RightStart Mathematics
|
|
|
- Silas Carroll
- 5 years ago
- Views:
Transcription
1 Most recent update: January 7, 2019 RigtStart Matematics Corrections and Updates for Level F/Grade 5 Lessons and Workseets, second edition LESSON / WORKSHEET CHANGE DATE CORRECTION OR UPDATE Lesson 7 04/18/2018 Lesson 16 Workseet 6 01/07/2019 Lesson 40 Workseet 29 01/07/2019 Lesson 41 12/29/2017 Lesson 54 Workseet 42-B 12/29/2017 Lesson 61 12/29/2017 Te Quotient and Remainder game instructions sould read: Place te dividend card, te multiplication card, first in te row, as sown below." Te second paragrap of Information on te workseet (and written in te lesson) sould read "In te expression 3 2, te exponent 2 means tat te number 3 is multiplied two times." See attaced pdf for te workseet. In te warm-up, te second sentence referring to dividing by te same number as been removed. See attaced pdf. On te second page in te middle of te page at te end of te paragrap, it sould read "Wat is te expression after multiplying by 10? [7.5/5]" It previously read 100. Te last equation in te "<, >, or " section sould read , not as printed. Answer is te lesson book is correct. Te tree answers for problems 2 4, Figure C, are wrong. Correct answers are igligted. Lesson 64 04/18/2018 Lesson 64 Workseet 52 04/11/2018 Lesson 66 Workseet 54 04/18/2018 Lesson 67 01/07/2019 Te answer for te last question in te Warm up sould be "multiply a side by itself or A s 2," not "multiply a side by 4 or A s 2." In te last cart on te page, te middle eading sould read Boundary Pairs 1, not Boundary Pairs. See attaced pdf. Questions sould read "Are te formulas for finding all correct?", not ""Are te formulas for finding are correct?" See attaced pdf. Te eigt measurements for te second and tird triangles in Problem 2 sould be 1.2, not 1.0. Tis canges te area to 0.78 in 2, not 0.7 in 2. See attaced pdf for te second page of te lesson.
2 Lesson 67 Workseet 55 01/07/2019 Lesson 70 Workseet 58 01/07/2019 Lesson 75 02/15/2018 Lesson 76 04/11/2018 Te instructions and figures ave canged sligtly. See attaced pdf. Te second sentence in Question 1 sould read, "Use a tangram to draw te eigt for bot triangles using te orizontal lines as te base." See attaced pdf. On te second page, te calculation for te triangular prism sould read 1/ for te base, calculating te volume at 19.7 cm 3. On te second page, last paragrap under te Problem 4 eading, te answer sould read 1,000,000,000, not 1,000, Lesson 91 04/18/2018 First answer for te warm up sould be 7 11/9 8 2/9, not 8 2/5. Lesson 94 04/18/2018 Answer for te tird Warm Up problem sould be 1 17/30. Lesson /07/2019 Lesson /18/2018 Lesson 134 Workseet /18/2018 Lesson /18/2018 Lesson 142 Workseet /18/2018 Te answers for te previous day's workseets as an incorrect answer (altoug it is rigt for Lesson 105). Te tird expression in te second column, 5/6 4/6, sould be 5/4, not 4/3. Last question in te conclusion sould read: Wat is 20 millimeters divided by 1 centimeter? [2], not Wat is 20 millimeters divided by 10 centimeters? [2] Information at te top of te page, conversion for km needs to read: 1 km 1000 m, not 1000 cm. See attaced pdf. Answer for Workseet 120-A, under te <, >, or section, 45 days < 2 monts. Second to last question and answer for Workseet 123 sould read: Wat is te name of a quadrilateral wit only two sides parallel? Answer trapezoid is correct. See attaced pdf. Lesson /07/2019 Question 22, sould be , not
