UNLV University of Nevada, Las Vegas
|
|
- Kathryn Ellis
- 6 years ago
- Views:
Transcription
1 UNLV University of Nevada, Las Vegas The Department of Mathematical Sciences Information Regarding Math 16 Final Eam Revised While all material covered in the syllabus is essential for success in the course, the following material will be stressed in the final eam for Math 16. Chapter/Section taken from the class tet: Precalculus (custom edition) by Stewart. Online Section Homework 1.1 6, 1,, 6, 8, 30, 38, 44, 56, 64, 74, 75, , 3, 33, 40, 50, 58, 68, 76, 8, 98, ,, 4, 3, 48, 54, 70, 7, 74, 78, 86, 94, 114, 1, , 8, 10, 14, 0, 30 36, 56, 60, 70, 80, 86, 88, 9 Eample Problem for Final Eam 1 1 (a) = (b) (c) and 330 (a) (b) 3 79 (c) Find if ,800,000,000,000 (d) Find if (3.10 )( ) (e) 4 (.410 ) (f) if a (g) a (a) Factor the following polynomial: (b) Factor the following polynomial: b 1 (a) (b) (also section.4) Let f ( ). The difference quotient for the f (3 h) f (3) 6 h 6 given function at = 3 is Qh ( ) for h h nonzero h. Rationalize the numerator of Q(h) and simplify the resulting epression. Evaluate the simplified epression at h = 0.
2 1.5 6, 36, 48, 60, 7, 86, 96, 110, 114, , 6, 30, 34, 38, 44, 5, 58, 64, , 34, 44, 50, 60, 6, 68, 88, 90, 101, 106, 111, ,, 8, 3, 34, 4, 46, 66, 94, 100, , 14, 16, 0, 4, 6, 8, 30, 3, 38, 56, 7, , 1, 0,, 30, 34, 36, 40, 44, 46, 48, 58, 6, 71, 76 (a) Solve the equation for. (b) Solve the following equation in the variable by factoring (c) (similar to problem #116) A large pond is stocked with fish. The fish population P(t) is modeled by the parabolic equation P( t) t 3t 58, where is the number of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 16? Give reasoning for the two answers. How many days will it take for the fish population to reach the minimum population? What is the minimum population? Show, also all the above answers by graphing the associated parabola modeling the fish population. (a) Find the value of from the following given proportional equations: 30 6 (similar to problem #5) y 80 y 35 y (b) (similar to problem #63) Betty and Karen have been hired to paint the houses in a new development. Working together the women can paint a house in two-thirds the time it takes Karen working alone. Betty takes 6 hours to paint a house alone. How long does it take Karen to paint a house working alone? (a) (eample #9 in tet) The relationship between the two temperature scales Celsius(C) and Fahrenheit(F) is given by the equation 9 F C 3. Find the range of temperatures in Fahrenheit scale if 5 the range of temperatures in the Celsius scale is given by 10 C 0. (similar to eample #9) (b) Solve the following inequality in the variable and write your answer 4 for the solution set using the interval notation: 0 or (a) Given that the tangent line to a circle is perpendicular to the adjoining radius at the point of contact, find the equation of the tangent line to the circle ( 1) ( y ) 5 at the point (4, )
3 . 6, 10, 1,, 4, 8, 40, 46, 50, 5, 54, 56, 58, 60, 6, 66, 81, , 8, 0, 8, 34, , 10, 1, 18,, 6, , 8, 10, 6, 44, 54, 60, 76, 78, 8, , 8, 10, 1, 14,, 4, 34, 36, 40, 44, 46, 5, , 14, 0,, 8, 34, 38, 44, 54, 8, 88 Modeling 8, 10, 18, 4, 30 with Functions , 18, 0, 40, 4, 44, 46, 64, 66, 77 (a) (also section 1.4) Let f ( ) 5. The difference quotient for the f (3 h) f (3) given function at = 3 is Qh ( ) for nonzero h. h Rationalize the numerator of Q(h) and simplify the resulting epression. Evaluate the simplified epression at h = 0. (a) (also sections.7 and 3.7) Using the transformations coordinates (shifting, reflecting, and stretching) or otherwise solve the following problem: For the function f() as defined below, determine the following : (a) the domain and range of f(), (b) the vertical and horizontal asymptotes, (c) and y intercepts, (d) the inverse function f 1 ( ), (e) the graph of f(). Is f() its own inverse? Yes or No f( ) (b) (also section 3.1) Graph the following: y 8 6 (c) (also section 3.1) Graph the following: (d) (also section 3.1) Graph the following: y (a) Given f ( ) 4 and g( ) 9, evaluate f g() f ( g()) and g f () g( f ()). 