...Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Sketching curves Exercise E, Question 2 Question: (a) Sketch the curve y = f(x) where f(x) = (x − 1)(x + 2). (b) On separate diagrams sketch the graphs of (i) y = f(x + 2) (ii) y = f(x) + 2. (c) Find the equations of the curves y = f(x + 2) and y = f(x) + 2, in terms of x, and use these equations to find the coordinates of the points where your graphs in part (b) cross the y-axis. Solution: (a) f(x) = 0 ⇒ x = 1, − 2 (b)(i) f(x + 2) is a horizontal translation of − 2. (ii) f(x) + 2 is a vertical translation of + 2 Since axis of symmetry of f(x) is at x = − , the same axis of symmetry applies to f(x) + 2. Since one root is at x = 0, the other must be symmetric at x = − 1. (c) y = f(x + 2) is y = (x + 1)(x + 4). So x = 0 ⇒ y = 4 1 2 file://C:\Users\Buba\kaz\ouba\c1_4_e_2.html 3/10/2013 Heinemann Solutionbank: Core Maths 1 C1 Page 2 of 2 y = f(x) + 2 is y = x © Pearson Education Ltd 2008 2 + x = x(x + 1). So x = 0 ⇒ y = 0 file://C:\Users\Buba\kaz\ouba\c1_4_e_2.html 3/10/2013 Heinemann Solutionbank: Core Maths 1 C1 Page 1 of 2 Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Sketching curves Exercise E, Question 4 Question: (a) Sketch the graph of y = f(x) where f(x) = x(x − 2)2 (b) Sketch the curves with equations y = f(x) + 2 and y = f(x + 2). (c) Find the coordinates of the points where the...
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...Case Study 1: The Big Data Challenges Judge how Volvo Car Corporation integrated the cloud infrastructure into its networks. The Volvo Car Corporation integrated the cloud infrastructure into its networks to capture data from Volvo vehicles to help build better cars and to help the customer have a better experience. Data is now being captured for use within the vehicle itself, and increasingly, for transmission via the cloud back to the manufacturer. At Volvo, those huge volumes streamed into a centralized analysis hub, the Volvo Data Warehouse, alongside data from customer relationship systems, dealership systems, and product development and design systems (Global Intelligence for the CIO, 2011). The Volvo Car Corporation wanted to create an effective marketing strategy to tie in with the movie trilogy Twilight franchise by creating an interactive game that would engage the global community. The idea for the game was that users could play to win a new Volvo XC60 car. However, the company's existing technology infrastructure could not provide the scalability required to fulfill the vision, and expanding it would be cost-prohibitive. After consulting with Microsoft Gold Certified Partner LBi to evaluate options, Volvo selected the Windows Azure cloud-computing platform (Microsoft, 2011). In an effort to address, its needs for a cost-effective infrastructure that provided the ability to quickly scale up to handle a high volume of traffic and that would also serve...
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...Worksheet Math 124 Week 1 Worksheet for Week 1: Circles and lines This worksheet is a review of circles and lines, and will give you some practice with algebra and with graphing. Also, this worksheet introduces the idea of “tangent lines” to circles. Later on in Math 124, you’ll learn how to find tangent lines to many other types of curves. 1. Two circles, called C1 and C2 , are graphed below. The center of C1 is at the origin, and the center of C2 is the point in the first quadrant where the line y = x intersects C1 . Suppose C1 has radius 2. C2 touches the x and y axes each in one point. What are the equations of the two circles? y y=x C2 x C1 Worksheet Math 124 Week 1 2. Let C be the circle of radius 5 centered at the origin. The tangent line to C at a point Q is the line through Q that’s perpendicular to the radial line connecting Q to the center. (See picture.) Use this information to find the equations of the tangent lines at P and Q below. y Q P x Note: Later in Math 124, you’ll learn how to find tangent lines to curves that are not circles! Page 2 Worksheet Math 124 Week 1 3. Sketch the circle of radius 2 centered at (3, −3) and the line L with equation y = 2x + 2. Find the coordinates of all the points on the circle where the tangent line is perpendicular to L. y x Page 3 Worksheet Math 124 Week 1 4. Draw the circle with equation x2 +y 2 = 25 and the points P = (−3, −4) and Q = (−8, 0). Explain why P is on...