3 Workseet 6, Square Numbers Warm-Up Divide. Use ceck numbers to ceck your answers. 4 ) ) ) INFORMATION: Exponents are a sortcut way of writing a number multiplied by itself a number of times. Te exponent is te small number written above te line. In te expression 3 2, te exponent 2 means tat te number 3 is multiplied two times. It means 3 3. We usually read it as 3 squared. In te same way, 4 2 means 4 4. Write 5 squared using exponents and using multiplication. Draw 1 2, 2 2, 3 2, 4 2, and 5 2 squares on te grid below. Label tem and find te values. On te multiplication table, evaluate and circle 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 8 2, 9 2, and Evaluate te following expressions. ( ) (3 + 4) (3 + 1) 2 (4 + 6) [10 2 (1 + 4)] [( ) (40 + 8)] 2 [( ) (5 3) 2 ] RigtStart Matematics Second Edition, F
4 Workseet 29, Dividing by Tents Warm-Up Multiply te numbers given. Use ceck numbers to ceck your work if you like ( ) 2 4 ( ) 3 8 ( ) ( ) ( ) ( ) Write te equations sown on te abacuses. Eac bead on te abacus represents If eac bead in te abacuses above suddenly explodes becoming ten times greater, wat appens to your answers? RigtStart Matematics Second Edition, F
5 Workseet 52, Area on te Geoboard A square formed by four pegs on te geoboard is 1 unit of area. Boundary points are pegs on te perimeter of te figure. A boundary pair is two boundary points. Fill in te table for eac figure below. Figures 1 to 5. Number of Pegs Area in Units Boundary Pairs Inside 1 2 Figures 6 to 8. Area in Units Number of Pegs Boundary Pairs Inside Figures 9 to 13. Area in Units Number of Pegs Boundary Pairs 1 Inside RigtStart Matematics Second Edition, F
6 Workseet 54, Introducing Formulas 1. Are te formulas for finding te perimeter, P, and area, A, of a rectangle all correct? Write yes or no. P w + + w + P 2w + 2 P w P 2(w + ) A 2(w ) A w w 2. Are te formulas for finding te perimeter, P, and area, A, of a square all correct? Write yes or no. P w + + w + P 2w + 2 P 2(w + ) P 4w A 2 (w + ) A w A w 2 A 2 w 3. Are te formulas for finding te perimeter, P, and area, A, of a parallelogram all correct? Write yes or no. P 2w + 2 P w s P 2(w + s) A 2(w ) A ws A w A w w s 4. Are te formulas for finding te perimeter, P, and area, A, of a triangle all correct? Write yes or no. P w + b + P 2w + 2 P w + b + a A w + A 1 2 (w ) A 1 2 A 1 2 w A w 2 (w + ) a w b RigtStart Matematics Second Edition, F
7 ACTIVITIES FOR TEACHING CONTINUED: Workseet 55, Problem 1. Tell te cild to read te instructions for te first problem. Tell im te eigts are drawn for im, but e needs to matc te correct eigts and widts. Te solutions are below. EXPLANATIONS CONTINUED: 135 A 3.7 cm 2 A 3.7 cm 2 A 3.7 cm 2 Problem 2. Tell im to complete te second problem on te workseet. Tell im to use te triangle to draw te perpendicular line. Te solutions are below. 1.5 in. Answers may vary sligtly. 1.1 in. 2.3 cm 2.1 cm 3.5 cm 2.4 cm 3.1 cm 3.2 cm A 1 2 w A A 1 2 w A A 1 2 w A in. 1.2 in. 1.2 in. 1.3 in. A 1 2 w A A 1 2 w A A 1 2 w A A 0.83 in 2 A 0.78 in 2 A 0.78 in 2 Ask: Wat kind of a triangle is tis? [isosceles acute triangle] Wy do you tink te answers are less accurate compared to Problem 1? [Rounding and te tents of an inc are larger tan te tents of a centimeter.] Problem 3. Tell te cild to complete te tird problem on te workseet. Tell im tat some of te sides of obtuse triangles need to be extended, wic is done for im. Te solutions are below. 3.0 cm Te calculated areas are not identical because te measurements are not exact. Te more accurate te measurements, te closer te calculated areas will be. 1.5 cm 5.6 cm 3.5 cm A 1 2 w A A 4.20 cm cm 2.5 cm A 1 2 w A A 4.35 cm 2 A 1 2 w A A 4.38 cm 2 In conclusion. Ask: Wat do you call a perpendicular line from a side of a triangle to te opposite vertex? [eigt] How many eigts are in a triangle? [tree] If tere is additional time following tis lesson, play te Find te Products game, found in Mat Card Games book, P33.
