Lesson 1 Aug. 23 -29 Overview of Abnormal Psychology-1

昂克英文君讲义Andy's English Class CurriculumUnit 1: Introduction to English- Greetings and introductions- Basic classroom phrases and expressions - Alphabet and pronunciation practice- Vocabulary building exercisesUnit 2: Grammar Basics- Parts of speech- Sentence structure and basic grammar rules - Subject-verb agreement- Present tense and present continuous tense Unit 3: Vocabulary Expansion- Common everyday vocabulary- Food, clothing, and daily objects- Family vocabulary- Descriptive words and adjectivesUnit 4: Numbers and Counting- Cardinal and ordinal numbers- Counting objects and people- Basic mathematical operations- Time and date expressionsUnit 5: Listening and Speaking Skills- Listening for comprehension- Responding to questions and requests- Giving directions and instructions- Conversational skills and role-playsUnit 6: Reading and Writing Skills- Reading comprehension exercises- Writing simple sentences and paragraphs- Describing events and experiences- Writing letters and emailsUnit 7: Cultural Knowledge- Learning about different cultures and customs- Holidays and celebrations around the world- Understanding cultural diversity- Language and communication in different cultures Unit 8: Intermediate Grammar- Past tense and past continuous tense- Future tense and future continuous tense- Conditional sentences- Reported speech and indirect questionsUnit 9: Practical Communication- Making appointments and reservations- Ordering food at a restaurant- Asking for and giving directions- Negotiating and problem-solving in EnglishUnit 10: Review and Assessment- Comprehensive review of all previously learned topics - Final assessment to evaluate students' progress- Feedback and suggestions for further improvement - Celebrating the completion of the course。

Rules of Arbitrationin force as from 1 January 1998Cost scales effective as of 1 January 2008International Chamber of CommerceInternational Court of Arbitration38, Cours Albert 1er75008 ParisFranceTel. +33 1 49 53 29 05Fax +33 1 49 53 29 33E-mail arb@Of the various languages in which the ICC Rules of Arbitration may be published, the English and French versions are the only official texts.ICC, the ICC logo, CCI, the CCI logo, International Chamber of Commerce, World Business Organization, WBO, International Court of Arbitration, ICC International Court of Arbitration (including Spanish, French, German and Arabic translations) are all trademarks of ICC, registered in several countries.© International Chamber of Commerce (ICC)All rights reserved. This collective work was initiated by ICC which holds all rights as defined in the French Code of Intellectual Property. No part of this publication may be reproduced or copied in any form or by any means, or translated, without the prior permission in writing of ICC.STANDARD ICC ARBITRATION CLAUSEIt is recommended that all parties wishing to make reference to ICC arbitration in their contracts use the following standard clause.Parties are reminded that it may be desirable for them to stipulate in the arbitration clause itself the law governing the contract, the number of arbitrators and the place and language of the arbitration. The parties’ free choice of the law governing the contract and of the place and language of the arbitration is not limited by the ICC Rules of Arbitration.Attention is called to the fact that the laws of certain countries require that parties to contracts expressly accept arbitration clauses, sometimes in a precise and particular manner.“All disputes arising out of or in connection with the present contract shall be finally settled under the Rules of Arbitration of the International Chamber of Commerce by one or more arbitrators appointed in accordance with the said Rules.”For translations of the above clause, please consult the web site of the ICC International Court of Arbitration:STANDARD CLAUSE FOR AN ICCPRE-ARBITRAL REFEREE PROCEDURE AND ICC ARBITRATIONParties wishing to have recourse to both the ICC pre-arbitral referee procedure and ICC arbitration should make specific reference to both procedures in their contracts. The following standard clause is recommended:“Any party to this contract shall have the right to have recourse to and shall be bound by the pre-arbitral referee procedure of the International Chamber of Commerce in accordance with its Rules for a Pre-Arbitral Referee Procedure.All disputes arising out of or in connection with the present contract shall be finally settled under the Rules of Arbitration of the International Chamber of Commerce by one or more arbitrators appointed in accordance with the said Rules of Arbitration.”For translations of the above clause, please consult the web site of the ICC International Court of Arbitration:RULES OF ARBITRATIONINTRODUCTORY PROVISIONSArticle 1International Court of Arbitration1The International Court of Arbitration (the “Court”) of the International Chamber of Commerce (the “ICC”) is the arbitration body attached to the ICC. The statutes of the Court are set forth in Appendix I. Members of the Court are appointed by the World Council of the ICC. The function of the Court is to provide for the settlement by arbitration of business disputes of an international character in accordance with the Rules of Arbitration of the International Chamber of Commerce (the “Rules”). If so empowered by an arbitration agreement, the Court shall also provide for the settlement by arbitration in accordance with these Rules of business disputes not of an international character.2The Court does not itself settle disputes. It has the function of ensuring the application of these Rules. It draws up its own Internal Rules (Appendix II).3The Chairman of the Court or, in the Chairman’s absence or otherwise at his request, one of its Vice-Chairmen shall have the power to take urgent decisions on behalf of the Court, provided that any such decision is reported to the Court at its next session.4As provided for in its Internal Rules, the Court may delegate to one or more committees composed of its members the power to take certain decisions, provided that any such decision is reported to the Court at its next session.5The Secretariat of the Court (the “Secretariat”) under the direction of its Secretary General (the “Secretary General”) shall have its seat at the headquarters of the ICC.Article 2DefinitionsIn these Rules:(i) “Arbitral Tribunal” includes one or more arbitrators.