MHF4U - Practice Mastery #8
|
|
|
- Tamsyn Long
- 5 years ago
- Views:
Transcription
1 MHF4U - Practice Master #8 Multiple Choice Identif the choice that best completes the statement or answers the question.. If, then a. b. c. d. 2.. The graph illustrates the motion of a person walking toward or awa from a CBR. Distance from the CBR is recorded on the vertical ais in metres. Elapsed time since the CBR was started up is recorded on the horizontal ais in seconds. s(t) Which of the following best describes the motion? The person is... t a. walking awa from the CBR and speeding c. walking awa from the CBR and slowing up. down b. walking toward the CBR and speeding up. d. walking toward the CBR and slowing down. 4. The function defined b has range If, then a. b. c. d. 7. If f = {(2,4), (4,-), (-,2)} then f - (-) = a. 4 b. 2 c. - d Evaluate a. -2 b. c. - d. 9. If then
2 0. The graph of has horizontal asmptote(s) with equation(s)... a. =2 b. =0 c. =2, =-2 d. =-. The function defined b... has domain 2. If then. is equal to... undefined 0 4. Evaluate a. b. c. d The slope of the tangent to the graph of at =5 is a. 0 b. 76 c. d A table of values for a function is shown on the right. A possible equation for this function is... a. b. c. d. 7. The function defined b... has range 8.
3 9. Which of the following is true? i) ii) a. i) onl b. ii) onl c. both d. neither 20. The I/O diagram for a function is... The equation for the inverse is 2 a. b. c. d. 2. Evaluate a. b. 0 c. 2 d The number of distinct real roots for the equatiion is a. 2 b. c. 4 d is a factor of i) ii) a. i onl b. ii onl c. i and ii d. neither 24. Which of the following equations is graphed below? 25. Which of the following is true? i) ii) a. i) onl b. ii) onl c. both d. neither 26. If where -80 θ 80, then a. θ = -50 or θ = 50 c. θ = 20 or θ = -20 b. θ = -20 or θ = -60 d. θ = -0 or θ = Factor completel: a. b. c. d.
4 28. Factor full 29. is equal to Simplif a. - 2 b. -2 c. 2 d. - 4
5 MHF4U - Practice Master #8 Answer Section MULTIPLE CHOICE. ANS: D The base is. The logarithm OF is the eponent that produces when is used as the base... i.e.,. 2. ANS: B wq. ANS: B With a negative slope, we know the distance from the CBR is decreasing, so the person is walking towards the CBR. The slope is becoming more and more negative, so the speed is also increasing. 4. ANS: A The I/O diagram will become... horizontal translation units to the right vertical translation units down subtract >0 subtract > - 4 = 4-5 The base function, looks like It has range Once the diagram is drawn, just follow the epression through the diagram to get the equation Alternativel, we could use the calculator to graph each one and compare to the graph of 5. ANS: B 6. ANS: A The base is 2, (as in part a or b). The logarithm OF is the eponent that produces when 2 is used as the base... i.e.,. 7. ANS: A
6 The ordered pair (4,-) shows us that f takes 4 and produces -. Therefore, f - takes - and produces 4. I.e., f - (-) = ANS: C because. We want the eponent (the logarithm). 9. ANS: A If a fraction is equal to zero then the numerator must be equal to zero and the denominator must not be equal to zero. I.e.,, but both and are undefined epressions. In this case, 0, 2, and 0.5 all make the numerator 0, but 0.5 also makes the denominator 0, so. 0. ANS: A. As, the 6 in the numerator and the -4 in the denominator become insignificant, so. As,, so the horizontal asmptote has equation =2.. ANS: A The I/O diagram for the function is... horizontal translation units to the left vertical translation 2 units up??0?0? 2 2 We know the base function has that, so we can work backwards through the I/O diagram to make determine Alternativel, we could use the calculator to graph it. 2. ANS: C U
7 So... if. ANS: A cdsa 4. ANS: D because. We want the eponent (the logarithm). 5. ANS: A Tpe the equation into Y on the calculator, GRAPH (and make sure the window is appropriate), then push 2nd PRGM to select DRAW. Push 5 to select TANGENT(, then push 5 and the calculator will displa X=5 on the bottom of the graph. Press ENTER, and it will draw the tangent line at =5 and will displa the equation (approimate) on the bottom of the screen. In this case the equation listed is = Its slope (0) is the instantaneous rate of change of the function at =5. 6. ANS: D Note that the inverse of this function (interchange and coordinates) is an eponential function with base 4 (common ratio between terms is 4). The inverse has equation, so the original has equation. 7. ANS: C The I/O diagram for the function is... horizontal translation units to the right vertical translation 2 units up??0?0? 2 subtract 2 We know the base function has that, so we can work forwards through the I/O diagram to make determine Alternativel, we could use the calculator to graph it. 8. ANS: A 9. ANS: C... the rule is... this is the composition of a function ( power of 2) and its inverse, so the output will be the same as the input....