8 Workseet 55, Area of Triangles 1. Find te area of te triangle below in tree different ways. Measure to te nearest tent of a centimeter. 2. Find te area of te triangle below in tree different ways. Measure to te nearest tent of an inc. Calculate your answer to te nearest undredts. 3. Find te area of te triangle below in tree different ways. Measure to te nearest tent of a centimeter. Calculate your answer to te nearest undredts. RigtStart Matematics Second Edition, F
9 Workseet 115, Converting between Systems INFORMATION: Te definition of an inc is: 1 in cm. Conversions you may need: 1 km (kilometer) 1000 m 1 mi 5280 ft 1 yd 36 in. Use dimensional analysis to solve te problems. Do not round. You may use a calculator. 1. Find ow many centimeters are in a foot. 1 ft 1 ft ft in. Does your answer agree wit a ruler? 2. Find ow many centimeters are in a yard. ft 1 yd Does your answer agree wit a yardstick? 3. Find ow many kilometers are in a mile. ft cm m km 1 mi Wic is longer, a kilometer or a mile? Round your answer to one decimal point. 4. How many miles are in a kilometer? Use your unrounded answer from Problem 3. Round to two decimal places. RigtStart Matematics Second Edition, F
10 Workseet 58, Area of Trapezoids 1. Find te area of te trapezoid by breaking it into two triangles as sown below. Use a tangram to draw te eigt for bot triangles using te orizontal lines as te base. A. Measure in centimeters. B. Write a formula for te area. w 1 w 2 2. Find te area of te parallelogram. Ten find te area of one trapezoid. A. Measure in centimeters. B. Write te formulas for te areas. w 1 w 2 3. Find te area of te trapezoid in square centimeters by adding te areas of te parallelogram and triangle. 4. Find te area of te trapezoid in square centimeters using any metod. RigtStart Matematics Second Edition, F
11 Workseet 123, Classifying Quadrilaterals Write te following terms in te cart: no name, trapezoid, parallelogram, rombus, kite, quadrilateral, square, and rectangle. Use your drawing tools to draw a sample figure in eac of te six boxes. Ten answer te questions below. a polygon wit 4 sides no parallel sides only 1 set of parallel sides 2 sets of parallel sides 2 pairs of adjacent equal sides equal sides rigt angles Wat is te name of a rombus wit rigt angles? Wat is te name of a rectangle wit congruent sides? Wat is te name of a parallelogram wit rigt angles? Wat is te name of a quadrilateral wit only two sides parallel? Wat tree quadrilaterals can be made wit tese lines: RigtStart Matematics Second Edition, F
1. Which one of the following expressions is not equal to all the others? 1 C. 1 D. 25x. 2. Simplify this expression as much as possible.
004 Algebra Pretest answers and scoring Part A. Multiple coice questions. Directions: Circle te letter ( A, B, C, D, or E ) net to te correct answer. points eac, no partial credit. Wic one of te following
1watt=1W=1kg m 2 /s 3
Appendix A Matematics Appendix A.1 Units To measure a pysical quantity, you need a standard. Eac pysical quantity as certain units. A unit is just a standard we use to compare, e.g. a ruler. In tis laboratory
Continuity and Differentiability Worksheet
Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;
7.1 Using Antiderivatives to find Area
7.1 Using Antiderivatives to find Area Introduction finding te area under te grap of a nonnegative, continuous function f In tis section a formula is obtained for finding te area of te region bounded between
REVIEW LAB ANSWER KEY
REVIEW LAB ANSWER KEY. Witout using SN, find te derivative of eac of te following (you do not need to simplify your answers): a. f x 3x 3 5x x 6 f x 3 3x 5 x 0 b. g x 4 x x x notice te trick ere! x x g
Work with a partner. a. Write a formula for the area A of a parallelogram.
COMMON CORE Learning Standard HSA-CED.A.4 1. Rewriting Equations and Formulas Essential Question How can you use a formula for one measurement to write a formula for a different measurement? Using an Area
LIMITS AND DERIVATIVES CONDITIONS FOR THE EXISTENCE OF A LIMIT
LIMITS AND DERIVATIVES Te limit of a function is defined as te value of y tat te curve approaces, as x approaces a particular value. Te limit of f (x) as x approaces a is written as f (x) approaces, as
Math 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006
Mat 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006 f(x+) f(x) 10 1. For f(x) = x 2 + 2x 5, find ))))))))) and simplify completely. NOTE: **f(x+) is NOT f(x)+! f(x+) f(x) (x+) 2 + 2(x+) 5 ( x 2
Time (hours) Morphine sulfate (mg)
Mat Xa Fall 2002 Review Notes Limits and Definition of Derivative Important Information: 1 According to te most recent information from te Registrar, te Xa final exam will be eld from 9:15 am to 12:15
Exam 1 Review Solutions
Exam Review Solutions Please also review te old quizzes, and be sure tat you understand te omework problems. General notes: () Always give an algebraic reason for your answer (graps are not sufficient),
Models and Applications
Models and Applications 1 Modeling Tis Not tis 2 In Tis Section Create mat model from verbal description Simple interest problems Percentage problems Geometry formulas Literal equations Angle measurements
Lab 6 Derivatives and Mutant Bacteria
Lab 6 Derivatives and Mutant Bacteria Date: September 27, 20 Assignment Due Date: October 4, 20 Goal: In tis lab you will furter explore te concept of a derivative using R. You will use your knowledge
How to Find the Derivative of a Function: Calculus 1
Introduction How to Find te Derivative of a Function: Calculus 1 Calculus is not an easy matematics course Te fact tat you ave enrolled in suc a difficult subject indicates tat you are interested in te
MAT 145. Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points
MAT 15 Test #2 Name Solution Guide Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points Use te grap of a function sown ere as you respond to questions 1 to 8. 1. lim f (x) 0 2. lim
Section 2.1 The Definition of the Derivative. We are interested in finding the slope of the tangent line at a specific point.