3 y 8 (a) (also sections.5 and 3.7) Using the transformations coordinates (shifting, reflecting, and stretching) or otherwise solve the following problem: For the function f() as defined below, determine the following : (a) the domain and range of f(), (b) the vertical and horizontal asymptotes, (c) and y intercepts, (d) the inverse function f 1 ( ), (e) the graph of f(). Is f() its own inverse? Yes or No f( ) (a) (also section.5) Graph the following: (b) (also section.5) Graph the following: 3 y 8 y 8 6
4 3. 6, 18, 0,, 8, 3, 40, , 8, 10, 14, 16, 4, 6, 36, 44, 54, , 1, 16, 30, 34, 4, 48, 56, 68, 74, 88, , 8, 14, 18, 0, 8, 38, 54, 64, , 1, 14, 4, 3, 34, 44, 48, 56, 6, 64, , 14, 16, 18,, 4, 8, 40, 46, 56, 70, , 10, 16, 18,, 34, , 16, 0 (a) (also section.5) Graph the following: 3 y 8 (a) Solve the following equations in the variable by using synthetic division and locating the rational roots first (or otherwise solve) (a) Find the real and imaginary parts of the comple number 3i 5 i (a) (also sections.5 and.7) Using the transformations coordinates (shifting, reflecting, and stretching) or otherwise solve the following problem: For the function f() as defined below, determine the following : (a) the domain and range of f(), (b) the vertical and horizontal asymptotes, (c) and y intercepts, (d) the inverse function f 1 ( ), (e) the graph of f(). Is f() its own inverse? Yes or No f( ) (b) Graph the following: 3 y , 10, 1, 14, 16, 18,, 4, 6, 30, 3, 36, 46, 58, 6, 64, 68, 86, 88, , 10, 16, 18, 0,, 6, 8, 30, 3, 36, 4, 46, 48, 5, 56, 58, 70, 71 (a) log (a) log3 81 log3 4 log3 3
5 4.5 4, 6, 10, 1, 16, 6, 30, 3, 34, 38, 44, 46, 48, 54, 60, 66, 76, , 10, 14, 18, 4, 6, 3, 36, , 1, 14, 38, 4, 44, 48, 58, 60, 66, 70, , 0, 30, 3, 38, ( 3 ) (43 ) 3 (a) Solve for in: 16 or in log (4 3) log log 13 b b. 3 b (b) Solve for in log ( 1) log log log 5 b b b b 4 or in (a) (also section 10.3) One group of customers bought 8 delue hamburgers, 6 orders of large fries, and 6 large colas for $6.10. A second group ordered 10 delue hamburgers, 6 large fries, and 8 larges colas for $ Is there sufficient information to determine the price of each food item? If not, construct a table showing the various possibilities assuming that the hamburgers cost between $1.75 and $.5, the fries between $0.75 and $1.00, and the colas between $0.60 and $0.90
6 10.3 6, 10, 16, 0, 38, 40, 54, 56 (a) Use the reduced row echelon form of the augmented matri to solve 3 y 3z y 5z 15 3y 6z 14 and then check your answer for the variable only by using the Cramer s rule. (b) Terry spent eactly $8 on eactly 10 Ties. Just 3 kinds are available, costing $, $3, and $4 per Tie, respectively. Find a general solution for the number of Ties of each kind that can be bought by using elementary row operations, and list three possible (feasible) solutions from the general solution if Terry must buy at least one Tie of each kind. (c) (also section 10.) One group of customers bought 8 delue hamburgers, 6 orders of large fries, and 6 large colas for $6.10. A second group ordered 10 delue hamburgers, 