8 20. ANS: A 2 The I/O diagram for the inverse will be... horizontal translation 2 units to the right vertical translation units down - 2 subtract - 2 subtract 2 = Once the diagram is drawn, just follow the epression through the diagram to get the equation Alternativel, we could use the calculator to graph each one and compare to the graph of the original. 2. ANS: C because. We want the eponent (the logarithm). 22. ANS: B The real roots are -5, 2, and -2. has no real roots. 2. ANS: B if, then So is not a factor of If, then So is a factor of 24. ANS: A
9 is the usual... has -ais as its horizontal asmptote, increases from left to right, crosses the -ais at. is the same as, so to get its graph reflect the original in the -ais. is the inverse of, so it has the -ais as a vertical asmptote, crosses the -ais at and then its coord. increases dramaticall as continues to increase. is the inverse of, so its graph can be found b reflecting in the -ais. OR ou could just make a table of values for each of and and then find the inverses of each. = ( ) = = log = log 25. ANS: A... the rule is... the rule is and... this is the composition of a function ( power of 2) and its inverse, so the output will be the same as the input ANS: A The unit circle shows us the coordinates of all points with principal angles 0, 45 and 60. It shows that at points H and J. These points are 0 awa from the ais, so the angles are -50 and 50
10 27. ANS: D Arrange the tiles into a rectangle: So 28. ANS: A First, we can see that + 5 is a factor of, because if f() =,. Go to the chart:
11 Therefore = 29. ANS: A cdsa 0. ANS: B Factor the numerator. Note that factoring out -, makes the other factor the same as the denominator. = Divide out identical factors = -2 if?4
MHF4U: Practice Mastery Test #3
MHF4U: Practice Mastery Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify a. b. 4x c. d. 2. Expand and simplify (2x + 1)(x - 3) a. b. c.
MCV4U - Practice Mastery Test #1
Name: Class: Date: ID: A MCVU - Practice Mastery Test # Multiple Choice Identify the choice that best completes the statement or answers the question.. Solve a + b = a b = 5 a. a= & b=- b. a=- & b= c.
MHF 4U 04 Rates of Change Sampler
Name: Class: Date: MHF 4U 04 Rates of Change Sampler 1. The tables below shows the concentration of CO 2 in the air in a room over time. The best estimate of the instantaneous rate of change of the CO
College Algebra Final, 7/2/10
NAME College Algebra Final, 7//10 1. Factor the polnomial p() = 3 5 13 4 + 13 3 + 9 16 + 4 completel, then sketch a graph of it. Make sure to plot the - and -intercepts. (10 points) Solution: B the rational
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review MAC 1 Spring 0 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) {-
8-1 Exploring Exponential Models
8- Eploring Eponential Models Eponential Function A function with the general form, where is a real number, a 0, b > 0 and b. Eample: y = 4() Growth Factor When b >, b is the growth factor Eample: y =
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) A)
Summer Mathematics Prep
Summer Mathematics Prep Entering Calculus Chesterfield County Public Schools Department of Mathematics SOLUTIONS Domain and Range Domain: All Real Numbers Range: {y: y } Domain: { : } Range:{ y : y 0}
Learning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1
College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,
Solutions to the Math 1051 Sample Final Exam (from Spring 2003) Page 1
Solutions to the Math 0 Sample Final Eam (from Spring 00) Page Part : Multiple Choice Questions. Here ou work out the problems and then select the answer that matches our answer. No partial credit is given
6.4 graphs OF logarithmic FUnCTIOnS
SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS
Math RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus
Math 0-03-RE - Calculus I Functions Page of 0 Definition of a function f() : Topics of Functions used in Calculus A function = f() is a relation between variables and such that for ever value onl one value.