(ii) “Claimant” includes one or more claimants and “Respondent” includes one or more respondents. (iii) “Award” includes, inter alia, an interim, partial or final Award.Article 3Written Notifications or Communications;Time Limits1All pleadings and other written communications submitted by any party, as well as all documents annexed thereto, shall be supplied in a number of copies sufficient to provide one copy for each party, plus one for each arbitrator, and one for the Secretariat. A copy of any communication from the Arbitral Tribunal to the parties shall be sent to the Secretariat.2All notifications or communications from the Secretariat and the Arbitral Tribunal shall be made to the last address of the party or its representative for whom the same are intended, as notified either by the party in question or by the other party. Such notification or communication may be made by delivery againstreceipt, registered post, courier, facsimile transmission, telex, telegram or any other means of telecommunication that provides a record of the sending thereof.3A notification or communication shall be deemed to have been made on the day it was received by the party itself or by its representative, or would have been received if made in accordance with the preceding paragraph.4Periods of time specified in or fixed under the present Rules shall start to run on the day following the date a notification or communication is deemed to have been made in accordance with the preceding paragraph. When the day next following such date is an official holiday, or a non-business day in the country where the notification or communication is deemed to have been made, the period of time shall commence on the first following business day. Official holidays and non-business days are included in the calculation of the period of time. If the last day of the relevant period of time granted is an official holiday or a non-business day in the country where the notification or communication is deemed to have been made, the period of time shall expire at the end of the first following business day.COMMENCING THE ARBITRATIONArticle 4Request for Arbitration1A party wishing to have recourse to arbitration under these Rules shall submit its Request for Arbitration (the “Request”) to the Secretariat, which shall notify the Claimant and Respondent of the receipt of the Request and the date of such receipt.2The date on which the Request is received by the Secretariat shall, for all purposes, be deemed to be the date of the commencement of the arbitral proceedings.3The Request shall, inter alia, contain the following information:a) the name in full, description and address of each of the parties;b) a description of the nature and circumstances of the dispute giving rise to the claim(s);c) a statement of the relief sought, including, to the extent possible, an indication of any amount(s)claimed;d) the relevant agreements and, in particular, the arbitration agreement;e) all relevant particulars concerning the number of arbitrators and their choice in accordance with theprovisions of Articles 8, 9 and 10, and any nomination of an arbitrator required thereby; andf) any comments as to the place of arbitration, the applicable rules of law and the language of thearbitration.4Together with the Request, the Claimant shall submit the number of copies thereof required by Article 3(1) and shall make the advance payment on administrative expenses required by Appendix III (“Arbitration Costs and Fees”) in force on the date the Request is submitted. In the event that the Claimant fails to comply with either of these requirements, the Secretariat may fix a time limit within which the Claimant must comply, failing which the file shall be closed without prejudice to the right of the Claimant to submit the same claims at a later date in another Request.5The Secretariat shall send a copy of the Request and the documents annexed thereto to the Respondent for its Answer to the Request once the Secretariat has sufficient copies of the Request and the required advance payment.6When a party submits a Request in connection with a legal relationship in respect of which arbitration proceedings between the same parties are already pending under these Rules, the Court may, at the request of a party, decide to include the claims contained in the Request in the pending proceedings provided that the Terms of Reference have not been signed or approved by the Court. Once the Terms of Reference have been signed or approved by the Court, claims may only be included in the pending proceedings subject to the provisions of Article 19.Article 5Answer to the Request; Counterclaims1Within 30 days from the receipt of the Request from the Secretariat, the Respondent shall file an Answer (the “Answer”) which shall, inter alia, contain the following information:a) its name in full, description and address;b) its comments as to the nature and circumstances of the dispute giving rise to the claim(s);c) its response to the relief sought;d) any comments concerning the number of arbitrators and their choice in light of the Claimant’sproposals and in accordance with the provisions of Articles 8, 9 and 10, and any nomination of an arbitrator required thereby; ande) any comments as to the place of arbitration, the applicable rules of law and the language of thearbitration.2The Secretariat may grant the Respondent an extension of the time for filing the Answer, provided the application for such an extension contains the Respondent’s comments concerning the number of arbitrators and their choice and, where required by Articles 8, 9 and 10, the nomination of an arbitrator. If the Respondent fails to do so, the Court shall proceed in accordance with these Rules.3The Answer shall be supplied to the Secretariat in the number of copies specified by Article 3(1).4A copy of the Answer and the documents annexed thereto shall be communicated by the Secretariat to the Claimant.5Any counterclaim(s) made by the Respondent shall be filed with its Answer and shall provide:a) a description of the nature and circumstances of the dispute giving rise to the counterclaim(s); andb) a statement of the relief sought, including, to the extent possible, an indication of any amount(s)counterclaimed.6The Claimant shall file a reply to any counterclaim within 30 days from the date of receipt of the counterclaim(s) communicated by the Secretariat. The Secretariat may grant the Claimant an extension of time for filing the reply.Article 6Effect of the Arbitration Agreement1Where the parties have agreed to submit to arbitration under the Rules, they shall be deemed to have submitted ipso facto to the Rules in effect on the date of commencement of the arbitration proceedings, unless they have agreed to submit to the Rules in effect on the date of their arbitration agreement.2If the Respondent does not file an Answer, as provided by Article 5, or if any party raises one or more pleas concerning the existence, validity or scope of the arbitration agreement, the Court may