6 large fries, and 8 larges colas for $ Is there sufficient information to determine the price of each food item? If not, construct a table showing the various possibilities assuming that the hamburgers cost between $1.75 and $.5, the fries between $0.75 and $1.00, and the colas between $0.60 and $ , 8, 10, 1, 14, , 0, 31, 3, (a) Evaluate the matri product , 38, 40, , 1, 14, 18, 5 6, 30, 40, 46 (a) Find the inverse matri of A 4 by elementary row operations (b) Given that 3 3 and are inverses of each other, by using the inverse of the appropriate matri, 5 3y 4z 15 solve the system of equations: 3 y 3z y z 14
7 10.6 6, 8, 10, 18, 0, 4, 8, 34, 44, 48, , 4, 30, 40, 4, , 14, 16, 30, , 10, 16, 0,, 3, 44, , 10, 14, 18,, 4, 6, 34, 38, 44, 46, 48 Find the partial fraction decomposition of the following rational functions: 3 (a) ( 1)( 1) (b) (c) (d) 3 75 ( )( 1) 8 ( 4) (a) Graph the following inequalities and shade the solution set: y 4 6y y14 Also find the common points of the two boundaries. Note that the first boundary equation is a circle of radius 5 centered at (,3). 4 3 (a) Find the coefficient of yin the binomial epansion of y 3
University of North Georgia Department of Mathematics
University of North Georgia Department of Mathematics Instructor: Berhanu Kidane Course: College Algebra Math 1111 Text Book: For this course we use the free e book by Stitz and Zeager with link: http://www.stitz-zeager.com/szca07042013.pdf
More informationA slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
More informationPractice Test 3 (longer than the actual test will be) 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.
MAT 115 Spring 2015 Practice Test 3 (longer than the actual test will be) Part I: No Calculators. Show work. 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.) a.
More informationRadical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:
Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical
More information2.3 BUILDING THE PERFECT SQUARE
16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized
More informationChapter 2: Functions and Graphs Lesson Index & Summary
Section 1: Relations and Graphs Cartesian coordinates Screen 2 Coordinate plane Screen 2 Domain of relation Screen 3 Graph of a relation Screen 3 Linear equation Screen 6 Ordered pairs Screen 1 Origin
More informationconstant EXAMPLE #4:
Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value
More informationLearn new definitions of familiar shapes such as parabolas, hyperbolas, and circles.
CHAPTER 11 To begin this chapter, you will revisit the parabola by investigating the principle that makes a satellite dish work. You will discover a new way to define a parabola and will use that new definition
More informationSection 7.2 Logarithmic Functions
Math 150 c Lynch 1 of 6 Section 7.2 Logarithmic Functions Definition. Let a be any positive number not equal to 1. The logarithm of x to the base a is y if and only if a y = x. The number y is denoted
More informationSection 2.3 Task List
Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications
More informationChapter 3 Exponential and Logarithmic Functions
Chapter 3 Exponential and Logarithmic Functions Section 1 Section 2 Section 3 Section 4 Section 5 Exponential Functions and Their Graphs Logarithmic Functions and Their Graphs Properties of Logarithms
More informationMath 154 :: Elementary Algebra
Math :: Elementary Algebra Section 9. Section 9. Section 9. Section 9. Section 9. Section 9.6 Math :: Elementary Algebra Section 9. Introduction to Square Roots. This answer should be in your own words..