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...Solution Nguyen Van Linh,11A2 Math, Highshool for gifted student, Ha Noi University of Science, Vietnam 4/1/2010 Problem: Given a cyclic pentagon ABCDE.AD ∩ EB = {X}, AD ∩ EC = {L}, AC ∩ EB = {Y }, AC ∩ BD = {Z}, EC ∩ BD = {T }. (EAX) ∩ (ABY ) = {A1 }, (ABY ) ∩ (BCZ) = {B1 }, (BZC) ∩ (DT C) = {C1 }, (DT C) ∩ (ELD) = {D1 }, (ELD) ∩ (EAX) = {E1 }. Prove that A1 B1 C1 D1 E1 is a cyclic pentagon. Solution: First we will express a lemma: Given a pentagon ABCDE.A1 , B1 , C1 , D1 , E1 , A2 , B2 , C2 , D2 , E2 are defined as the figure below. Then AA2 , BB2 , CC2 , DD2 , EE2 are concurrent. A2 A y1 E x3 z3 C1 x2 E2 E3 y 2 O B1 D1 x1 A3 D3 z2 C3 B B2 B3 E1 y3 A1 D2 D C2 z1 C Proof: Denote A3 = AA2 ∩ BE, similar we define B3 , C3 , D3 , E3 . Denote O1 = AA3 ∩ EE3 , O2 = AA3 ∩ BB3 . We will show that O1 ≡ O2 ⇔ Applying Menelaus’s theorem : AO1 EA3 E3 C1 . . =1 A3 O1 EC1 E3 A AO1 AO2 = .(∗) O 1 A3 O2 A3 AO2 A3 B B3 D1 . . = 1. A3 O2 BD1 B3 A EA3 E3 C1 A3 B B3 D1 So (∗) is true iff . = . (∗∗) EC1 E3 A BD1 B3 A Put BD1 = x1 , D1 C1 = x2 , C1 E = x3 , AC1 = y1 , C1 B1 = y2 , B1 D = y3 , CE1 = z1 , E1 D1 = z2 , D1 A = z3 . BA3 A3 C1 x2 (x2 + x1 ) We have A3 D1 .A3 B = A3 C1 .A3 E then = . So we can calculate EA3 = ,similar EA3 A3 D1 x1 + 2x2 + x3 with E3 C1 , E3 A, A3 B, B3 D1 , B3 A. and 1 y2 (y2 + y3 ) z2 (z2 + z1 ) x2 (x2 + x1 ) x2 (x2 + x3 ) + x3 ...
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...Download Now for Free PDF Ebook Lakeside Hospital Case Solution at our Online Ebook Library. Get Lakeside Hospital Case Solution PDF file for free from our online library LAKESIDE HOSPITAL CASE SOLUTION PDF Download: LAKESIDE HOSPITAL CASE SOLUTION PDF LAKESIDE HOSPITAL CASE SOLUTION PDF - Are you looking for Ebook lakeside hospital case solution PDF? You will be glad to know that right now lakeside hospital case solution PDF is available on our online library. With our online resources, you can find lakeside hospital case solution or just about any type of ebooks, for any type of product. Best of all, they are entirely free to find, use and download, so there is no cost or stress at all. lakeside hospital case solution PDF may not make exciting reading, but lakeside hospital case solution is packed with valuable instructions, information and warnings. We also have many ebooks and user guide is also related with lakeside hospital case solution PDF, include : Applied Calculus 4th Edition Even Answers, Basic Chemical Solutions, Catalytic Solutions Inc Case Study, Calculus Early Transcendentals 7th Edition Yonsei Solutions, Congress Scavenger Hunt Answers, College Algebra Textbook Answers 2, Congress Of Vienna Guided Answers, Chapter 18 Study Guide Answers, English Grammar Third Edition Answer Key, Fac1502 Oct Nov 2012 Solution Docx, Food Safety Test Questions And Answers, Hayden Mcneil Bio 101 Lab Manual Answers, Harcourt Trophies 5th Grade Answer Key, Holt Mathematics Lesson 9...