decide, without prejudice to the admissibility or merits of the plea or pleas, that the arbitration shall proceed if it is prima facie satisfied that an arbitration agreement under the Rules may exist. In such a case, any decision as to the jurisdiction of the Arbitral Tribunal shall be taken by the Arbitral Tribunal itself. If the Court is not so satisfied, the parties shall be notified that the arbitration cannot proceed. In such a case, any party retains the right to ask any court having jurisdiction whether or not there is a binding arbitration agreement.3If any of the parties refuses or fails to take part in the arbitration or any stage thereof, the arbitration shall proceed notwithstanding such refusal or failure.4Unless otherwise agreed, the Arbitral Tribunal shall not cease to have jurisdiction by reason of any claim that the contract is null and void or allegation that it is non-existent, provided that the Arbitral Tribunal upholds the validity of the arbitration agreement. The Arbitral Tribunal shall continue to have jurisdiction to determine the respective rights of the parties and to adjudicate their claims and pleas even though the contract itself may be non-existent or null and void.THE ARBITRAL TRIBUNALArticle 7General Provisions1Every arbitrator must be and remain independent of the parties involved in the arbitration.2Before appointment or confirmation, a prospective arbitrator shall sign a statement of independence and disclose in writing to the Secretariat any facts or circumstances which might be of such a nature as to call into question the arbitrator’s independence in the eyes of the parties. The Secretariat shall provide such information to the parties in writing and fix a time limit for any comments from them.3An arbitrator shall immediately disclose in writing to the Secretariat and to the parties any facts or circumstances of a similar nature which may arise during the arbitration.4The decisions of the Court as to the appointment, confirmation, challenge or replacement of an arbitrator shall be final and the reasons for such decisions shall not be communicated.5By accepting to serve, every arbitrator undertakes to carry out his responsibilities in accordance with these Rules.6Insofar as the parties have not provided otherwise, the Arbitral Tribunal shall be constituted in accordance with the provisions of Articles 8, 9 and 10.Article 8Number of Arbitrators1The disputes shall be decided by a sole arbitrator or by three arbitrators.2Where the parties have not agreed upon the number of arbitrators, the Court shall appoint a sole arbitrator, save where it appears to the Court that the dispute is such as to warrant the appointment of three arbitrators. In such case, the Claimant shall nominate an arbitrator within a period of 15 days from the receipt of the notification of the decision of the Court, and the Respondent shall nominate an arbitrator within a period of 15 days from the receipt of the notification of the nomination made by the Claimant.3Where the parties have agreed that the dispute shall be settled by a sole arbitrator, they may, by agreement, nominate the sole arbitrator for confirmation. If the parties fail to nominate a sole arbitrator within 30 days from the date when the Claimant’s Request for Arbitration has been received by the other party, or within such additional time as may be allowed by the Secretariat, the sole arbitrator shall be appointed by the Court.4Where the dispute is to be referred to three arbitrators, each party shall nominate in the Request and the Answer, respectively, one arbitrator for confirmation. If a party fails to nominate an arbitrator, the appointment shall be made by the Court. The third arbitrator, who will act as chairman of the Arbitral Tribunal, shall be appointed by the Court, unless the parties have agreed upon another procedure for such appointment, in which case the nomination will be subject to confirmation pursuant to Article 9. Should such procedure not result in a nomination within the time limit fixed by the parties or the Court, the third arbitrator shall be appointed by the Court.Article 9Appointment and Confirmation of the Arbitrators1In confirming or appointing arbitrators, the Court shall consider the prospective arbitrator’s nationality, residence and other relationships with the countries of which the parties or the other arbitrators are nationals and the prospective arbitrator’s availability and ability to conduct the arbitration in accordance with these Rules. The same shall apply where the Secretary General confirms arbitrators pursuant to Article 9(2).2The Secretary General may confirm as co-arbitrators, sole arbitrators and chairmen of Arbitral Tribunals persons nominated by the parties or pursuant to their particular agreements, provided they have filed a statement of independence without qualification or a qualified statement of independence has not given rise to objections. Such confirmation shall be reported to the Court at its next session. If the Secretary General considers that a co-arbitrator, sole arbitrator or chairman of an Arbitral Tribunal should not be confirmed, the matter shall be submitted to the Court.3Where the Court is to appoint a sole arbitrator or the chairman of an Arbitral Tribunal, it shall make the appointment upon a proposal of a National Committee of the ICC that it considers to be appropriate. If the Court does not accept the proposal made, or if the National Committee fails to make the proposal requested within the time limit fixed by the Court, the Court may repeat its request or may request a proposal from another National Committee that it considers to be appropriate.4Where the Court considers that the circumstances so demand, it may choose the sole arbitrator or the chairman of the Arbitral Tribunal from a country where there is no National Committee, provided that neither of the parties objects within the time limit fixed by the Court.5The sole arbitrator or the chairman of the Arbitral Tribunal shall be of a nationality other than those of the parties. However, in suitable circumstances and provided that neither of the parties objects within the time limit fixed by the Court, the sole arbitrator or the chairman of the Arbitral Tribunal may be chosen from a country of which any of the parties is a national.Where the Court is to appoint an arbitrator on behalf of a party which has failed to nominate one, it shall make the appointment upon a proposal of the National Committee of the country of which that party is a national. If the Court does not accept the proposal made, or if the National Committee fails to make the proposal requested within the time limit fixed by the Court, or if the country of which the said party is a national has