8,15

时间:2018-02-03   来源:学生随笔   点击:

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8,15 第一篇_数列3,8,15,24,35…的一个通项公式为( )

一、整体解读

试卷紧扣教材和考试说明,从考生熟悉的基础知识入手,多角度、多层次地考查了学生的数学理性思维能力及对数学本质的理解能力,立足基础,先易后难,难易适中,强调应用,不偏不怪,达到了“考基础、考能力、考素质”的目标。试卷所涉及的知识内容都在考试大纲的范围内,几乎覆盖了高中所学知识的全部重要内容,体现了“重点知识重点考查”的原则。

1.回归教材,注重基础

试卷遵循了考查基础知识为主体的原则,尤其是考试说明中的大部分知识点均有涉及,其中应用题与抗战胜利70周年为背景,把爱国主义教育渗透到试题当中,使学生感受到了数学的育才价值,所有这些题目的设计都回归教材和中学教学实际,操作性强。

2.适当设置题目难度与区分度

选择题第12题和填空题第16题以及解答题的第21题,都是综合性问题,难度较大,学生不仅要有较强的分析问题和解决问题的能力,以及扎实深厚的数学基本功,而且还要掌握必须的数学思想与方法,否则在有限的时间内,很难完成。

3.布局合理,考查全面,着重数学方法和数学思想的考察

在选择题,填空题,解答题和三选一问题中,试卷均对高中数学中的重点内容进行了反复考查。包括函数,三角函数,数列、立体几何、概率统计、解析几何、导数等几大版块问题。这些问题都是以知识为载体,立意于能力,让数学思想方法和数学思维方式贯穿于整个试题的解答过程之中。

8,15 第二篇_0,2,8,15,( ) A.24B.25C.26 D.27

一、整体解读

试卷紧扣教材和考试说明,从考生熟悉的基础知识入手,多角度、多层次地考查了学生的数学理性思维能力及对数学本质的理解能力,立足基础,先易后难,难易适中,强调应用,不偏不怪,达到了“考基础、考能力、考素质”的目标。试卷所涉及的知识内容都在考试大纲的范围内,几乎覆盖了高中所学知识的全部重要内容,体现了“重点知识重点考查”的原则。

1.回归教材,注重基础

试卷遵循了考查基础知识为主体的原则,尤其是考试说明中的大部分知识点均有涉及,其中应用题与抗战胜利70周年为背景,把爱国主义教育渗透到试题当中,使学生感受到了数学的育才价值,所有这些题目的设计都回归教材和中学教学实际,操作性强。

2.适当设置题目难度与区分度

选择题第12题和填空题第16题以及解答题的第21题,都是综合性问题,难度较大,学生不仅要有较强的分析问题和解决问题的能力,以及扎实深厚的数学基本功,而且还要掌握必须的数学思想与方法,否则在有限的时间内,很难完成。

3.布局合理,考查全面,着重数学方法和数学思想的考察

在选择题,填空题,解答题和三选一问题中,试卷均对高中数学中的重点内容进行了反复考查。包括函数,三角函数,数列、立体几何、概率统计、解析几何、导数等几大版块问题。这些问题都是以知识为载体,立意于能力,让数学思想方法和数学思维方式贯穿于整个试题的解答过程之中。

8,15 第三篇_8.15招聘需求

【电商网站产品经理】

职位描述

1. 负责公司电商平台“家园商城”的产品设 UCD方法论,制订高保真原型和相关PRD文档;

3、制订整个产品线的各类流程图与思维导图,能与公司现有的运营体系无缝对接,并按上级指示协调各部门最终确认产品方案;

4、负责定期进行数据采集、统计分析以及对竞争对手情况分析跟踪;并通过数据和用户反馈,分析用户需求及行为,不断改进和提升产品的质量,制订产品迭代与实施计划;

5、负责电商平台各模块的生命周期管理,持续优化产品,达成业务目标;

6、参与运营和市场部门在产品推广阶段的方案制定工作,制订运营部门的运营策略和指导;

7、负责电商与数据后台的工作流设计,能与多个部门协作,保证产品从概念设计到开发到上线的如期顺利完成;

8、负责产品版本管理,每次迭代结束,更新产品白皮书,对业务部门进行产品培训与演示。

岗位要求:

1. 本科以上学历,3年以上互联网项目产品经理相关工作经验,熟悉各类互联网产品,对当前国内外流行的互联网产品有一定接触和研究;

2. 有电子商务类网站或电商团队工作经验(重要),对家装互联网有一定了解者优先;

3. 具备一定的交互设计能力和UI审美能力;

4. 具备市场调研、市场竞争、市场需求分析能力,具备基本项目管理和协调、沟通能力;

5. 能够对产品提出系统性改进建议与产品优化建议。

【UI设计工程师】

岗位职责:

1、负责公司PC端“家园商城”电商网站和移动端“家装秀”社交App的UI/UE设计和其他产品视觉效果的美术创意及设计制作工作;

2、参与产品整体设计,规划产品的UI设计方案;