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...AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH Fall’ 2014-2015 MID-TERM EXAM SCHEDULE [Revised on October 12, 2014] Day 1: Saturday (October 18, 2014) TIME Campus 1, 5 & 4 PRINCIPLES OF ECONOMICS ECONOMIC GEOGRAPHY MEASUREMENT & INSTRUMENTATION BASIC PLANNING CATERING & BANQUET MGMT. [THM] SELECTION AND STAFFING [HRM] INTRODUCTION TO PSYCHOLOGY Campus 7 SECTIONS A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R A,B,C,D,E,F,G,H,I,J A A A A,B,C A A,B,C1,C2,C3,C4,C5 A,B A,B,C A A,B,C,D,E,F A,B,C A,B,C A A,B,C,D B,C,D,E,F,G,I,J,K,L A A,B,C,D,E,F,G,H,I,J,K,L,M,N,O A A A,B,C,D,E,G A A A,B A,B,C,D,E,F,G,H A,E,F,G,H,I A A,B,C A A A,B A A A A A,B,C,D,E,F,G,H,I,J,K,L,M,N A,B,C,D,E,F,G 9:3011:30 CHEMISTRY BRAND & PRODUCT MGMT.[MKT.] GLOBAL FINANCE GLOBAL FINANCE (ECO) MODERN PHYSICS SOFTWARE DEV. & PRO. MGMT. THEORY OF COMPUTATION PROFESSIONAL PRACTICE FINANCIAL INSTITUTIONS AND MARKETS LEGAL ENVIRONMENT IN BUSINESS CYBER JOURNALISM 12-2 PHYSICS 2 STRUCTURE-II (REINFORCED CONCRETE DESIGN) STRUCTURE-I (BASIC MECHANICS OF SOLIDS) CONTROL SYSTEM ADVANCED SOCIOLINGUISTICS & WORLD ENGLISHES ROMANTIC POETRY FINANCIAL STATEMENT ANALYSIS BASICS IN SOCIAL SCIENCE ENTREPRENEURSHIP DEVELOPMENT MUSIC APPRICATION TRAINING & DEVELOPMENT [HRM] COMPUTER VISION & PATTERN RECOGNITION VISUAL ENVIRONMENT SOFTWARE REQUIREMENT ENG. RURAL MARKETING [MKT.] INTRODUCTION TO COMMUNICATION PROFESSIONAL ENGLISH TRADE & DEVELPOMENT IN ECONOMICS STATISTICS & PROBABILITY POWER STATIONS 3-5 Revised on October12, 2014 ...
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...GLOBAL FINANCE MODERN PHYSICS THEORY OF COMPUTATION FINANCIAL INSTITUTIONS AND MARKETS LEGAL ENVIRONMENT IN BUSINESS BRAND & PRODUCT MGMT.[MKT.] INTRO. TO SOCIOLINGUISTICS 12-2 3-5 PHYSICS 2 LEGAL SYSTEM OF BANGLADESH [LAW] BUILDING AND FINISH MATERIALS STRUCTURE-I (BASIC MECHANICS OF SOLIDS) CONTROL SYSTEM BASICS IN SOCIAL SCIENCE ENTREPRENEURSHIP DEVELOPMENT TRAINING & DEVELOPMENT [HRM] SOFTWARE REQUIREMENT ENG. RURAL MARKETING [MKT.] PROFESSIONAL PRACTICE STATISTICS & PROBABILITY STATISTICS & PROBABILITY CONTEMPORARY ISSUES IN GLOBAL ECONOMY INTRODUCTION TO ECONOMICS PUBLIC SPEAKING POWER STATIONS Released on March 29, 2016 SECTIONS A,B,C,D,E,F,G,H,I,J,K,L,M,O,P,Q,R A,B,C,D,E A A,B A A A,B A,C1,C2,C3,C4,C5,C6,C7,C8 A A A,B,C A,B,C,D,E,F,G,H A,B,C,D,E,F,G,H,I A,B,C B,C,D,I,J A,B A A,B,C,D,E,F,G,H,I,J,K,L,M,N,O F1 A A A,C,D A,B,C,E,F,G,H,I, A,B,C,E,F,G,H,I A A,B,C A A N,O,P,Q A,B,C,D,E,F,G,H,I,J,K,L,M A A A A,B,C,D,E,F,G Day 2: April 24, 2016 (Sunday) TIME Building 1, 5 & 4 BUSINESS MATHEMATICS – 1 BASICS IN NATURAL SCIENCE ISLAMIC FINANCE & BANKING CONTEMPORARY ARCH. THEORY Building 7 COMPUTER NETWORKS MULTIMEDIA SYSTEMS ANALOG ELECTRONICS 1 9:3011:30 INTERMEDIATE MICROECONOMICS BIOMEDICAL INST. MEASUREMENT & DESIGN SALES MANAGEMENT [MKT.] INTRODUCTION TO SOCIOLOGY LOGIC AND PHILISOPHY 12-2 BUSINESS...