We want to determine what the graph of an exponential function. y = a x looks like for all values of a such that 0 > a > 1
Section 5 B: Graphs of Decreasing Eponential Functions We want to determine what the graph of an eponential function y = a looks like for all values of a such that 0 > a > We will select a value of a such
3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
Name Date. Work with a partner. Each graph shown is a transformation of the parent function
3. Transformations of Eponential and Logarithmic Functions For use with Eploration 3. Essential Question How can ou transform the graphs of eponential and logarithmic functions? 1 EXPLORATION: Identifing
Chapter 8 Notes SN AA U2C8
Chapter 8 Notes SN AA U2C8 Name Period Section 8-: Eploring Eponential Models Section 8-2: Properties of Eponential Functions In Chapter 7, we used properties of eponents to determine roots and some of
a 2 x y 1 x 1 y SOL AII.1a
SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas
AP Calculus AB Summer Assignment Mrs. Berkson
AP Calculus AB Summer Assignment Mrs. Berkson The purpose of the summer assignment is to prepare ou with the necessar Pre- Calculus skills required for AP Calculus AB. Net ear we will be starting off the
MCR3U - Practice Mastery Test #6
Name: Class: Date: MCRU - Practice Mastery Test #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Factor completely: 4x 2 2x + 9 a. (2x ) 2 b. (4x )(x )
MCR3U - Practice Mastery Test #9 & #10
Name: Class: Date: MCRU - Practice Mastery Test #9 & #0 Multiple Choice Identify the choice that best completes the statement or answers the question.. Factor completely: 4x 0x + 5 a. (x + 5)(x 5) b. (4x
is on the graph of y = f 1 (x).
Objective 2 Inverse Functions Illustrate the idea of inverse functions. f() = 2 + f() = Two one-to-one functions are inverses of each other if (f g)() = of g, and (g f)() = for all in the domain of f.
a 2 x y 1 y SOL AII.1a
SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas
review math0410 (1-174) and math 0320 ( ) aafinm mg
Eam Name review math04 (1-174) and math 0320 (17-243) 03201700aafinm0424300 mg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif. 1) 7 2-3 A)
AP Calculus AB Summer Assignment Mrs. Berkson
AP Calculus AB Summer Assignment Mrs. Berkson The purpose of the summer assignment is to prepare ou with the necessar Pre- Calculus skills required for AP Calculus AB. Net ear we will be starting off the
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. D) D: (-, 0) (0, )
Midterm Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the domain and graph the function. ) G(t) = t - 3 ) 3 - -3 - - 3 - - -3
Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE
The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test
ALGEBRA 1 CP FINAL EXAM REVIEW
ALGEBRA CP FINAL EXAM REVIEW Alg CP Sem Eam Review 0 () Page of 8 Chapter 8: Eponents. Write in rational eponent notation. 7. Write in radical notation. Simplif the epression.. 00.. 6 6. 7 7. 6 6 8. 8
HSML Honors or AP Calculus Course Preparedness Test
HSML Honors or AP Calculus Course Preparedness Test High School Math Live wants parents to be well informed. We want our student to be placed in the appropriate course so that the will be successful and
Coordinate geometry. + bx + c. Vertical asymptote. Sketch graphs of hyperbolas (including asymptotic behaviour) from the general
A Sketch graphs of = a m b n c where m = or and n = or B Reciprocal graphs C Graphs of circles and ellipses D Graphs of hperbolas E Partial fractions F Sketch graphs using partial fractions Coordinate
KEY IDEAS. Chapter 1 Function Transformations. 1.1 Horizontal and Vertical Translations Pre-Calculus 12 Student Workbook MHR 1
Chapter Function Transformations. Horizontal and Vertical Translations A translation can move the graph of a function up or down (vertical translation) and right or left (horizontal translation). A translation
First Semester Final Review NON-Graphing Calculator
Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through
Exponential and Logarithmic Functions
Lesson 6 Eponential and Logarithmic Fu tions Lesson 6 Eponential and Logarithmic Functions Eponential functions are of the form y = a where a is a constant greater than zero and not equal to one and is
Differentiation and applications
FS O PA G E PR O U N C O R R EC TE D Differentiation and applications. Kick off with CAS. Limits, continuit and differentiabilit. Derivatives of power functions.4 C oordinate geometr applications of differentiation.5
Name: Class: Date: Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.
Class: Date: Ch 9a On-Line Test Multiple Choice Identif the letter of the choice that best completes the statement or answers the question. 1. Is the relationship between the variables in the table a direct
Instructor: Imelda Valencia Course: A3 Honors Pre Calculus
Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus 01 017 Assignment: Summer Homework for those who will be taking FOCA 017 01 onl available until Sept. 15 1. Write the epression
STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs
STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic
(2.5) 1. Solve the following compound inequality and graph the solution set.
Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.
where a 0 and the base b is a positive number other
7. Graph Eponential growth functions No graphing calculators!!!! EXPONENTIAL FUNCTION A function of the form than one. a b where a 0 and the base b is a positive number other a = b = HA = Horizontal Asmptote:
Polynomials and Quadratics
PSf Paper 1 Section A Polnomials and Quadratics Each correct answer in this section is worth two marks. 1. A parabola has equation = 2 2 + 4 + 5. Which of the following are true? I. The parabola has a
AP Calculus AB Summer Assignment
AP Calculus AB Summer Assignment Name: When you come back to school, it is my epectation that you will have this packet completed. You will be way behind at the beginning of the year if you haven t attempted
is on the graph of y = f 1 (x).
Objective 2 Inverse Functions Illustrate the idea of inverse functions. f() = 2 + f() = Two one-to-one functions are inverses of each other if (f g)() = of g, and (g f)() = for all in the domain of f.
Algebra(2(Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the(
Algebra((Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the( first(week(of(school.( ( ( Please(visit(the(CHS(website(to(view(answers(to(
CHAPTER 1-5 CREDIT INTERVENTION ASSIGNMENT
MHFU NAME: DATE: CHAPTER - CREDIT INTERVENTION ASSIGNMENT Circle the best option and write our choice in the space provided Show our work clearl and in the correct order on separate sheets Which one of
13. x 2 = x 2 = x 2 = x 2 = x 3 = x 3 = x 4 = x 4 = x 5 = x 5 =
Section 8. Eponents and Roots 76 8. Eercises In Eercises -, compute the eact value... 4. (/) 4. (/). 6 6. 4 7. (/) 8. (/) 9. 7 0. (/) 4. (/6). In Eercises -4, perform each of the following tasks for the
136 Maths Quest 10 for Victoria
Quadratic graphs 5 Barr is a basketball plaer. He passes the ball to a team mate. When the ball is thrown, the path traced b the ball is a parabola. Barr s throw follows the quadratic equation =.5 +. +.5.
Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1
Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab
Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.
Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to
The standard form of the equation of a circle is based on the distance formula. The distance formula, in turn, is based on the Pythagorean Theorem.
Unit, Lesson. Deriving the Equation of a Circle The graph of an equation in and is the set of all points (, ) in a coordinate plane that satisf the equation. Some equations have graphs with precise geometric
MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T GRAPHING LINEAR INEQUALITIES & SET NOTATION - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INEQUALITY = a mathematical statement that contains one of these four inequalit signs: ,.
Section 5.1: Functions
Objective: Identif functions and use correct notation to evaluate functions at numerical and variable values. A relationship is a matching of elements between two sets with the first set called the domain
Chapter 1 Functions and Models
Chapter 1 Functions and Models 1.2 Mathematical Models: A catalog of Essential Functions A mathematical model is a mathematical description of a real world situations such as the size of a population,
Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!
Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).
Nova Scotia Examinations Mathematics 12 Web Sample 2. Student Booklet
Nova Scotia Eaminations Mathematics Web Sample Student Booklet General Instructions - WEB SAMPLE* This eamination is composed of two sections with the following suggested time allotment: Selected-Response
12x y (4) 2x y (4) 5x y is the same as
Name: Unit #6 Review Quadratic Algebra Date: 1. When 6 is multiplied b the result is 0 1 () 9 1 () 9 1 () 1 0. When is multiplied b the result is 10 6 1 () 7 1 () 7 () 10 6. Written without negative eponents
Math 111 Lecture Notes
A rational function is of the form R() = p() q() where p and q are polnomial functions. The zeros of a rational function are the values of for which p() = 0, as the function s value is zero where the value
1. For each of the following, state the domain and range and whether the given relation defines a function. b)
Eam Review Unit 0:. For each of the following, state the domain and range and whether the given relation defines a function. (,),(,),(,),(5,) a) { }. For each of the following, sketch the relation and
Review of Essential Skills and Knowledge
Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope
Exponential and Logarithmic Functions
Eponential and Logarithmic Functions 6 Figure Electron micrograph of E. Coli bacteria (credit: Mattosaurus, Wikimedia Commons) CHAPTER OUTLINE 6. Eponential Functions 6. Logarithmic Properties 6. Graphs
decreases as x increases.
