECTION 5-2 IDENTITIES Reciprocal Identities sin x = ( 1 / csc x ) csc x = ( 1 / sin x ) cos x = ( 1 / sec x ) sec x = ( 1 / cos x ) tan x = ( 1 / cot x
More informationChapter 8B - Trigonometric Functions (the first part)
Fry Texas A&M University! Spring 2016! Math 150 Notes! Section 8B-I! Page 79 Chapter 8B - Trigonometric Functions (the first part) Recall from geometry that if 2 corresponding triangles have 2 angles of
More informationDuVal High School Summer Review Packet AP Calculus
DuVal High School Summer Review Packet AP Calculus Welcome to AP Calculus AB. This packet contains background skills you need to know for your AP Calculus. My suggestion is, you read the information and
More informationSkill 6 Exponential and Logarithmic Functions
Skill 6 Exponential and Logarithmic Functions Skill 6a: Graphs of Exponential Functions Skill 6b: Solving Exponential Equations (not requiring logarithms) Skill 6c: Definition of Logarithms Skill 6d: Graphs
More informationSkill 6 Exponential and Logarithmic Functions
Skill 6 Exponential and Logarithmic Functions Skill 6a: Graphs of Exponential Functions Skill 6b: Solving Exponential Equations (not requiring logarithms) Skill 6c: Definition of Logarithms Skill 6d: Graphs
More informationAlgebra 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 informationAlgebra 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 informationCALCULUS ASSESSMENT REVIEW
CALCULUS ASSESSMENT REVIEW DEPARTMENT OF MATHEMATICS CHRISTOPHER NEWPORT UNIVERSITY 1. Introduction and Topics The purpose of these notes is to give an idea of what to expect on the Calculus Readiness
More informationAP Calculus Summer Packet
AP Calculus Summer Packet Going into AP Calculus, there are certain skills that have been taught to you over the previous tears that we assume you have. If you do not have these skills, you will find that
More informationPrecalculus Review. Functions to KNOW! 1. Polynomial Functions. Types: General form Generic Graph and unique properties. Constants. Linear.
Precalculus Review Functions to KNOW! 1. Polynomial Functions Types: General form Generic Graph and unique properties Constants Linear Quadratic Cubic Generalizations for Polynomial Functions - The domain
More information2. Algebraic functions, power functions, exponential functions, trig functions
Math, Prep: Familiar Functions (.,.,.5, Appendix D) Name: Names of collaborators: Main Points to Review:. Functions, models, graphs, tables, domain and range. Algebraic functions, power functions, exponential
More informationfunction independent dependent domain range graph of the function The Vertical Line Test
Functions A quantity y is a function of another quantity x if there is some rule (an algebraic equation, a graph, a table, or as an English description) by which a unique value is assigned to y by a corresponding
More informationCalculus. Weijiu Liu. Department of Mathematics University of Central Arkansas 201 Donaghey Avenue, Conway, AR 72035, USA
Calculus Weijiu Liu Department of Mathematics University of Central Arkansas 201 Donaghey Avenue, Conway, AR 72035, USA 1 Opening Welcome to your Calculus I class! My name is Weijiu Liu. I will guide you
More informationComposition of Functions
Math 120 Intermediate Algebra Sec 9.1: Composite and Inverse Functions Composition of Functions The composite function f g, the composition of f and g, is defined as (f g)(x) = f(g(x)). Recall that a function
More informationFunctions and their Graphs
Chapter One Due Monday, December 12 Functions and their Graphs Functions Domain and Range Composition and Inverses Calculator Input and Output Transformations Quadratics Functions A function yields a specific
More informationSummer 2017 Review For Students Entering AP Calculus AB/BC
Summer 2017 Review For Students Entering AP Calculus AB/BC Holy Name High School AP Calculus Summer Homework 1 A.M.D.G. AP Calculus AB Summer Review Packet Holy Name High School Welcome to AP Calculus
More informationSummer Work for Students Entering Calculus
For the problems sets which start on page 6 write out all solutions clearly on a separate sheet of paper. Show all steps and circle your answer. The following are examples of different types of problems.
More informationGiven an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r :
Given an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r : To convert from radians (rad) to degrees ( ) and vice versa, use the
More informationPractice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.
More information2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2
29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with
More information2.1 Limits, Rates of Change and Slopes of Tangent Lines
2.1 Limits, Rates of Change and Slopes of Tangent Lines (1) Average rate of change of y f x over an interval x 0,x 1 : f x 1 f x 0 x 1 x 0 Instantaneous rate of change of f x at x x 0 : f x lim 1 f x 0
More informationUnit Circle. Return to. Contents
Unit Circle Return to Table of Contents 32 The Unit Circle The circle x 2 + y 2 = 1, with center (0,0) and radius 1, is called the unit circle. Quadrant II: x is negative and y is positive (0,1) 1 Quadrant
More informationThe above statement is the false product rule! The correct product rule gives g (x) = 3x 4 cos x+ 12x 3 sin x. for all angles θ.
Math 7A Practice Midterm III Solutions Ch. 6-8 (Ebersole,.7-.4 (Stewart DISCLAIMER. This collection of practice problems is not guaranteed to be identical, in length or content, to the actual exam. You
More informationMath 105 Exit Exam Review
Math 105 Exit Exam Review The review below refers to sections in the main textbook Modeling the Dynamics of Life, 2 nd edition by Frederick F. Adler. (This will also be the textbook for the subsequent
More informationSANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET
SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET 017-018 Name: 1. This packet is to be handed in on Monday August 8, 017.. All work must be shown on separate paper attached to the packet. 3.