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...[pic] ENGD3016 Solid Mechanics Assignment 1: Finite Element Analysis Name: Wei Zhang ID: P14021978 Date: Dec17th 2015 Abstract 1.0 Introduction 2.0 Objectives 3.0 Matlab 4.0 Solidworks 4.1 Model of truss 1 4.2 Model of truss 2 5.0 Comparison of the two trusses 6.0 Comparison between MATLAB and SOLIDWORKS 6.1 Comparison of results 6.2 Advantages and disadvantages 7.0 Conclusion Appendix Abstract The purpose of this report is to based on two different 2D pictures of trusses to finite element analysis from two ways. First carried out the selection of materials, and choosing the size of the pipe. Two methods were used two different software for finite element analysis, solidworks and MATLAB. By comparing the simulation results with two software to make sure which is the better way. It was found that the results of MATLAB are more accurate, solidworks results more intuitive. According to the calculation results of the two methods, truss 2 is more reliable. 1.0 Introduction Finite element analysis method using a mathematical approximation of the real physical system to simulation. Also use simple and interacting elements, namely unit, you can use a limited number of unknown quantities to approximate the infinite unknowns real system.The engineering is relying on the...
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...12-2 PHYSICS 2 STRUCTURE-II (REINFORCED CONCRETE DESIGN) STRUCTURE-I (BASIC MECHANICS OF SOLIDS) CONTROL SYSTEM DATA WAREHOUSING AND DATA MINING [CS] PHONETICS AND PHONOLOGY LANGUAGE TESTING FINANCIAL STATEMENT ANALYSIS BASICS IN SOCIAL SCIENCE ENTREPRENEURSHIP DEVELOPMENT MUSIC APPRICATION GLOBAL OPERATIONS MANAGEMENT MULTIMEDIA SYSTEMS [CS] TRAINING & DEVELOPMENT COMPUTER VISION & PATTERN RECOGNITION 3-5 VISUAL ENVIRONMENT SOFTWARE REQUIREMENT ENG. STATISTICS & PROBABILITY INTRODUCTION TO STATISTICS [ECO] POWER STATIONS RURAL MARKETING ADVERTISING AND PUBLIC POLICY INTRODUCTION TO SOCIOLINGUISTICS CONTEMPORARY ISSUES IN GLOBAL ECONOMY [ECO] Campus 7 SECTIONS A,B,C,D,E,F,G,H,I,J,K A,B,C,D,E,F,G,H A,B,D A A A A,B A,B,B1,B2,B3,B4,B6,B8,B9,B10, C1,C2, C3,C5,C6,C7,C4,D A A,B,C,D,E,F,G,H A A A A A,B A,B,C,D A A,B,D,E B,C,D,E,F,G,H,I,J,K,L A A,B,C,D,E,F,G,H,I,J,K,L,M,N A A A,B,C,D,G A A A A,B A,B,C,D,E,F,G,H,I,J,L,M A,B,C,E,F,G,H,I A A A A,B A A A A,B,C,D,E,F,G,H,I,J,K A A,B,C,D,E,F,G A A A A 9:3011:30 Released on February 04, 2014 Day 2: March 02, 2014( Sunday) TIME Campus 1, 5 & 4 MATHEMATICS -1 (ECO) MATHEMATICS -2 (ECO) FUNDAMENTALS OF MATHEMATICS BUSINESS MATHEMATICS – 1 BASICS IN NATURAL SCIENCE ISLAMIC FINANCE & BANKING PROFESSIONAL PRACTICE...