Popper 6: Review of skills: Find tis difference quotient. f ( x ) f ( x) if f ( x) x Answer coices given in audio on te video. Section.1 Te Definition of te Derivative We are interested in finding te slope
Alaska Mathematics Standards Vocabulary Word List Grade 4
1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal
Polynomials 3: Powers of x 0 + h
near small binomial Capter 17 Polynomials 3: Powers of + Wile it is easy to compute wit powers of a counting-numerator, it is a lot more difficult to compute wit powers of a decimal-numerator. EXAMPLE
INTRODUCTION AND MATHEMATICAL CONCEPTS
INTODUCTION ND MTHEMTICL CONCEPTS PEVIEW Tis capter introduces you to te basic matematical tools for doing pysics. You will study units and converting between units, te trigonometric relationsips of sine,
Exponentials and Logarithms Review Part 2: Exponentials
Eponentials and Logaritms Review Part : Eponentials Notice te difference etween te functions: g( ) and f ( ) In te function g( ), te variale is te ase and te eponent is a constant. Tis is called a power
1 Limits and Continuity
1 Limits and Continuity 1.0 Tangent Lines, Velocities, Growt In tion 0.2, we estimated te slope of a line tangent to te grap of a function at a point. At te end of tion 0.3, we constructed a new function
Math 34A Practice Final Solutions Fall 2007
Mat 34A Practice Final Solutions Fall 007 Problem Find te derivatives of te following functions:. f(x) = 3x + e 3x. f(x) = x + x 3. f(x) = (x + a) 4. Is te function 3t 4t t 3 increasing or decreasing wen
INTRODUCTION AND MATHEMATICAL CONCEPTS
Capter 1 INTRODUCTION ND MTHEMTICL CONCEPTS PREVIEW Tis capter introduces you to te basic matematical tools for doing pysics. You will study units and converting between units, te trigonometric relationsips
Harbor Creek School District
Numeration Unit of Study Big Ideas Algebraic Concepts How do I match a story or equation to different symbols? How do I determine a missing symbol in an equation? How does understanding place value help
Higher Derivatives. Differentiable Functions
Calculus 1 Lia Vas Higer Derivatives. Differentiable Functions Te second derivative. Te derivative itself can be considered as a function. Te instantaneous rate of cange of tis function is te second derivative.
WYSE Academic Challenge 2004 Sectional Mathematics Solution Set
WYSE Academic Callenge 00 Sectional Matematics Solution Set. Answer: B. Since te equation can be written in te form x + y, we ave a major 5 semi-axis of lengt 5 and minor semi-axis of lengt. Tis means
b 1 A = bh h r V = pr
. Te use of a calculator is not permitted.. All variables and expressions used represent real numbers unless oterwise indicated.. Figures provided in tis test are drawn to scale unless oterwise indicated..
2.11 That s So Derivative
2.11 Tat s So Derivative Introduction to Differential Calculus Just as one defines instantaneous velocity in terms of average velocity, we now define te instantaneous rate of cange of a function at a point
CA LI FOR N I A STA N DA R DS TE ST CSG00185 C D CSG10066
LI FOR N I ST N R S TE ST 1 Wic of te following est descries deductive reasoning? using logic to draw conclusions ased on accepted statements accepting te meaning of a term witout definition defining matematical
MVT and Rolle s Theorem
AP Calculus CHAPTER 4 WORKSHEET APPLICATIONS OF DIFFERENTIATION MVT and Rolle s Teorem Name Seat # Date UNLESS INDICATED, DO NOT USE YOUR CALCULATOR FOR ANY OF THESE QUESTIONS In problems 1 and, state
1 2 x Solution. The function f x is only defined when x 0, so we will assume that x 0 for the remainder of the solution. f x. f x h f x.