Chapter Review FREQUENTLY ASKED Questions Q: How can ou identif an eponential function from its equation? its graph? a table of values? A: The eponential function has the form f () 5 b, where the variable
Exponential, Logistic, and Logarithmic Functions
CHAPTER 3 Eponential, Logistic, and Logarithmic Functions 3.1 Eponential and Logistic Functions 3.2 Eponential and Logistic Modeling 3.3 Logarithmic Functions and Their Graphs 3.4 Properties of Logarithmic
The American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet
The American School of Marrakesh Algebra Algebra Summer Preparation Packet Summer 016 Algebra Summer Preparation Packet This summer packet contains eciting math problems designed to ensure our readiness
1. Simplify each expression and write all answers without negative exponents. for variable L.
MATH 0: PRACTICE FINAL Spring, 007 Chapter # :. Simplif each epression and write all answers without negative eponents. ( ab ) Ans. b 9 7a 6 Ans.. Solve each equation. 5( ) = 5 5 Ans. man solutions + 7
Polynomial and Rational Functions
Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define
H.Algebra 2 Summer Review Packet
H.Algebra Summer Review Packet 1 Correlation of Algebra Summer Packet with Algebra 1 Objectives A. Simplifing Polnomial Epressions Objectives: The student will be able to: Use the commutative, associative,
Chapter 12 and 13 Math 125 Practice set Note: the actual test differs. Given f(x) and g(x), find the indicated composition and
Chapter 1 and 13 Math 1 Practice set Note: the actual test differs. Given f() and g(), find the indicated composition. 1) f() = - ; g() = 3 + Find (f g)(). Determine whether the function is one-to-one.
Math Review Packet #5 Algebra II (Part 2) Notes
SCIE 0, Spring 0 Miller Math Review Packet #5 Algebra II (Part ) Notes Quadratic Functions (cont.) So far, we have onl looked at quadratic functions in which the term is squared. A more general form of
Higher. Functions and Graphs. Functions and Graphs 15
Higher Mathematics UNIT UTCME Functions and Graphs Contents Functions and Graphs 5 Set Theor 5 Functions 6 Inverse Functions 9 4 Eponential Functions 0 5 Introduction to Logarithms 0 6 Radians 7 Eact Values
Graphing Calculator Computations 2
Graphing Calculator Computations A) Write the graphing calculator notation and B) Evaluate each epression. 4 1) 15 43 8 e) 15 - -4 * 3^ + 8 ^ 4/ - 1) ) 5 ) 8 3 3) 3 4 1 8 3) 7 9 4) 1 3 5 4) 5) 5 5) 6)
If we plot the position of a moving object at increasing time intervals, we get a position time graph. This is sometimes called a distance time graph.
Physics Lecture #2: Position Time Graphs If we plot the position of a moving object at increasing time intervals, we get a position time graph. This is sometimes called a distance time graph. Suppose a
1.2 Functions and Their Properties PreCalculus
1. Functions and Their Properties PreCalculus 1. FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1. 1. Determine whether a set of numbers or a graph is a function. Find the domain of a function given
Algebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T7 GRAPHING LINEAR EQUATIONS REVIEW - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) TWO VARIABLE EQUATIONS = an equation containing two different variables. ) COEFFICIENT = the number in front
Answers for the problems can be found at the end of this packet starting on Page 12.
MAC 0 Review for Final Eam The eam will consists of problems similar to the ones below. When preparing, focus on understanding and general procedures (when available) rather than specific question. Answers
Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs
Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The
Chapter One. Chapter One
Chapter One Chapter One CHAPTER ONE Hughes Hallett et al c 005, John Wile & Sons ConcepTests and Answers and Comments for Section.. Which of the following functions has its domain identical with its range?
Diagnostic Tests Study Guide
California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra
review for math TSI 55 practice aafm m
Eam TSI Name review for math TSI practice 01704041700aafm042430m www.alvarezmathhelp.com MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the
A. Simplifying Polynomial Expressions
A. Simplifing Polnomial Epressions I. Combining Like Terms - You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same eponent(s). E. 1: 5-7 + 10 +
ZETA MATHS. Higher Mathematics Revision Checklist
ZETA MATHS Higher Mathematics Revision Checklist Contents: Epressions & Functions Page Logarithmic & Eponential Functions Addition Formulae. 3 Wave Function.... 4 Graphs of Functions. 5 Sets of Functions
Name Please print your name as it appears on the class roster.
Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes
One of your primary goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan.