no National Committee, the Court shall be at liberty to choose any person whom it regards as suitable. The Secretariat shall inform the National Committee, if one exists, of the country of which such person is a national.Article 10Multiple Parties1Where there are multiple parties, whether as Claimant or as Respondent, and where the dispute is to be referred to three arbitrators, the multiple Claimants, jointly, and the multiple Respondents, jointly, shall nominate an arbitrator for confirmation pursuant to Article 9.2In the absence of such a joint nomination and where all parties are unable to agree to a method for the constitution of the Arbitral Tribunal, the Court may appoint each member of the Arbitral Tribunal and shall designate one of them to act as chairman. In such case, the Court shall be at liberty to choose any person it regards as suitable to act as arbitrator, applying Article 9 when it considers this appropriate.Article 11Challenge of Arbitrators1A challenge of an arbitrator, whether for an alleged lack of independence or otherwise, shall be made by the submission to the Secretariat of a written statement specifying the facts and circumstances on which the challenge is based.2For a challenge to be admissible, it must be sent by a party either within 30 days from receipt by that party of the notification of the appointment or confirmation of the arbitrator, or within 30 days from the date when the party making the challenge was informed of the facts and circumstances on which the challenge is based if such date is subsequent to the receipt of such notification.3The Court shall decide on the admissibility and, at the same time, if necessary, on the merits of a challenge after the Secretariat has afforded an opportunity for the arbitrator concerned, the other party or parties and any other members of the Arbitral Tribunal to comment in writing within a suitable period of time. Such comments shall be communicated to the parties and to the arbitrators.Article 12Replacement of Arbitrators1An arbitrator shall be replaced upon his death, upon the acceptance by the Court of the arbitrator’s resignation, upon acceptance by the Court of a challenge, or upon the request of all the parties.2An arbitrator shall also be replaced on the Court’s own initiative when it decides that he is prevented de jure or de facto from fulfilling his functions, or that he is not fulfilling his functions in accordance with the Rules or within the prescribed time limits.3When, on the basis of information that has come to its attention, the Court considers applying Article 12(2), it shall decide on the matter after the arbitrator concerned, the parties and any other members of the Arbitral Tribunal have had an opportunity to comment in writing within a suitable period of time. Such comments shall be communicated to the parties and to the arbitrators.4When an arbitrator is to be replaced, the Court has discretion to decide whether or not to follow the original nominating process. Once reconstituted, and after having invited the parties to comment, the Arbitral Tribunal shall determine if and to what extent prior proceedings shall be repeated before the reconstituted Arbitral Tribunal.5Subsequent to the closing of the proceedings, instead of replacing an arbitrator who has died or been removed by the Court pursuant to Articles 12(1) and 12(2), the Court may decide, when it considers it appropriate, that the remaining arbitrators shall continue the arbitration. In making such determination, the Court shall take into account the views of the remaining arbitrators and of the parties and such other matters that it considers appropriate in the circumstances.THE ARBITRAL PROCEEDINGSArticle 13Transmission of the File to the Arbitral TribunalThe Secretariat shall transmit the file to the Arbitral Tribunal as soon as it has been constituted, provided the advance on costs requested by the Secretariat at this stage has been paid.Article 14Place of the Arbitration1The place of the arbitration shall be fixed by the Court unless agreed upon by the parties.2The Arbitral Tribunal may, after consultation with the parties, conduct hearings and meetings at any location it considers appropriate unless otherwise agreed by the parties.3The Arbitral Tribunal may deliberate at any location it considers appropriate.Article 15Rules Governing the Proceedings1The proceedings before the Arbitral Tribunal shall be governed by these Rules and, where these Rules are silent, by any rules which the parties or, failing them, the Arbitral Tribunal may settle on, whether or not reference is thereby made to the rules of procedure of a national law to be applied to the arbitration.2In all cases, the Arbitral Tribunal shall act fairly and impartially and ensure that each party has a reasonable opportunity to present its case.Article 16Language of the ArbitrationIn the absence of an agreement by the parties, the Arbitral Tribunal shall determine the language or languages of the arbitration, due regard being given to all relevant circumstances, including the language of the contract.Article 17Applicable Rules of Law1The parties shall be free to agree upon the rules of law to be applied by the Arbitral Tribunal to the merits of the dispute. In the absence of any such agreement, the Arbitral Tribunal shall apply the rules of law which it determines to be appropriate.2In all cases the Arbitral Tribunal shall take account of the provisions of the contract and the relevant trade usages.3The Arbitral Tribunal shall assume the powers of an amiable compositeur or decide ex aequo et bono only if the parties have agreed to give it such powers.Article 18Terms of Reference; Procedural Timetable1As soon as it has received the file from the Secretariat, the Arbitral Tribunal shall draw up, on the basis of documents or in the presence of the parties and in the light of their most recent submissions, a document defining its Terms of Reference. This document shall include the following particulars:a) the full names and descriptions of the parties;b) the addresses of the parties to which notifications and communications arising in the course of thearbitration may be made;c) a summary of the parties’ respective claims and of the relief sought by each party, with an indicationto the extent possible of the amounts claimed or counterclaimed;d) unless the Arbitral Tribunal considers it inappropriate, a list of issues to be determined;e) the full names, descriptions and addresses of the arbitrators;f) the place of the arbitration; andg) particulars of the applicable procedural rules and, if such is the case, reference to the power conferredupon the Arbitral Tribunal to act as amiable compositeur or to decide ex aequo et bono.2The Terms of Reference