Problem. Let f x x. Using te definition of te derivative prove tat f x x Solution. Te function f x is only defined wen x 0, so we will assume tat x 0 for te remainder of te solution. By te definition of
California 5 th Grade Standards / Excel Math Correlation by Lesson Number
(Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with
WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5
May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 NUMBER AND NUMBER SENSE 5.1 The student will a. read, write, and identify the place values
Consider a function f we ll specify which assumptions we need to make about it in a minute. Let us reformulate the integral. 1 f(x) dx.
Capter 2 Integrals as sums and derivatives as differences We now switc to te simplest metods for integrating or differentiating a function from its function samples. A careful study of Taylor expansions
4. The slope of the line 2x 7y = 8 is (a) 2/7 (b) 7/2 (c) 2 (d) 2/7 (e) None of these.
Mat 11. Test Form N Fall 016 Name. Instructions. Te first eleven problems are wort points eac. Te last six problems are wort 5 points eac. For te last six problems, you must use relevant metods of algebra
3.4 Worksheet: Proof of the Chain Rule NAME
Mat 1170 3.4 Workseet: Proof of te Cain Rule NAME Te Cain Rule So far we are able to differentiate all types of functions. For example: polynomials, rational, root, and trigonometric functions. We are
Combining functions: algebraic methods
Combining functions: algebraic metods Functions can be added, subtracted, multiplied, divided, and raised to a power, just like numbers or algebra expressions. If f(x) = x 2 and g(x) = x + 2, clearly f(x)
MTH 119 Pre Calculus I Essex County College Division of Mathematics Sample Review Questions 1 Created April 17, 2007
MTH 9 Pre Calculus I Essex County College Division of Matematics Sample Review Questions Created April 7, 007 At Essex County College you sould be prepared to sow all work clearly and in order, ending
GRADE 7 MATHEMATICS NEW TEKS. STAAR Readiness Review and Practice. Use with Your Students!
Use wit Your Students! GRADE MATHEMATICS STAAR Readiness Review and Practice NEW TEKS Readiness TEKS Lessons Over autentic STAAR practice items -step approac for efficient remediation STAAR is a registered
Average Rate of Change
Te Derivative Tis can be tougt of as an attempt to draw a parallel (pysically and metaporically) between a line and a curve, applying te concept of slope to someting tat isn't actually straigt. Te slope
Phy 231 Sp 02 Homework #6 Page 1 of 4
Py 231 Sp 02 Homework #6 Page 1 of 4 6-1A. Te force sown in te force-time diagram at te rigt versus time acts on a 2 kg mass. Wat is te impulse of te force on te mass from 0 to 5 sec? (a) 9 N-s (b) 6 N-s
Introduction to Derivatives
Introduction to Derivatives 5-Minute Review: Instantaneous Rates and Tangent Slope Recall te analogy tat we developed earlier First we saw tat te secant slope of te line troug te two points (a, f (a))
We name Functions f (x) or g(x) etc.
Section 2 1B: Function Notation Bot of te equations y 2x +1 and y 3x 2 are functions. It is common to ave two or more functions in terms of x in te same problem. If I ask you wat is te value for y if x
A = h w (1) Error Analysis Physics 141
Introduction In all brances of pysical science and engineering one deals constantly wit numbers wic results more or less directly from experimental observations. Experimental observations always ave inaccuracies.
. Compute the following limits.
Today: Tangent Lines and te Derivative at a Point Warmup:. Let f(x) =x. Compute te following limits. f( + ) f() (a) lim f( +) f( ) (b) lim. Let g(x) = x. Compute te following limits. g(3 + ) g(3) (a) lim
MATH 1020 Answer Key TEST 2 VERSION B Fall Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
Math 312 Lecture Notes Modeling
Mat 3 Lecture Notes Modeling Warren Weckesser Department of Matematics Colgate University 5 7 January 006 Classifying Matematical Models An Example We consider te following scenario. During a storm, a
1. AB Calculus Introduction
1. AB Calculus Introduction Before we get into wat calculus is, ere are several eamples of wat you could do BC (before calculus) and wat you will be able to do at te end of tis course. Eample 1: On April
1 The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256) 1.1 Limits Consider the function determined by the formula 3. x since at this point
MA00 Capter 6 Calculus and Basic Linear Algebra I Limits, Continuity and Differentiability Te concept of its (p.7 p.9, p.4 p.49, p.55 p.56). Limits Consider te function determined by te formula f Note
CCSD Practice Proficiency Exam Spring 2011
Spring 011 1. Use te grap below. Weigt (lb) 00 190 180 170 160 150 140 10 10 110 100 90 58 59 60 61 6 6 64 65 66 67 68 69 70 71 Heigt (in.) Wic table represents te information sown in te grap? Heigt (in.)