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...MATH 4450 - HOME WORK 5 (1) Let V be a R−vector space and < , > be an inner product. Prove that if {v1 , · · · , vn } is a set of mutually orthogonal non-zero vectors, then this set is also linearly independent. Proof: We are given (vi , vj ) = 0 if i = j and (vi , vi ) = 1. To prove that the set if linearly independent, we set a1 v1 + · · · + an vn = 0. Now taking inner product with vj on both sides, we get n ai (vi , vj ) = (0, vj ). Since inner products are linear in the first i=1 variable, we get n ai (v1 , vj ) = 0, and this gives aj = 0. Thus we are done. i=1 (2) Let V be a vector space and < , > be an inner product. Then show that (a) < 0, v >= 0 for any v ∈ V . Proof: < 0, v >=< 0 + 0, v >=< 0, v > + < 0, v >. Subtracting < 0, v > from both sides, we get < 0, v >= 0. (b) Show that for a fixed u ∈ V , < u, v >= 0 for any v ∈ V , then u = 0. Proof: Take v = u. Then we have < u, u >= 0, i.e., ||u||2 = 0. This implies that u = 0. (3) Let V be a vector space and < , > be an inner product and B = {v1 , · · · , vn } be an orthonormal basis for V . If c1 , · · · , cn ∈ K are scalars, then show that there is a unique v ∈ V such that < v, vi >= ci . Proof: Let v = n ci vi . Now taking inner product with vj on both sides, we get i=1 (v, vj ) = n ci (vi , vj ). Orthogonality implies that (vi , vj ) = 0 for i = j. Hence we get i=1 (v, vj ) = cj (vj , vj ). Since vj is non-zero (why?), we get ci = (v, vj )/||vj ||2 = (v, vj ). This proves existence. Uniqueness follows from the properties...
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...▪ Excel Spreadsheet Formulas Numbers and Mathematical Calculations Microsoft Excel has many functions that you can use. Functions allow you to quickly and easily find an average, the highest number, the lowest number, a count of the number of items in a list, and make many other useful calculations. Reference Operators Reference operators refer to a cell or a group of cells. There are two types of reference operators, range and union. A range reference refers to all the cells between and including the reference. A range reference consists of two cell addresses separated by a colon. The reference A1:A3 includes cells A1, A2, and A3. The reference A1:C3 includes A1, A2, A3, B1, B2, B3, C1, C2, and C3. A union reference includes two or more references. A union reference consists of two or more cell addresses separated by a comma. The reference A7,B8,C9 refers to cells A7, B8, and C9. Functions Microsoft Excel has a set of prewritten formulas called functions. Functions differ from regular formulas in that you supply the value but not the operators, such as +, -, *, or /. For example, you can use the SUM function to add. When using a function, remember the following: o Use an equal sign to begin a formula. o Specify the function name. o Enclose arguments within parentheses. o Use a comma to separate arguments. Here is an example of a function: =SUM(2,13,A1,B27) In this function: o The equal sign begins the function. o SUM is...