More informationProlegomena. Chapter Using Interval Notation 1
Chapter 1 Prolegomena 1.1 Using Interval Notation 1 Interval notation is another method for writing domain and range. In set builder notation braces (curly parentheses {} ) and variables are used to express
More informationNAME DATE PERIOD 6(7 5) 3v t 5s t. rv 3 s
- NAME DATE PERID Skills Practice Epressions and Formulas Find the value of each epression.. 8 2 3 2. 9 6 2 3. (3 8) 2 (4) 3 4. 5 3(2 2 2) 6(7 5) 5. [ 9 0(3)] 6. 3 4 7. (68 7)3 2 4 3 8. [3(5) 28 2 2 ]5
More informationDIVISION BY FRACTIONS
DIVISION BY FRACTIONS 6.. 6.. Division by fractions introduces three methods to help students understand how dividing by fractions works. In general, think of division for a problem like 8 as, In 8, how
More information5.1, 5.2, 5.3 Properites of Exponents last revised 12/4/2010
48 5.1, 5.2, 5.3 Properites of Exponents last revised 12/4/2010 Properites of Exponents 1. *Simplify each of the following: a. b. 2. c. d. 3. e. 4. f. g. 5. h. i. j. Negative exponents are NOT considered
More informationEstimating Tolerance Accuracy (Rounding, including sig. fig.) Scientific notation
S3 Pathways for learning in Maths Pathway 1 (Lower) Pathway 2 (Middle) Pathway 3 (Upper) Targets Complete coverage of level 3 experiences and outcomes in Mathematics Cover level 4 experiences and outcomes
More informationPREREQUISITE/PRE-CALCULUS REVIEW
PREREQUISITE/PRE-CALCULUS REVIEW Introduction This review sheet is a summary of most of the main topics that you should already be familiar with from your pre-calculus and trigonometry course(s), and which
More informationBlock: Date: Name: REVIEW Linear Equations. 7.What is the equation of the line that passes through the point (5, -3) and has a slope of -3?
Name: REVIEW Linear Equations 1. What is the slope of the line y = -2x + 3? 2. Write the equation in slope-intercept form. Block: Date: 7.What is the equation of the line that passes through the point
More informationMHF4U - Unit 6 Test. Multiple Choice - Answer on SCANTRON Identify the choice that best completes the statement or answers the question.
MHF4U - Unit 6 Test Multiple Choice - Answer on SCANTRON Identify the choice that best completes the statement or answers the question 1 The function has the point (10, 1) on its graph Find the coordinates
More information8.1 Day 1: Understanding Logarithms
PC 30 8.1 Day 1: Understanding Logarithms To evaluate logarithms and solve logarithmic equations. RECALL: In section 1.4 we learned what the inverse of a function is. What is the inverse of the equation
More informationUnit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3)
Unit 1 Introduction to Precalculus Linear Equations in Two Variables (Unit 1.3) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Find
More informationExponential and Logarithmic Functions
Name Date Chapter 3 Eponential and Logarithmic Functions Section 3.1 Eponential Functions and Their Graphs Objective: In this lesson ou learned how to recognize, evaluate, and graph eponential functions.
More information8.1 Exponential Growth 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations.
8.1 Exponential Growth Objective 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations. Key Terms Exponential Function Asymptote Exponential Growth Function
More informationPre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis
Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis Objectives: Students will be able to: Analyze the features of a rational function: determine domain,
More informationGraphing Exponential Functions
Graphing Eponential Functions What is an Eponential Function? Eponential functions are one of the most important functions in mathematics. Eponential functions have many scientific applications, such as
More informationTHE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs.
THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs. Exercise #1: Consider the function y = f (x) shown on the graph below. (a) Evaluate each of the following:
More information7.1 Solving Quadratic Equations by Graphing
Math 2201 Date: 7.1 Solving Quadratic Equations by Graphing In Mathematics 1201, students factored difference of squares, perfect square trinomials and polynomials of the form x 2 + bx + c and ax 2 + bx
More informationAlgebra 1 Online:
Dear Algebra 2 Students, Within this packet you will find mathematical concepts and skills learned in Algebra 1 that are the foundation from which Algebra 2 is built. These concepts need to be reviewed
More informationLesson 11: Linear Functions, Part 2