Grade Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts.
Unit 1 Number Theory 1 a B Find the prime factorization of numbers (Lesson 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1b BD Rename numbers written in exponential
Precalculus Test 2 Practice Questions Page 1. Note: You can expect other types of questions on the test than the ones presented here!
Precalculus Test 2 Practice Questions Page Note: You can expect oter types of questions on te test tan te ones presented ere! Questions Example. Find te vertex of te quadratic f(x) = 4x 2 x. Example 2.
5.1 We will begin this section with the definition of a rational expression. We
Basic Properties and Reducing to Lowest Terms 5.1 We will begin tis section wit te definition of a rational epression. We will ten state te two basic properties associated wit rational epressions and go
Exercises for numerical differentiation. Øyvind Ryan
Exercises for numerical differentiation Øyvind Ryan February 25, 2013 1. Mark eac of te following statements as true or false. a. Wen we use te approximation f (a) (f (a +) f (a))/ on a computer, we can
Chapter 1 Functions and Graphs. Section 1.5 = = = 4. Check Point Exercises The slope of the line y = 3x+ 1 is 3.
Capter Functions and Graps Section. Ceck Point Exercises. Te slope of te line y x+ is. y y m( x x y ( x ( y ( x+ point-slope y x+ 6 y x+ slope-intercept. a. Write te equation in slope-intercept form: x+
Material for Difference Quotient
Material for Difference Quotient Prepared by Stepanie Quintal, graduate student and Marvin Stick, professor Dept. of Matematical Sciences, UMass Lowell Summer 05 Preface Te following difference quotient
The derivative function
Roberto s Notes on Differential Calculus Capter : Definition of derivative Section Te derivative function Wat you need to know already: f is at a point on its grap and ow to compute it. Wat te derivative
2.8 The Derivative as a Function
.8 Te Derivative as a Function Typically, we can find te derivative of a function f at many points of its domain: Definition. Suppose tat f is a function wic is differentiable at every point of an open
lim 1 lim 4 Precalculus Notes: Unit 10 Concepts of Calculus
Syllabus Objectives: 1.1 Te student will understand and apply te concept of te limit of a function at given values of te domain. 1. Te student will find te limit of a function at given values of te domain.
Function Composition and Chain Rules
Function Composition and s James K. Peterson Department of Biological Sciences and Department of Matematical Sciences Clemson University Marc 8, 2017 Outline 1 Function Composition and Continuity 2 Function
2.3. Applying Newton s Laws of Motion. Objects in Equilibrium
Appling Newton s Laws of Motion As ou read in Section 2.2, Newton s laws of motion describe ow objects move as a result of different forces. In tis section, ou will appl Newton s laws to objects subjected
Blueprint Algebra I Test
Blueprint Algebra I Test Spring 2003 2003 by te Commonwealt of Virginia Department of Education, James Monroe Building, 101 N. 14t Street, Ricmond, Virginia, 23219. All rigts reserved. Except as permitted
Section 2: The Derivative Definition of the Derivative
Capter 2 Te Derivative Applied Calculus 80 Section 2: Te Derivative Definition of te Derivative Suppose we drop a tomato from te top of a 00 foot building and time its fall. Time (sec) Heigt (ft) 0.0 00
Finding and Using Derivative The shortcuts
Calculus 1 Lia Vas Finding and Using Derivative Te sortcuts We ave seen tat te formula f f(x+) f(x) (x) = lim 0 is manageable for relatively simple functions like a linear or quadratic. For more complex
NUMERICAL DIFFERENTIATION. James T. Smith San Francisco State University. In calculus classes, you compute derivatives algebraically: for example,
NUMERICAL DIFFERENTIATION James T Smit San Francisco State University In calculus classes, you compute derivatives algebraically: for example, f( x) = x + x f ( x) = x x Tis tecnique requires your knowing
Math Test No Calculator
Mat Test No Calculator MINUTES, QUESTIONS Turn to Section of your answer seet to answer te questions in tis section. For questions -, solve eac problem, coose te best answer from te coices provided, and