shall be signed by the parties and the Arbitral Tribunal. Within two months of the date on which the file has been transmitted to it, the Arbitral Tribunal shall transmit to the Court the Terms of Reference signed by it and by the parties. The Court may extend this time limit pursuant to a reasoned request from the Arbitral Tribunal or on its own initiative if it decides it is necessary to do so.3If any of the parties refuses to take part in the drawing up of the Terms of Reference or to sign the same, they shall be submitted to the Court for approval. When the Terms of Reference have been signed in accordance with Article 18(2) or approved by the Court, the arbitration shall proceed.4When drawing up the Terms of Reference, or as soon as possible thereafter, the Arbitral Tribunal, after having consulted the parties, shall establish in a separate document a provisional timetable that it intends to follow for the conduct of the arbitration and shall communicate it to the Court and the parties. Any subsequent modifications of the provisional timetable shall be communicated to the Court and the parties. Article 19New ClaimsAfter the Terms of Reference have been signed or approved by the Court, no party shall make new claims or counterclaims which fall outside the limits of the Terms of Reference unless it has been authorized to do so by the Arbitral Tribunal, which shall consider the nature of such new claims or counterclaims, the stage of the arbitration and other relevant circumstances.Article 20Establishing the Facts of the Case1The Arbitral Tribunal shall proceed within as short a time as possible to establish the facts of the case by all appropriate means.2After studying the written submissions of the parties and all documents relied upon, the Arbitral Tribunal shall hear the parties together in person if any of them so requests or, failing such a request, it may of its own motion decide to hear them.3The Arbitral Tribunal may decide to hear witnesses, experts appointed by the parties or any other person, in the presence of the parties, or in their absence provided they have been duly summoned.4The Arbitral Tribunal, after having consulted the parties, may appoint one or more experts, define their terms of reference and receive their reports. At the request of a party, the parties shall be given the opportunity to question at a hearing any such expert appointed by the Tribunal.5At any time during the proceedings, the Arbitral Tribunal may summon any party to provide additional evidence.6The Arbitral Tribunal may decide the case solely on the documents submitted by the parties unless any of the parties requests a hearing.7The Arbitral Tribunal may take measures for protecting trade secrets and confidential information.Article 21Hearings1When a hearing is to be held, the Arbitral Tribunal, giving reasonable notice, shall summon the parties to appear before it on the day and at the place fixed by it.2If any of the parties, although duly summoned, fails to appear without valid excuse, the Arbitral Tribunal shall have the power to proceed with the hearing.3The Arbitral Tribunal shall be in full charge of the hearings, at which all the parties shall be entitled to be present. Save with the approval of the Arbitral Tribunal and the parties, persons not involved in the proceedings shall not be admitted.4The parties may appear in person or through duly authorized representatives. In addition, they may be assisted by advisers.Article 22Closing of the Proceedings。

Chapter 1.Variables, Expressions and Integers PREREQUISITE SKILLS QUIZReview Vocabulary sumdifferenceproductquotientfactor Preparing for Success To prepare for success in this chapter, test your knowledgeof these concepts and skills. You may want to look at the pages referred to in bluefor additional review.Vocabulary Copy and complete the statement using a review word.1. In the multiplication equation 12 ×5 =60, 12 and 5 are called and60 iscalled the .2. When you divide one number by another, the result is called the .Find the sum or difference.3. 7.2 +13.7=4. 2.41 +34.6=5. 10.5 -7.3=6. 27.1 -18.6= Find the product or quotient.7. 3.2 ×1.4= 8. 0.5 ×27= 9. 27.88 ÷8.2= 10. 11.9 ÷1.7=NOTETAKING STRATEGIESKEEPING A NOTEBOOK Some useful items to put in your notebook include the following.Note WorthyYou will find a notetaking strategy at the beginning of each chapter. Look for additional notetaking and study strategies throughout the chapter. • assignments • formulas • rules and properties • vocabulary • symbols • worked-out examples When you copy examples into your notebook, you may find it helpful to draw a diagram. Include comments that make the solution process clear. For example, a diagram can help you to order the numbers 3.2, 3.09, 3, 3.15, 3.12, and 3.02 from least to greatest.Draw a number line and graph the numbers:Write the numbers in the order in which they appear from left to right: 3, 3.02, 3.09, 3.12, 3.15, 3.2.In Lesson 1.8, you may want to include a diagram of acoordinate plane in your notebook.Lesson 1.1Expressions and VariablesVocabulary numerical expression variable variable expression evaluateverbal model Before: You evaluated numerical expressions.Now:You’ll evaluate and write variable expressions.Why? So you can find the amount left on a gift card, as in Ex. 39.Blue Whales During its summer feeding season, a blue whale eats about 4 tons of food every day.To find about how many tons of food a blue whale eats in a given number of days, you can multiply the number of days by 4, as shown in the table.A numerical expression consists of numbers and operations. In thet able, the expression 4 p10 is a numerical expression. It can also bewritten as 4 ×10 or 4(10).A variable is a letter used to represent one or more numbers. Av ariable expression consists of numbers, variables, and operations.O ne way you can use a variable expression is to generalize a pattern,a s in the table. The variable expression 4٠d represents the amount offood a blue whale can eat in d days. You can also write 4٠d as 4d.To evaluate a variable expression, substitute a number for each variable and evaluate the resulting numerical expression.Study StrategyExample1. Evaluating a Variable ExpressionWhen you write a variable expression involving multiplication, avoid using the symbol × . It may be confusedw ith the variable x.Evaluate the expression 4 ×d when d = 120 to find about how many tons of food a blue whale eats in a feeding season of 120 days. Solution4٠d = 4٠120 Substitute 120 for d.= 480 Multiply.Answer A blue whale eats about 480 tons of food in 120 days.Example 2. Evaluating Expressions with Two VariablesEvaluate the expression when x =10 and y =4.a. x + y = 10 +4 Substitute 10 for x and 4 for y.