Lesson 11 continues the study of linear functions. In this lesson, we look at how to write linear equations in slope-intercept and general form and applications where these may be used. We also look at
More information3.3 Properties of Logarithms
Section 3.3 Properties of Logarithms 07 3.3 Properties of Logarithms Change of Base Most calculators have only two types of log keys, one for common logarithms (base 0) and one for natural logarithms (base
More informationMath + 4 (Red) SEMESTER 1. { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations
Math + 4 (Red) This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive
More informationLesson 8. Diana Pell. Monday, January 27
Lesson 8 Diana Pell Monday, January 27 Section 5.2: Continued Richter scale is a logarithmic scale used to express the total amount of energy released by an earthquake. The Richter scale gives the magnitude
More informationSM3 Lesson 2-3 (Intercept Form Quadratic Equation)
SM3 Lesson 2-3 (Intercept Form Quadratic Equation) Factor the following quadratic expressions: x 2 + 11x + 30 x 2 10x 24 x 2 8x + 15 Standard Form Quadratic Equation (x + 5)(x + 6) (x 12)(x + 2) (x 5)(x
More informationOutcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
More informationLesson Plan Mr. Baglos Course: Honors Algebra II As of: 4/2/18. After School: 2:30-3:30 Room 2232
Lesson Plan Mr. Baglos Course: Honors Algebra II As of: 4/2/18 After School: 2:30-3:30 Room 2232 HW: Finish all notes for the day, do the assignment from your HMH workbook, Gizmos, your Math Journal, and
More information3.1 Solving Systems by Graphing. In consistent systems, Independent systems consist of. Three Cases: A. consistent and independent
3.1 Solving Systems by Graphing In consistent systems, 2. y Independent systems consist of Three Cases: x A. consistent and independent B. inconsistent and independent 3. y C. consistent and dependent
More informationInstructor Notes for Chapter 4
Section 4.1 One to One Functions (Day 1) Instructor Notes for Chapter 4 Understand that an inverse relation undoes the original Understand why the line y = xis a line of symmetry for the graphs of relations
More informationAlex Benn. Math 7 - Outline First Semester ( ) (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days
Math 7 - Outline First Semester (2016-2017) Alex Benn (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days 0.1 Classroom Rules Multiplication Table Unit 1 Measuring
More informationTennessee Senior Bridge Mathematics
A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts
More informationAlgebra 1 B Semester Exam Review
Algebra 1 B 014 MCPS 013 014 Residual: Difference between the observed (actual) value and the predicted (regression) value Slope-Intercept Form of a linear function: f m b Forms of quadratic functions:
More informationChapter 6: Linear Relations
Chapter 6: Linear Relations Section 6. Chapter 6: Linear Relations Section 6.: Slope of a Line Terminolog: Slope: The steepness of a line. Also known as the Rate of Change. Slope = Rise: The change in
More information5.1N Key Features of Rational Functions
5.1N Key Features of Rational Functions A. Vocabulary Review Domain: Range: x-intercept: y-intercept: Increasing: Decreasing: Constant: Positive: Negative: Maximum: Minimum: Symmetry: End Behavior/Limits:
More informationLesson 5.4 Exercises, pages
Lesson 5.4 Eercises, pages 8 85 A 4. Evaluate each logarithm. a) log 4 6 b) log 00 000 4 log 0 0 5 5 c) log 6 6 d) log log 6 6 4 4 5. Write each eponential epression as a logarithmic epression. a) 6 64
More information2. Be able to evaluate a trig function at a particular degree measure. Example: cos. again, just use the unit circle!
Study Guide for PART II of the Fall 18 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 be
More informationTrigonometry. An Overview of Important Topics
Trigonometry An Overview of Important Topics 1 Contents Trigonometry An Overview of Important Topics... 4 UNDERSTAND HOW ANGLES ARE MEASURED... 6 Degrees... 7 Radians... 7 Unit Circle... 9 Practice Problems...
More informationINTRODUCTION TO LOGARITHMS
INTRODUCTION TO LOGARITHMS Dear Reader Logarithms are a tool originally designed to simplify complicated arithmetic calculations. They were etensively used before the advent of calculators. Logarithms
More informationMath 10/11 Honors Section 3.6 Basic Trigonometric Identities
Math 0/ Honors Section 3.6 Basic Trigonometric Identities 0-0 - SECTION 3.6 BASIC TRIGONOMETRIC IDENTITIES Copright all rights reserved to Homework Depot: www.bcmath.ca I) WHAT IS A TRIGONOMETRIC IDENTITY?