Geometric Formulas (page 474) Name
LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:
PRE-ALGEBRA SUMMARY WHOLE NUMBERS
PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in
Solutions Manual for Precalculus An Investigation of Functions
Solutions Manual for Precalculus An Investigation of Functions David Lippman, Melonie Rasmussen 1 st Edition Solutions created at Te Evergreen State College and Soreline Community College 1.1 Solutions
1 1. Rationalize the denominator and fully simplify the radical expression 3 3. Solution: = 1 = 3 3 = 2
MTH - Spring 04 Exam Review (Solutions) Exam : February 5t 6:00-7:0 Tis exam review contains questions similar to tose you sould expect to see on Exam. Te questions included in tis review, owever, are
( ( ) cos Chapter 21 Exercise 21.1 Q = 13 (ii) x = Q. 1. (i) x = = 37 (iii) x = = 99 (iv) x =
Capter 1 Eercise 1.1 Q. 1. (i) = 1 + 5 = 1 (ii) = 1 + 5 = 7 (iii) = 1 0 = 99 (iv) = 41 40 = 9 (v) = 61 11 = 60 (vi) = 65 6 = 16 Q.. (i) = 8 sin 1 = 4.1 5.5 (ii) = cos 68 = 14.7 1 (iii) = sin 49 = 15.9
Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
California 3 rd Grade Standards / Excel Math Correlation by Lesson Number
California 3 rd Grade Standards / Lesson (Activity) L1 L2 L3 L4 L5 L6 L7 L8 Excel Math Lesson Objective Learning about the tens place and the ones place; adding and subtracting two-digit numbers; learning
CHAPTER (A) When x = 2, y = 6, so f( 2) = 6. (B) When y = 4, x can equal 6, 2, or 4.
SECTION 3-1 101 CHAPTER 3 Section 3-1 1. No. A correspondence between two sets is a function only if eactly one element of te second set corresponds to eac element of te first set. 3. Te domain of a function
3.1 Extreme Values of a Function
.1 Etreme Values of a Function Section.1 Notes Page 1 One application of te derivative is finding minimum and maimum values off a grap. In precalculus we were only able to do tis wit quadratics by find
Excursions in Computing Science: Week v Milli-micro-nano-..math Part II
Excursions in Computing Science: Week v Milli-micro-nano-..mat Part II T. H. Merrett McGill University, Montreal, Canada June, 5 I. Prefatory Notes. Cube root of 8. Almost every calculator as a square-root
Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
WORD RESOURCE CARDS 2 5 = cubic unit 12 cubic units. 1 in. 1 square mm 1 mm 2. 1 in. 1 cm 1 cm. 1 square inch 1 in. 2
WORD RESOURCE CARDS volume 1 cubic unit 12 cubic units product 2 5 = 10 5 2 10 2 5 10 3 5 square unit 1 in. 1 in. 1 cm 1 cm 1 square mm 1 mm 2 1 square inch 1 in. 2 1 square centimeter 1 cm 2 The Grades
Derivatives of Exponentials
mat 0 more on derivatives: day 0 Derivatives of Eponentials Recall tat DEFINITION... An eponential function as te form f () =a, were te base is a real number a > 0. Te domain of an eponential function
pancakes. A typical pancake also appears in the sketch above. The pancake at height x (which is the fraction x of the total height of the cone) has
Volumes One can epress volumes of regions in tree dimensions as integrals using te same strateg as we used to epress areas of regions in two dimensions as integrals approimate te region b a union of small,
4R & 4A Math Pacing Guides
GRADING PERIOD: 1st Nine Weeks Getting to Know You - Community Building 4.14- Data a. Collect data, using observations, surveys, measurement, polls, or questionnaires. b. Organize data into a chart or
2.1 THE DEFINITION OF DERIVATIVE
2.1 Te Derivative Contemporary Calculus 2.1 THE DEFINITION OF DERIVATIVE 1 Te grapical idea of a slope of a tangent line is very useful, but for some uses we need a more algebraic definition of te derivative
Section 15.6 Directional Derivatives and the Gradient Vector
Section 15.6 Directional Derivatives and te Gradient Vector Finding rates of cange in different directions Recall tat wen we first started considering derivatives of functions of more tan one variable,
5. (a) Find the slope of the tangent line to the parabola y = x + 2x
MATH 141 090 Homework Solutions Fall 00 Section.6: Pages 148 150 3. Consider te slope of te given curve at eac of te five points sown (see text for figure). List tese five slopes in decreasing order and