= 14 Add.b. xy = 10(4) Substitute 10 for x and 4 for y.=40 Multiply.Checkpoint Evaluate the expression when x =6 and y =12.1. y +82. 9 -x3. y -x4. xyWriting Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variableexpression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The tableshows common words and phrases that indicate mathematical operations.Watch OutCommon Words and Phrases that Indicate Operations Addition Subtraction Multiplication DivisionOrder is important in subtraction and division expressions.“The difference ofa number and 7” means n - 7, not7 -n. “The quotient of a number and 5”meansn/5, not 5/n. Plus minus times divided by the sum of the difference of the product of divided into increased by decreased by multiplied by the quotient of total fewer than ofmore than less thanadded to subtracted fromExample 3. Writing a Variable ExpressionB aseball You plan to divide the 120 players in a baseball league intoteams with the same number of players. Use a verbal model to write avariable expression for the number of teams if you know the numberof players on each team.SolutionReading Algebra L et p represent the number of players on each team. The word divide indicates division.W hen you write a variable e xpression involving division, u se a fraction bar instead of t he division symbol ÷. For example, write “the quotient of n and 12 as n/12.in league =120 /pVocabulary Check 1. Identify the variable in the expression 21 +d.2. Compare and contrast the expressions 2 +x and 2 +3.Skill Check E valuate the expression when x =4.3. 10 -x4. x + 75. 2x6. 32/xEvaluate the expression when m 5 and n 6.7. n/2 8. m + n9. n - m10. MnGuided Problem Solving 11.Astronauts In 2002, astronauts Carl Walz and Dan Bursch spent 196 days inorbit. How many sunrises did they see?1An astronaut in orbit circles Earth every 90 minutes and sees16 sunrises each day. Let d be the number ofdays an astronaut is in orbit. Write a variable expression for the number of sunrises seen in d days.2Identify the value of d for Walz’s and Bursch’s 2002 space flight.3Find the number of sunrises Walz and Bursch saw.Practice and Problem SolvingE valuate the expression when x =6.12. x + 3 13. 15 -x14. 2x15. x/316. 20x17. 24/x 18. 30 -x19. 15 +xEvaluate the expression when a =4, b =2, and c =16.20. a + b21. c - a22. ab23. a/b24. bc 25. c/a26. a–b 27. c/b28. b + c29. c - b30. ac31. a + cWrite a variable expression to represent the phrase.32. The product of 72 and 33. The difference of a numbera number and 134. 13 more than a number 35. The sum of a number and 9.436. The quotient of a number and 3 37. A number divided by 4138. Error Analysis Describe and correct thedifference of a number and 31.39. Gift Card You can evaluate the expression 50 -d to find the amount you have left on a $50 gift card after youhave spent d dollars. Find the amount left after you have spent $18.40. Music Competition The doublebar graph shows three students’scores in a music competition. Astudents ’ final score is the sum of the points for technique t and forinterpretation i.a. Write a variable expression for astudent’s final score.b. Find each student’s final score.c. Interpret You earn 35 points fortechnique. At least how many points must you earn for interpretation to have a higherscore than students A, B, and C?Evaluate the expression when a = 2.5, b = 15, and c = 3.5.41. a + b 42. b - c 43. bc 44. a + c45. b /a 46. c – a 47. c /a 48. acWrite a variable expression to represent the phrase.49. The number of inches in x feet 50. The number of pounds in y ounces 51. DVD Rentals You belong to an online DVD rental service. Youryearly rental budget is $200. Each rental costs $4.a. Copy and complete the table.b. Write a variable expression forthe cost of r rentals.c. Write a variable expression forthe amount of your budget leftafter r rentals.d. Writing How many DVDs will you be able to rent before the $200 is spent? Explain how you found your answer. 52. Extended Problem SolvingIn football, each field goal (FG) isworth 3 points. Each kicked pointafter touchdown (PAT ) is worth1 point. The table shows careertotals for three leading kickers.a. Let p be the number of points after touchdown that a kicker scored,and let f be the number of field goals. Write a variable expression for the total number of points.b. Evaluate Find the total number of points for each kicker.c. Compare List the players in order from least total number of pointsto greatest.53. Critical Thinking Are there any values of the variable a for which theexpressions 2 + a and 2a have the same value? Explain.Logical Reasoning Describe the pattern shown in the table. Then write av ariable expression involving n to complete the table. In the table, thet hree dots indicate that the pattern continues.54. Cost of item (dollars) 1.00 2.00 3.00 4.00 ...nCost with tax (dollars) 1.05 2.10 3.15 4.20 ...?55.C ost of item (dollars) 1.00 1.50 2.00 2.50 .. n.Cost with coupon (dollars) 0.50 1.00 1.50 2.00 ...?56.Challenge The plastic tips on the ends of a shoelace are called aglets.Suppose a sneaker factory produces p pairs of shoes each hour and isin operation for h hours each day. Write a variable expression for thenumber of single aglets the factory uses each day. Evaluate theexpression when p = 200 and h = 24. Explain what your answer means. Mixed Review Find the sum or difference.57. 3.2 +4.7 58. 5.1 +6.8 59. 7.3 -2.1 60. 9.9 -5.4Find the product or quotient.61. 8(13.2) 62. 12.5/563. 24.32/3.264. (6.5)(4.3)65. Order the decimals from least to greatest: 8.9, 8.79, 7.98, 9.87, 7.8, 9.78.Standardized Test Practice 66. Multiple Choice Write a variable expression for a length of time inminutes if you know the number s of seconds.A. s + 60B. s/60C. 60sD. 60/s67. Multiple Choice Evaluate the expression x - y when x = 12.8 and y = 4.F.3.2G. 8.8H. 12.4I. 13.2 Lesson 1.2Powers and ExponentsVocabulary power base exponent Before: You multiplied whole numbers and decimals.Now:You’ll use powers to describe repeated multiplication.Why? So you can find the total number of e-mails sent, as in Ex. 29.A power is the result of a repeated multiplication of the same factor.F or example, the number 125 is a power because 125 =5 •5 •5. A powercan be written in a form that has two parts: a number called the base and a number called the exponent. The exponent shows the number of times the base is used as a factor.The table shows how to read and write powers. Numbers raised to thefirst power, such as 121, are usually written without the exponent.Note W orthy E xampl e1.U si n g E xponents Write the product using an exponent.Write additional examples of your own in your notebook. For each product, identify the base and the exponent, then write the product using an exponent. a. 13•13•13•13=134 The base 13 is used as a factor 4 times.b. (0.2)(0.2)(0.2)=(0.2)3 The base 0.2 is used as a factor 3 times.c. n•n•n•n•n•n=n6 The base n is used as a factor 6 times.d. t•t•t•t•t = t5 The base t is used as a factor 5 times.Checkpoint Write the product using an exponent.1. 