More informationCHAPTER 6. Section Two angles are supplementary. 2. Two angles are complementary if the sum of their measures is 90 radians
SECTION 6-5 CHAPTER 6 Section 6. Two angles are complementary if the sum of their measures is 90 radians. Two angles are supplementary if the sum of their measures is 80 ( radians).. A central angle of
More informationPRE-CALCULUS FORM IV. Textbook: Precalculus with Limits, A Graphing Approach. 4 th Edition, 2005, Larson, Hostetler & Edwards, Cengage Learning.
PRE-CALCULUS FORM IV Tetbook: Precalculus with Limits, A Graphing Approach. 4 th Edition, 2005, Larson, Hostetler & Edwards, Cengage Learning. Course Description: This course is designed to prepare students
More informationSemester 2 Final Exam Study Guide
Unit 4 Identify the following for each function: domain, range, x-intercept, y-intercept, and asymptote. Then graph the function. f(x) = log 2 x 2. f(x) = log(x). f(x) = log 2 (x 1) Identify the following
More informationTrigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry Copyright Cengage Learning. All rights reserved. What You Should Learn Evaluate trigonometric
More information1! i 3$ (( )( x! 1+ i 3)
Math 4C Fall 2008 Final Exam (Name) (PID) (Section) Read each question carefully; answer each question completely. Show all work: no credit for unsupported answers. Attach additional sheets if necessary.
More informationIntegration by Triangle Substitutions
Integration by Triangle Substitutions The Area of a Circle So far we have used the technique of u-substitution (ie, reversing the chain rule) and integration by parts (reversing the product rule) to etend
More informationA Library of Functions
LibraryofFunctions.nb 1 A Library of Functions Any study of calculus must start with the study of functions. Functions are fundamental to mathematics. In its everyday use the word function conveys to us
More informationTrigonometry Learning Strategies. What should students be able to do within this interactive?
Trigonometry Learning Strategies What should students be able to do within this interactive? Identify a right triangle. Identify the acute reference angles. Recognize and name the sides, and hypotenuse
More informationStudy Guide for Benchmark #1 Window of Opportunity: March 4-11
Study Guide for Benchmark #1 Window of Opportunity: March -11 Benchmark testing is the department s way of assuring that students have achieved minimum levels of computational skill. While partial credit
More informationWhat students need to know for BC CALCULUS
What students need to know for BC CALCULUS 018-019 NAME: This is a MANDATORY assignment that will be GRADED. It is due the first day of the course. Your teacher will determine how it will be counted (i.e.
More informationHonors Algebra 2 Chapter 14 Page 1
Section. (Introduction) Graphs of Trig Functions Objectives:. To graph basic trig functions using t-bar method. A. Sine and Cosecant. y = sinθ y y y y 0 --- --- 80 --- --- 30 0 0 300 5 35 5 35 60 50 0
More informationFUNCTIONS AND MODELS
1 FUNCTIONS AND MODELS FUNCTIONS AND MODELS 1.6 Inverse Functions and Logarithms In this section, we will learn about: Inverse functions and logarithms. INVERSE FUNCTIONS The table gives data from an experiment
More informationAP Calculus AB Summer Assignment 2016
AP Calculus AB Name Dates: Start Finish AP Calculus AB Summer Assignment 016 Welcome to AP Calculus AB. This packet is a review of Advanced Algebra & Pre-Calculus topics that you will use continuously
More informationTRIGONOMETRIC RATIOS AND GRAPHS
Mathematics Revision Guides Trigonometric Ratios and Graphs Page 1 of 15 M.K. HOME TUITION Mathematics Revision Guides Level: AS / A Level AQA : C2 Edexcel: C2 OCR: C2 OCR MEI: C2 TRIGONOMETRIC RATIOS
More information1. Trigonometry.notebook. September 29, Trigonometry. hypotenuse opposite. Recall: adjacent
Trigonometry Recall: hypotenuse opposite adjacent 1 There are 3 other ratios: the reciprocals of sine, cosine and tangent. Secant: Cosecant: (cosec θ) Cotangent: 2 Example: Determine the value of x. a)
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More informationSection Inverse Trigonometry. In this section, we will define inverse since, cosine and tangent functions. x is NOT one-to-one.
Section 5.4 - Inverse Trigonometry In this section, we will define inverse since, cosine and tangent functions. RECALL Facts about inverse functions: A function f ) is one-to-one if no two different inputs
More information5 Trigonometric Functions
5 Trigonometric Functions 5.1 The Unit Circle Definition 5.1 The unit circle is the circle of radius 1 centered at the origin in the xyplane: x + y = 1 Example: The point P Terminal Points (, 6 ) is on
More information12) y = -2 sin 1 2 x - 2
Review -Test 1 - Unit 1 and - Math 41 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find and simplify the difference quotient f(x + h) - f(x),
More informationThe Other Trigonometric
The Other Trigonometric Functions By: OpenStaxCollege A wheelchair ramp that meets the standards of the Americans with Disabilities Act must make an angle with the ground whose tangent is or less, regardless
More informationObjectives 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 informationThe six trigonometric functions
PRE-CALCULUS: by Finney,Demana,Watts and Kennedy Chapter 4: Trigonomic Functions 4.: Trigonomic Functions of Acute Angles What you'll Learn About Right Triangle Trigonometry/ Two Famous Triangles Evaluating
More informationChetek-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