PROBLEM SOLVING One of our primar goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan. Step Step Step Step Understand the problem. Read the problem
Math 103 Final Exam Review Problems Rockville Campus Fall 2006
Math Final Eam Review Problems Rockville Campus Fall. Define a. relation b. function. For each graph below, eplain why it is or is not a function. a. b. c. d.. Given + y = a. Find the -intercept. b. Find
INTRODUCTION GOOD LUCK!
INTRODUCTION The Summer Skills Assignment for has been developed to provide all learners of our St. Mar s Count Public Schools communit an opportunit to shore up their prerequisite mathematical skills
7-1. Exploring Exponential Models. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Cross out the expressions that are NOT powers.
7-1 Eploring Eponential Models Vocabular Review 1. Cross out the epressions that are NOT powers. 16 6a 1 7. Circle the eponents in the epressions below. 5 6 5a z Vocabular Builder eponential deca (noun)
Conic Sections CHAPTER OUTLINE. The Circle Ellipses and Hyperbolas Second-Degree Inequalities and Nonlinear Systems FIGURE 1
088_0_p676-7 /7/0 :5 PM Page 676 (FPG International / Telegraph Colour Librar) Conic Sections CHAPTER OUTLINE. The Circle. Ellipses and Hperbolas.3 Second-Degree Inequalities and Nonlinear Sstems O ne
Evaluate Logarithms and Graph Logarithmic Functions
TEKS 7.4 2A.4.C, 2A..A, 2A..B, 2A..C Before Now Evaluate Logarithms and Graph Logarithmic Functions You evaluated and graphed eponential functions. You will evaluate logarithms and graph logarithmic functions.
Student s Printed Name:
MATH 060 Test Fall 08 Calculus of One Variable I Version A KEY Sections.. Student s Printed Name: Instructor: XID: C Section: No questions will be answered during this eam. If ou consider a question to
Derivatives 2: The Derivative at a Point
Derivatives 2: The Derivative at a Point 69 Derivatives 2: The Derivative at a Point Model 1: Review of Velocit In the previous activit we eplored position functions (distance versus time) and learned
Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.
Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have
The letter m is used to denote the slope and we say that m = rise run = change in y change in x = 5 7. change in y change in x = 4 6 =
Section 4 3: Slope Introduction We use the term Slope to describe how steep a line is as ou move between an two points on the line. The slope or steepness is a ratio of the vertical change in (rise) compared
McKinney High School AP Calculus Summer Packet
McKinne High School AP Calculus Summer Packet (for students entering AP Calculus AB or AP Calculus BC) Name:. This packet is to be handed in to our Calculus teacher the first week of school.. ALL work
Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function.
Unit 2 Notes Packet on Quadratic Functions and Factoring
Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a
Information Knowledge
ation ledge -How m lio Learner's Name: ALGEBRA II CAPACITY TRANSCRIPT Equations & Inequalities (Chapter 1) [L1.2.1, A1.1.4, A1.2.9, L3.2.1] Linear Equations and (Chapter 2) [L1.2.1, A1.2.9, A2.3.3, A3.1.2,
Law of Sines, Law of Cosines, Heron s Formula:
PreAP Math Analsis nd Semester Review Law of Sines, Law of Cosines, Heron s Formula:. Determine how man solutions the triangle has and eplain our reasoning. (FIND YOUR FLOW CHART) a. A = 4, a = 4 ards,
Algebra/Pre-calc Review
Algebra/Pre-calc Review The following pages contain various algebra and pre-calculus topics that are used in the stud of calculus. These pages were designed so that students can refresh their knowledge
AB Calculus 2013 Summer Assignment. Theme 1: Linear Functions
01 Summer Assignment Theme 1: Linear Functions 1. Write the equation for the line through the point P(, -1) that is perpendicular to the line 5y = 7. (A) + 5y = -1 (B) 5 y = 8 (C) 5 y = 1 (D) 5 + y = 7
3.1 Graphing Quadratic Functions. Quadratic functions are of the form.
3.1 Graphing Quadratic Functions A. Quadratic Functions Completing the Square Quadratic functions are of the form. 3. It is easiest to graph quadratic functions when the are in the form using transformations.
5.6 RATIOnAl FUnCTIOnS. Using Arrow notation. learning ObjeCTIveS
CHAPTER PolNomiAl ANd rational functions learning ObjeCTIveS In this section, ou will: Use arrow notation. Solve applied problems involving rational functions. Find the domains of rational functions. Identif