10•10•102. (4.3)(4.3)3. x•x•x•x4. Critical Thinking Evaluate each power: 02, 03, 04. Use your results towrite a rule for the value of 0 raised to any nonzero whole numberexponent.E xampl e2.E val u ati n g P owers w i t h V ari a bl e sEvaluate the expression x4 when x =0.5.x4 = (0.5)4 Substitute 0.5 for x.=(0.5)(0.5)(0.5)(0.5) Use 0.5 as a factor 4 times.=0.0625 Multiply.Checkpoint Evaluate the expression when m =3.5. m26. m37. m48. m5U sing Formulas A formula describes a relationship between quantities.Some formulas involve powers. For example, you can use a formula tofind the area of a square or the volume of a cube.Area is measured in square units, such as square feet (ft2) or squarec entimeters (cm2). Volume is measured in cubic units, such as cubicinches (in.3) or cubic meters (m3).Exampl e 2. U si n g P owers i n F ormul a s I ce Sculpture An artist uses a cube-shaped block of ice to make an icesculpture for a competition. Find thevolume of the block of ice.SolutionUse the formula for the volume of a cube.V =s 3 Write the formula.=(20)3Substitute 20 for s. In the Real WorldIce Sculpture A cubic inch ofi ce weighs about 0.03 pound. If t he artist carves away about 2000 cubic inches from the b lock in Example 3, about how much does the resultingsculpture weigh?Exercises=8000 Evaluate power. Answer The volume of the block of ice is 8000 cubic inches. Checkpoint Find the area of a square with the given side length. 9. 9 meters 10. 11 inches 11. 1.5 centimeters Guided Practice Vocabulary Check1. Identify the base and the exponent in the expression 135.2. How are the expressions 34 and 43 different? Skill CheckW rite the power in words and as a repeated multiplication. Then evaluate the power. 3. 122 4. (0.3)3 5. (1.2)3 6. 54 Evaluate the expression when k = 6. 7. k 2 8. k 3 9. k 4 10. k 5 11. Gift Box A gift box has the shape of a cube with an edge length of 14 inches. Find the volume of the box.12. Error Analysis Describe and correct the error in writing 23 as a repeated multiplication. Practice and Problem Solving Write the product using an exponent. 13. 32 • 32 14. 11 • 11 •11 15. 6 • 6 •6 • 6• 6 16. 2 • 2 • 2 • 2 17. (5.6)(5.6)(5.6) 18. (1.7)(1.7) 19. z • z • z 20. n •n •n •n Write the power in words and as a repeated multiplication. Then evaluate the power.21. 83 22. 25 23. 106 24. 123 25. 93 26. 44 27. (0.2)2 28. (0.6)4 29. Extended Problem Solving You send an e-mail to 4 friends. Each friend sends the e-mail to 4 more friends. Each of those friends sends it to 4 friends, and so on. a. Copy and complete the table. b. Calculate Find the number of e-mails sent at stage 9. c. Estimate Estimate the stage at which more than 1,000,000 e-mails will be sent. Use a calculator to check your estimate. Evaluate the expression when n 7 and when n 0.4. 30. n 2 31. n 3 32. n 4 33. n 5 34. Writing The square of a number is the second power of the number. The cube of a number is the third power of the number. Explain why these names are reasonable. 35. Critical Thinking Explain why 1 raised to any power is equal to 1. 36. Aquariums An aquarium has a square base with a side length of 15 inches. You fill the aquarium with water to a height of 15 inches. a. Find the volume of the water in the aquarium. b. A cubic inch of water weighs approximately 0.036 pound. Find the approximate weight of the water in the aquarium. 37. Patterns The table shows sums of odd numbers. a. Copy and complete the table. Identify any pattern that you see. b. Write a variable expression for the sum of the first n odd numbers. c. Use your expression from part (b) to find the sum of the first 100 odd numbers. 38. Challenge Find values of x, y, and z so that each of the expressions x 2, y 3, and z 6 has a value of 64.Mixed Review Find the product or quotient.39. (2.5)(7.1) 40. (2.3)(8.4) 41. 1.2 ÷ 2.4 42. 5.2 ÷ 1.2543. Olympics The bar graph shows the number of gold medals won by thefour countries with the most goldmedals in the 2000 OlympicSummer Games. How many goldmedals did the four countries winin all?Evaluate the expression when x = 15.44. x + 4 45. 200 -x46. x - 11 47. 3xStandardized TestPractice 48. Multiple Choice Which expression has a value of 81?A. 43B. 34C. 28D. 27349. Short Response Compare eachnumber in the top row of the table withthe number below it. Describe anypattern you see. Complete the tablewith a variable expression involving n.1 2 3 4 ... n1 8 27 64 ... ?Student ReferenceReview thist opic in preparationf or solving problems i n Lesson 1.3. For a r eview of problems olving strategies.A Problem Solving PlanYou can use the following 4-step plan to solve a problem.1.Read and Understand Read the problem carefully. Identify the questionand any important information.2.Make a Plan Decide on a problem solving strategy.3.Solve the Problem Use the problem solving strategy to answer thequestion.4.Look Back Check that your answer is reasonable.Reading and PlanningExample You plan to ship 5 books to a friend. The table shows the masseso f the books. Is it possible to ship the books in 2 boxes, each with a mass of6 kilograms or less? Explain.Book A B C D EMass (kg) 1.4 2.1 3.8 1.9 2.5Read and UnderstandWhat do you know?The mass of each box must be 6 kilograms or less.The table gives the mass of each book.What do you want to find out?Is it possible to put the books in 2 boxes so that each box has a mass of6 kilograms or less?Make a PlanHow can you relate what you know to what you want to find out?Check that the total mass of the books doesn’t exceed 12 kilograms. If it does, you can’t divide the books as you want.Use the strategy guess, check, and revise to choose books for each box.Solving and Looking BackTo solve the problem from page 14 about shipping books, carry out the plan. Then check the answer.Solve the ProblemThe total mass of the books is 1.4 +2.1 +3.8 +1.9 +2.5 =11.7 kg, so it may be possible to ship the books as you want.N ow use the strategy guess, check, and revise.Put the 3 lightest books in one box and the2 heaviest in the other. The mass of thesecond box is more than 6 kg.Try switching books B and E. The mass ofeach box is less than 6 kg.Answer It is possible to ship the books in 2 boxes, each with a mass of6 kg or less. Put books A, D, and E in one box and books C and B in the other.Look BackIt makes sense that the box with 3 books contains the 2 lightest books andthe box with 2 books contains the heaviest book. So, the answer is reasonable.CheckpointTest your knowledge of the problem solving plan by solving these problems.1. Pool Schedules A community pool offers3 swim sessions each Saturday morning.Each session lasts 35 minutes, with10 minutes between sessions. The final sessionends at 11:05 A.M. At what time does the first session begin?2. Theater Seating The center section of a theater has 10 rows. There are 41 seats inrow 10, 38 seats in row 9, 35 seats in row 8, and so on. How many seats are in row 1?3. Movie Marathon You have invited friends over to watch movies. You have rented 4 movies:one action, one science fiction, one comedy, and one animated. In how many different orders can you watch the movies?Lesson 1.3Order of OperationsVocabulary order of operations,Before：You performed basic operations.Nowadays：You’ll use order of operations to evaluate expressions. Why？