More informationMath 122: Final Exam Review Sheet
Exam Information Math 1: Final Exam Review Sheet The final exam will be given on Wednesday, December 1th from 8-1 am. The exam is cumulative and will cover sections 5., 5., 5.4, 5.5, 5., 5.9,.1,.,.4,.,
More informationProducts of Linear Functions
Math Objectives Students will understand relationships between the horizontal intercepts of two linear functions and the horizontal intercepts of the quadratic function resulting from their product. Students
More informationCPM EDUCATIONAL PROGRAM
CPM EDUCATIONAL PROGRAM SAMPLE LESSON: ALGEBRA TILES FOR FACTORING AND MORE HIGH SCHOOL CONTENT ALGEBRA TILES (MODELS) Algebra Tiles are models that can be used to represent abstract concepts. Th packet
More informationLesson 3.4 Completing the Square
Lesson 3. Completing the Square Activity 1 Squares of Binomials 1. a. Write a formula for the square of a binomial: ÐB :Ñ œ Notice that the constant term of the trinomial is coefficient of the linear term
More informationSection 5.2 Graphs of the Sine and Cosine Functions
A Periodic Function and Its Period Section 5.2 Graphs of the Sine and Cosine Functions A nonconstant function f is said to be periodic if there is a number p > 0 such that f(x + p) = f(x) for all x in
More informationWARM UP. 1. Expand the expression (x 2 + 3) Factor the expression x 2 2x Find the roots of 4x 2 x + 1 by graphing.
WARM UP Monday, December 8, 2014 1. Expand the expression (x 2 + 3) 2 2. Factor the expression x 2 2x 8 3. Find the roots of 4x 2 x + 1 by graphing. 1 2 3 4 5 6 7 8 9 10 Objectives Distinguish between
More informationPrecalculus ~ Review Sheet
Period: Date: Precalculus ~ Review Sheet 4.4-4.5 Multiple Choice 1. The screen below shows the graph of a sound recorded on an oscilloscope. What is the period and the amplitude? (Each unit on the t-axis
More informationUnit 5 Radical Functions & Combinatorics
1 Graph of y Unit 5 Radical Functions & Combinatorics x: Characteristics: Ex) Use your knowledge of the graph of y x and transformations to sketch the graph of each of the following. a) y x 5 3 b) f (
More informationHow to Graph Trigonometric Functions
How to Graph Trigonometric Functions This handout includes instructions for graphing processes of basic, amplitude shifts, horizontal shifts, and vertical shifts of trigonometric functions. The Unit Circle
More informationEstimating Tolerance Accuracy (Rounding, including sig. fig.) Scientific notation
S3 Pathways for learning in Maths Pathway 1 (Lower) Pathway 2 (Middle) Pathway 3 (Upper) Targets Complete coverage of level 3 experiences and outcomes in Mathematics Cover level 4 experiences and outcomes
More informationChapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
More informationRECTANGULAR EQUATIONS OF CONICS. A quick overview of the 4 conic sections in rectangular coordinates is presented below.
RECTANGULAR EQUATIONS OF CONICS A quick overview of the 4 conic sections in rectangular coordinates is presented below. 1. Circles Skipped covered in MAT 124 (Precalculus I). 2. s Definition A parabola
More informationUnit 11: Linear Equations and Inequalities
Section 11.1: General Form ax + by = c Section 11.2: Applications General Form Section 11.3: Linear Inequalities in Two Variables Section 11.4: Graphing Linear Inequalities in Two Variables KEY TERMS AND
More informationPART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below:
Math (L-3a) Learning Targets: I can find the vertex from intercept solutions calculated by quadratic formula. PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to
More informationUse the Point-Slope Form to Write the Equation of a Line
Math 90 8.3 "Writing Equations of Lines" Objectives: * Use the point-slope form to write the equation of a line. * Use the slope-intercept form to write the equation of a line. * Use slope as an aid when
More informationMath Lecture 2 Inverse Functions & Logarithms
Math 1060 Lecture 2 Inverse Functions & Logarithms Outline Summary of last lecture Inverse Functions Domain, codomain, and range One-to-one functions Inverse functions Inverse trig functions Logarithms
More informationWarm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.
Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.
More informationGraphs, Linear Equations and Functions
Graphs, Linear Equations and Functions There are several ways to graph a linear equation: Make a table of values Use slope and y-intercept Use x and y intercepts Oct 5 9:37 PM Oct 5 9:38 PM Example: Make
More information~~Final Exam Review~~
MATH 9 ~~Final Exam Review~~ Unit #1: Square Roots and Surface Area NAME: DATE: CLASS: 90 1. 100 is a perfect square. What does this mean? 2. Find all of the perfect squares between 1 and 100. 3. Complete
More informationUse smooth curves to complete the graph between and beyond the vertical asymptotes.