MATH 1020 TEST 2 VERSION A FALL 2014 ANSWER KEY. Printed Name: Section #: Instructor:
ANSWER KEY Printed Name: Section #: Instructor: Please do not ask questions during tis eam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide
Mathematics 105 Calculus I. Exam 1. February 13, Solution Guide
Matematics 05 Calculus I Exam February, 009 Your Name: Solution Guide Tere are 6 total problems in tis exam. On eac problem, you must sow all your work, or oterwise torougly explain your conclusions. Tere
Lesson 6: The Derivative
Lesson 6: Te Derivative Def. A difference quotient for a function as te form f(x + ) f(x) (x + ) x f(x + x) f(x) (x + x) x f(a + ) f(a) (a + ) a Notice tat a difference quotient always as te form of cange
f a h f a h h lim lim
Te Derivative Te derivative of a function f at a (denoted f a) is f a if tis it exists. An alternative way of defining f a is f a x a fa fa fx fa x a Note tat te tangent line to te grap of f at te point
Numeracy. Introduction to Measurement
Numeracy Introduction to Measurement Te metric system originates back to te 700s in France. It is known as a decimal system because conversions between units are based on powers of ten. Tis is quite different
2011 Fermat Contest (Grade 11)
Te CENTRE for EDUCATION in MATHEMATICS and COMPUTING 011 Fermat Contest (Grade 11) Tursday, February 4, 011 Solutions 010 Centre for Education in Matematics and Computing 011 Fermat Contest Solutions Page
Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12
1. (a) 3. (a) 4 3 (b) (a) t = 5: 9. (a) = 11. (a) The equation of the line through P = (2, 3) and Q = (8, 11) is y 3 = 8 6
A Answers Important Note about Precision of Answers: In many of te problems in tis book you are required to read information from a grap and to calculate wit tat information. You sould take reasonable
LIMITATIONS OF EULER S METHOD FOR NUMERICAL INTEGRATION
LIMITATIONS OF EULER S METHOD FOR NUMERICAL INTEGRATION LAURA EVANS.. Introduction Not all differential equations can be explicitly solved for y. Tis can be problematic if we need to know te value of y
Analysis of California Mathematics standards to Common Core standards Grade 4
Analysis of California Mathematics standards to Common Core standards Grade 4 Strand CA Math Standard Domain Common Core Standard (CCS) Alignment Comments in Reference to CCS Strand Number Sense CA Math
Section 2.4: Definition of Function
Section.4: Definition of Function Objectives Upon completion of tis lesson, you will be able to: Given a function, find and simplify a difference quotient: f ( + ) f ( ), 0 for: o Polynomial functions
Chapter 2. Limits and Continuity 16( ) 16( 9) = = 001. Section 2.1 Rates of Change and Limits (pp ) Quick Review 2.1
Capter Limits and Continuity Section. Rates of Cange and Limits (pp. 969) Quick Review..... f ( ) ( ) ( ) 0 ( ) f ( ) f ( ) sin π sin π 0 f ( ). < < < 6. < c c < < c 7. < < < < < 8. 9. 0. c < d d < c
Teaching Differentiation: A Rare Case for the Problem of the Slope of the Tangent Line
Teacing Differentiation: A Rare Case for te Problem of te Slope of te Tangent Line arxiv:1805.00343v1 [mat.ho] 29 Apr 2018 Roman Kvasov Department of Matematics University of Puerto Rico at Aguadilla Aguadilla,
Chapter 4: Numerical Methods for Common Mathematical Problems
1 Capter 4: Numerical Metods for Common Matematical Problems Interpolation Problem: Suppose we ave data defined at a discrete set of points (x i, y i ), i = 0, 1,..., N. Often it is useful to ave a smoot
Differential Calculus (The basics) Prepared by Mr. C. Hull
Differential Calculus Te basics) A : Limits In tis work on limits, we will deal only wit functions i.e. tose relationsips in wic an input variable ) defines a unique output variable y). Wen we work wit
11-19 PROGRESSION. A level Mathematics. Pure Mathematics
SSaa m m pplle e UCa ni p t ter DD iff if erfe enren tiatia tiotio nn - 9 RGRSSIN decel Slevel andmatematics level Matematics ure Matematics NW FR 07 Year/S Year decel S and level Matematics Sample material
St. Ann s Academy - Mathematics
St. Ann s Academy - Mathematics Students at St. Ann s Academy will be able to reason abstractly and quantitatively. Students will define, explain, and understand different types of word problems (simple