So you can find the height of a boojum, as in Ex. 28.Flower Flag There are about2000 plants in each of the50 stars of this flower flag.There are about 64,100 plants in each of the 7 short stripes and 106,700 plants in each of the 6 long stripes. The bluecontains about 198,900plants. You can approximate the total number of plants by evaluating the expression50•2000 + 7•64,100 + 6•106,700 + 198,900.To evaluate expressions involving more than one operation,mathematicians have agreed on a set of rules called the oroperations.Note Worthy Order ofOperations1. Evaluate expressions inside grouping symbols.You should include material that appears on a notebook like the one shown in your own notebook.2. Evaluate powers.3. Multiply and divide from left to right.4. Add and subtract from left to right.Example 1. Using Order of OperationsTo approximate the total number of plants in the flower flag describedabove, use the order of operations to evaluate the expression 50•2000 + 7•64,100 + 6•106,700 + 198,900Write expression.= 100,000 + 448,700 + 640,200 + 198,900 Multiply.=1,387,800 Add.Answer There are approximately 1,387,800 plants in the flower flag.Grouping Symbols Parentheses ( ), brackets [ ], and fraction bars arec ommon grouping symbols. Grouping symbols indicate operations thats hould be performed first. For example, compare the expressions3•2 + 5 and 3(2 + 5). To evaluate 3•2 + 5, you multiply first, then add.To evaluate 3(2 + 5), you add first, then multiply.Example 2. Using Grouping SymbolsEvaluate the expression.a. 8(17 - 2.3) = 8(14.7) Subtract within parentheses.= 117.6 Multiply.Watch Out b. 14+612−7= (14 + 6) ÷ (12 - 7) Rewrite fraction as division.When grouping symbols appear inside other grouping symbols, as in part (c) of Example 2, work from the innermost grouping symbols out. = 20÷5Evaluate within parentheses. = 4 Divide.c. 5 •[36 - (13 + 9)] = 5• [36 - 22] Add within parentheses.= 5 •14Subtract within brackets. = 70 Multiply.Checkpoint Evaluate the expression.1. 28 - 63 ÷ 72. 52 + 12.5•43. 9•6 + 27÷34. 10(1.5 + 0.6)5. 70−9.23+56. 72 ÷ [(11 - 7)•2]Example 3. Evaluating Variable ExpressionsStudy Strategy E valuate the expression when x =2 and y =5.a. 4(x +y) = 4(2 +5) Substitute 2 for x and 5 for y.Y ou can use the first letters of t he words of the sentenceP lease Excuse My Dear Aunt Sally to help you remember t he order of operations.P parenthesesE exponents = 4(7) Add within parentheses. = 28 Multiply.b. 3(x +y)2 = 3(2 +5)2 Substitute 2 for x and 5 for y. = 3(7)2 Add within parentheses. = 3(49) Evaluate power.M/D multiplication and divisionA/S addition and subtraction147 Multiply.Checkpoint Evaluate the expression when x =4 and y =2.7. 1.2(x + 3) 8. 1.2x + 3 9. 3x - 2y10. 0.5[y - (x - 2)] 11. x2 – y 12. 2(x - y)2Example 4. Using a Problem Solving PlanSewing You buy a pattern and enough material to make two pillows.The pattern costs $5. Each pillow requires $3.95 worth of fabric and abutton that costs $.75. Find the total cost.SolutionRead and Understand You buy one pattern plus fabric and buttons for two pillows. Youare asked to find the total cost.Make a Plan Write a verbal model.Solve the Problem Write and evaluate an expression.Total cost =5 +2(3.95 +0.75) Substitute values into verbal model.=5 +2(4.70) Add within parentheses.= 5 +9.40 Multiply.= 14.40 Add.Answer The total cost is $14.40.Look Back Use estimation to check that the answer is reasonable. Thec ost of materials for each pillow is about $4 +$1 =$5. The total cost isabout $5 +2($5) =$15. The answer is reasonable.1.3 E xercisesGuided PracticeVocabulary Check 1. Give three examples of grouping symbols.2. Describe in order the steps you would take to evaluate the expression 12(x - 3)2 when x = 5.Skill Check Evaluate the expression. 3. 15 - 3•4 4. 48 ÷ 6 + 2 5. 3•8 + 5•4 6. 18+127−2 7. 17 - (32 - 2) 8. 4[15 - (2 + 5)]9. Twin Convention The table shows the numbers of sets of twins, triplets, quadruplets, and quintuplets registered at a twin convention. Write and evaluate an expression for the total number of people who registered at the convention. Practice and Problem SolvingE valuate the expression.10. 47.7 - 12•3 11. 11•7 - 9•5 12. 14 ÷ 7 + 36 ÷ 413. 5.8(3) + 3(1.1) 14. 36−122+836 15. 9.8+2.27−59.82 16. 5(21 - 32) 17. 7[2.5 + 3(12 - 7)] 18. 84 ÷ [(18 - 16) •3]Evaluate the expression when x = 3, y = 4, and z = 5.19. 0.25y + x 20. 0.25(y + x) 21. 4(z - x) 22. 6.5y x−1 23. x + 24.4y24.4 24. 7z- x 2 25. x + 2[z - (y - 1)] 26. (x + y)2 - 3.6 27. y + (z - 1)2 28. Plants A boojum is a very slow-growing cactus.One fifty-year-old boojum is 1.5 meters talland has been growing about 0.03 meter each year. Assume the growth pattern continues.a. Write an expression for the height in metersof the boojum y years from now.b. Apply How tall will the boojum be in 50 years?29. Craft Fair Your school is setting up a row of5 tables for a craft fair. Each table is 72 inches long. The space between each pair ofneighboring tables must be 48 inches. Write andevaluate an expression to find the length of thespace needed for the tables from the beginningof the first table to the end of the last table.30. Basketball In basketball, players score points by making free throwsworth 1 point each, field goals worth 2 points each, and field goalsworth 3 points each. A player scores 4 free throws, 7 two-point field goals, and 2 three-point field goals. Write and evaluate an expressionfor the total number of points the player scores.31. Movies You buy 4 videotapes for $14.99 each and 3 DVDs for $19.99each. Find the total cost of the movies.Evaluate the expression when x = 4 and y = 3.26.5y2 32. 5x2 2y33. 7(x2 5y) 34. x935.y2 x1 36. Cell Phone You and your sister share cell phone service. You divide thebill equally, including the monthly fee of $39 plus $.30 for eachadditional minute beyond your free minutes.a. Write an expression for your share of the bill in a month when youare charged for m extra minutes.b. Apply One month, you are charged for 125 additional minutes. Findyour share of the bill.。