5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve
More informationThe Math Projects Journal
PROJECT OBJECTIVE The House Painter lesson series offers students firm acquisition of the skills involved in adding, subtracting and multipling polnomials. The House Painter lessons accomplish this b offering
More informationTasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem.
Grade 8 Math C1 TC Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Expressions and
More information7.1 INTRODUCTION TO PERIODIC FUNCTIONS
7.1 INTRODUCTION TO PERIODIC FUNCTIONS *SECTION: 6.1 DCP List: periodic functions period midline amplitude Pg 247- LECTURE EXAMPLES: Ferris wheel, 14,16,20, eplain 23, 28, 32 *SECTION: 6.2 DCP List: unit
More information= means divide. There are 2 ways to perform this division. Long Division or Synthetic Division. means divide x 2 into 3x 3 + x 2 4x 13
Section 4 1B: Synthetic Division means divide There are 2 ways to perform this division. Long Division or Synthetic Division Long division requires you divide the binomial into the polynomial. means divide
More informationEssential Mathematics. Study Guide #1
Math 54CM Essential Mathematics Name Date Study Guide # Exam # is closed book and closed notes. NO CALCULATORS. Please clearly show any work necessary to get partial credit. Be sure to show your answer
More informationHW#02 (18 pts): All recommended exercises from JIT (1 pt/problem)
Spring 2011 MthSc103 Course Calendar Page 1 of 7 January W 12 Syllabus/Course Policies BST Review Th 13 Basic Skills Test F 14 JIT 1.1 1.3: Numbers, Fractions, Parentheses JIT 1.1: 2, 6, 8, 9 JIT 1.2:
More informationGraphing Exponential Functions Answer Key Algebra 2
Graphing Answer Key Algebra 2 Free PDF ebook Download: Graphing Answer Key Algebra 2 Download or Read Online ebook graphing exponential functions answer key algebra 2 in PDF Format From The Best User Guide
More informationMath 147 Section 5.2. Application Example
Math 147 Section 5.2 Logarithmic Functions Properties of Change of Base Formulas Math 147, Section 5.2 1 Application Example Use a change-of-base formula to evaluate each logarithm. (a) log 3 12 (b) log
More informationb = 7 The y-intercept is 7.
State the x- and y-intercepts of each equation. Then use the intercepts to graph the equation. 1. y = 2x + 7 To find the x-intercept, substitute 0 for y and solve for x. y = 2x + 7 0 = 2x + 7 7 = 2x 3.5
More informationPage 1 of 52 Youtube.com/c/StayLearningNewdelhi
Page 1 of 52 www.vijayadarsh.com Youtube.com/c/StayLearningNewdelhi Contact@vijayAdarsh.com +919268373738 About StayLearning StayLearning (a Division of AASS) believes in educating their students with
More information171S5.4p Properties of Logarithmic Functions. November 20, CHAPTER 5: Exponential and Logarithmic Functions. Examples. Express as a product.
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions
More information6.4 & 6.5 Graphing Trigonometric Functions. The smallest number p with the above property is called the period of the function.
Math 160 www.timetodare.com Periods of trigonometric functions Definition A function y f ( t) f ( t p) f ( t) 6.4 & 6.5 Graphing Trigonometric Functions = is periodic if there is a positive number p such
More informationMath 1205 Trigonometry Review
Math 105 Trigonometry Review We begin with the unit circle. The definition of a unit circle is: x + y =1 where the center is (0, 0) and the radius is 1. An angle of 1 radian is an angle at the center of
More informationSummer Math Practice: 7 th Pre-Algebra Entering 8 th Algebra 1
Summer Math Practice: 7 th Pre-Algebra Entering 8 th Algebra 1 Dear Students and Parents, The summer math requirement is due to Mr. Cyrus the first day back in August. The objective is to make sure you
More informationMath 154 :: Elementary Algebra
Math :: Elementary Algebra Section. Section. Section. Section. Section. Math :: Elementary Algebra Section. The Rectangular (Cartesian) Coordinate System. The variable x usually represents the independent
More informationMath 9 Comprehensive Review Package - Answers. Unit 1 - Square Roots & Surface Area. Math 9 PAT Review Answers MULTIPLE CHOICE
Math 9 Comprehensive Review Package - Answers Unit 1 - Square Roots & Surface Area 1. ANS: A 2. ANS: C 3. ANS: D 4. ANS: D 5. ANS: C 6. ANS: 7. ANS: 18 8. ANS: The length of side s is about 7.1 cm. 9.