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...=IF(ISBLANK(B5),””,B5) -This code looks at cell B5 if it is empty it will leave the cell this formula is in blank but if B5 has something in it then it will return what is in B5. Also the 2nd B5 in this formula can be anything adding other cells, returning the value of another cell, a lookup function, or whatever you need it to be an example will up this will follow later down the page. =VLOOKUP(J7, B4:C41, 2, FALSE) - This code here is a vertical lookup function. What is says/does is this it will look in cell J7 then it will look in the column B from B4 down to B41 if there is a match to J7 the it will return the value in the cell beside it from column C. For example say B22 has the same information as J7 then it would return to you what is in C22. The 2 in the formula refers to the column in the selected range B4:C41 but you can expand on this. For example you can say D2:Z54 and all you have to do is tell it what column you want so if you wanted what was in column K then you would put an 8. Remember this formula will be in a cell that is not involved with the formula. With this formula you will be putting your information you want to look up in J7 and the results will be displayed in the cell that you have this formula. In the beginning of this statement I told you this is a vertical lookup function well if you change the V to an H it will then become a horizontal lookup function. SO if this was a horizontal lookup function then the formula would look like this....
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...March 28, 2008 22:40 Applicable Analysis ArticleApplAnalHomogVolChoquetMikeliclast Applicable Analysis Vol. 00, No. 00, March 2008, 1{22 RESEARCH ARTICLE Laplace transform approach to the rigorous upscaling of the in¯nite adsorption rate reactive °ow under dominant Peclet number through a pore z Catherine Choquet a and Andro Mikeli¶c b ¤ aUniversit¶e P. C¶ezanne, LATP UMR 6632, Facult¶e des Sciences et Techniques de Saint-J¶er^ome, 13397 Marseille Cedex 20, FRANCE bUniversit¶e de Lyon, Lyon, F-69003, FRANCE; Universit¶e Lyon 1, Institut Camille Jordan, UFR Math¶ematiques, Site de Gerland, B^at. A, 50, avenue Tony Garnier 69367 Lyon Cedex 07, FRANCE (submitted on March 31, 2008) In this paper we undertake a rigorous derivation of the upscaled model for reactive °ow through a narrow and long two-dimensional pore. The transported and di®used solute par- ticles undergo the in¯nite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts' boundary conditions. The transport and reaction pa- rameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter " being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of...
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...HKUST – Department of Computer Science and Engineering COMP 2711: Discrete Math Tools for CS – Spring 2012 # Final Examination Date: 25 May 2012 Time: 16:30–19:30 Venue: HALL Name: Email: Instructions Student ID: Lecture and Tutorial: • This is a closed book exam. It consists of 9 questions and 19 pages. • Please write your name, student ID, email, lecture section and tutorial on this page. • For each subsequent page, please write your student ID at the top of the page in the space provided. • Please sign the honor code statement on page 2. • Answer all the questions within the space provided on the examination paper. You may use the back of the pages for your rough work. The last three pages are scrap paper and may also be used for rough work. Each question is on a separate page. This is for clarity and is not meant to imply that each question requires a full page answer. Many can be answered using only a few lines. • Unless otherwise specified you must always explain how you derived your answer. A number without an explanation will be considered an incorrect answer. Questions 1 2 3 4 5 6 7 8 9 Total Points 10 11 10 10 12 10 15 10 12 100 Score Student ID: As part of HKUST’s introduction of an honor code, the HKUST Senate has recommended that all students be asked to sign a brief declaration printed on examination answer books that their answers are their own work, and that they are aware of the regulations relating to academic integrity. Following this...
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...The visual supports that I have chosen for Maria’s daily schedule include a group of numbers to signify math, a blue and white “Bathroom Break” image, a picture of the resource room for her resource room time, a music note, art sign and P.E for her different specials depending on the day. I also included a lunch sack for lunch time, a book for core reading time, a picture of a group of students reading for reading interventions groups, a picture of the playground for recess, a molecule for science, a thumbs up for choice time, and lastly, a bell for dismissal. A1a. Explain why the visuals you have included are developmentally appropriate for Maria: The visuals that I have chosen are developmentally appropriate because they are at her age level. Maria is a ten-year-old girl who is in fourth grade. Her reading assessments show that she is between yearend of first grade and beginning third grade level for reading. Because there was such a vast range in her reading abilities, I chose some pictures that had words and others that did not. I made sure not to use any younger kid pictures as to ensure that I was...
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