More informationWelcome Accelerated Algebra 2!
Welcome Accelerated Algebra 2! Tear-Out: Pgs. 348-354 (classwork) Pg. 355 (homework) U5H6: Pg. 355 #7-9, 11-12,14-16, 18-23 Updates: U5Q2 will be January 30 th U5T will be February 6 th Agenda (1) Warm-Up!
More informationMthSc 103 Test #1 Spring 2011 Version A JIT , 1.8, , , , 8.1, 11.1 ANSWER KEY AND CUID: GRADING GUIDELINES
Student s Printed Name: ANSWER KEY AND CUID: GRADING GUIDELINES Instructor: Section # : You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes,
More informationHPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means:
Number and Numeration MA.7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical
More informationThe Slope of a Line. units corresponds to a horizontal change of. m y x y 2 y 1. x 1 x 2. Slope is not defined for vertical lines.
0_0P0.qd //0 : PM Page 0 0 CHAPTER P Preparation for Calculus Section P. (, ) = (, ) = change in change in Figure P. Linear Models and Rates of Change Find the slope of a line passing through two points.
More information2.6. Slope-Intercept Form Working Under Pressure. My My Notes ACTIVITY
Slope-Intercept Form SUGGESTED LEARNING STRATEGIES: Shared Reading, Marking the Tet, Questioning the Tet, Visualization, Create Representations, Think/Pair/Share, Note Taking M M Notes ACTIVITY. When a
More information6.1.3 Where do the solutions begin and end?
6.1.3 Where do the solutions begin and end? One Variable Inequalities Word
More informationMA Lesson 16 Sections 2.3 and 2.4
MA 1500 Lesson 16 Sections.3 and.4 I Piecewise Functions & Evaluating such Functions A cab driver charges $4 a ride for a ride less than 5 miles. He charges $4 plus $0.50 a mile for a ride greater than
More informationSlope. Domain 2 Lesson 11. Getting the Idea
Domain Lesson Slope Common Core Standard: 8.EE. Getting the Idea The graph of a linear equation is a straight line. The steepness of the line is called its slope. The slope shows the rate at which two
More informationAlgebra 1B. Chapter 6: Linear Equations & Their Graphs Sections 6-1 through 6-7 & 7-5. COLYER Fall Name: Period:
Chapter 6: Linear Equations & Their Graphs Sections 6-1 through 6-7 & 7-5 COLYER Fall 2016 Name: Period: What s the Big Idea? Analyzing Linear Equations & Inequalities What can I expect to understand when
More informationCumulative Review : MAT-032 (Algebra B) 2013
Perform the indicated operations and simplify: ( 7. 8. 9. Add 10. Subtract from 1 Subtract from the sum of and 1 Subtract the sum of and from 7. 8. 9. 10. 1 1 Factor completely: 7. 8. 7. 8. Factor completely:
More information14.2 Limits and Continuity
14 Partial Derivatives 14.2 Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. Let s compare the behavior of the functions Tables 1 2 show values of f(x,
More informationUNIT 2: FACTOR QUADRATIC EXPRESSIONS. By the end of this unit, I will be able to:
UNIT 2: FACTOR QUADRATIC EXPRESSIONS UNIT 2 By the end of this unit, I will be able to: o Represent situations using quadratic expressions in one variable o Expand and simplify quadratic expressions in
More informationThe 21 st Century Wireless Classroom Network for AP Calculus
The 21 st Century Wireless Classroom Network for AP Calculus In this exploratory hands-on workshop, we will be solving Calculus problems with the HP Prime Graphing Calculator and the HP Wireless Classroom
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More information4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.
4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept
More informationLinear Inequalities in One and Two Variables
Date:10/18/2014 Topic IV: Graphing Linear Inequalities in Two Variables 4 th Class Objective: the students will Graphing Linear Inequalities in Two Variables Real-World Applications Agenda: Bell ringer
More information