3、与产品经理及产品开发人员沟通协作,完善产品视觉化内容的设计;提出用户体验改进意见和建议,持续优化产品 ;对产品各阶段交互原型进行评测,最大化的提升用户体验满意度;

4、帮助产品经理进行各种产品的易用性和功能分析,进行用户研究。

任职要求:

1、美术、工业设计和计算机相关专业,本科及以上学历;

2、扎实的美术功底,2年以上互联网公司交互设计、产品设计经验,1年以上移动互联网产品设计经验;

3、精通网页和手机App的UI设计设计;精通用户体验设计;具备对流行趋势敏锐的洞察力,能把握不同设计风格,并用视觉设计来引导用户;具有较强的互联网产品的可用性分析及用户行为分析能力; 精通人机交互理论和原则,可以根据商业需求,设计合理的界面原型及交互流程;

4、能够熟练使用各类设计软件,如:Photoshop、Dreamweaver、Fireworks、Illustrator和常用的原型设计工具(Axure等);

5、熟悉HTML5,CSS3等新的Web界面技术,能很好的把握色彩、排版、页面架构和布局;

6、良好的沟通表达能力,积极主动,眼界开阔,良好的创意思维、创新精神和理解能力。

【Android/IOS开发主管】

岗位职责:

1、负责公司移动社交APP“家装秀”(Android版或IOS版)项目的架构设计、开发、测试与维护;

2、负责“家装秀”Android或IOS开发团队的管理,包括功能拆解、任务分配及进度把控等;

3、人机交互界面的设计,为用户提供良好交互体验;

4、完成核心/重要模块的设计、编码、测试以及相关文档;

5、参与代码设计、审核和检查。

岗位要求:

1、计算机相关专业本科以上学历,2年以上的android或IOS项目开发的领导经验;

2、有互联网应用系统需求分析、设计、开发3年以上经历,要求有项目开发领导经验;

3、熟悉HTTP、TCP/IP通讯协议;熟悉iPhone/Android SDK开发环境及底层API调用,能够熟练运用XCode和其它开发工具;

4、熟悉面向对象编程,熟悉内存释放编程技巧;

5、具备良好的专业英文资料阅读能力;对技术有热情,快速的学习适应能力;热情诚恳,善于沟通。

8,15 第四篇_完形填空词汇8-15

1.after 在……之后;2. already 已经3. always 一直,总是;4. almost 几乎;

5.around 大约,周围;6.at 在;7.alone独自地;8.and 和;9.again又一地,再一地;10.accept接受;11.allow允许;12.ask问;13.away 离开;14.air空气;

15.arm手臂;16.afraid害怕;17.accident 事故;18.attitude态度;19.anything任何事情 20.angry生气;21.adventure冒险;22.action行动;23.activity活动;

24. advantage 优势;25.agreement同意,协议;26.avoid避免;27.appear出现;

28. awake醒着

1.beside在……旁边;2. back后面;3.between在(两者之间);4.before在……之前;5. by在……旁,到……时(为止);6.because因为;7. break打破;8. beat打败,战胜;9. business商业,事务,职责;10.breath呼吸;11. bring拿来 ;

12.body身体;13. believe相信;14. better比较好;15. boring无聊的,令人厌烦的;16.brave勇敢的;17. built建造;18.brighten(使)发光,发亮

1.cloud云;2. condition条件;3. catch拿着,抓住;4. completely完全地;

5. change改变;6.check检查,核对;7.cover盖,覆盖;8. cut切 9.celebrate庆祝;10.children孩子们;11.company公司,伙伴;12.come来;13. clear清楚的,明确的;14.choose选择;15.cold冷的

1.decision决定;2.direction方向;3.down向下;4.deep深的;5.do做,干;

6.disappear消失;7.directly直接地,马上;8.disturb打断;9.drive开车,驾驶;10.different不同的;11.dig挖;12.divide分,划分;13.darken变黑,使暗淡;14.dream梦,梦想;15.difficult困难的;16.develop发展

1.exercise锻炼,练习;2.experience经验,经历;3.excited兴奋的;4.environment环境;5.eye眼睛;6.enjoy喜欢,享受;7.everything一切事情;8.expect期待,盼望;9.explain解释;10.expensive昂贵的;11.excitement兴奋,激动;

12.encouragement鼓励;13.ever曾经;14.each每,各自的;15.enter进入;16.exist

存在

1.fly飞;2.forward前方的,向前的;3.free自由的,免费的;4.fight打架,战斗;5.fighter好斗的人,战士;6.for为了,对于;7.fear害怕,恐惧;8.follow跟随;9.fit使适合,健康;10.fantastic幻想的,极好的;11.find发现,找到;

12.found发现(find的过去式),建立;13.foolish愚蠢的,笨的

1.get得到,获得,买到;2.get on上车;3.go去,前往

1.hit打,击,碰撞;2.hard困难的,努力的,辛苦的;2.hurt受伤;3.high高的;

4.heavy重的;5.hand手;6.his他的;7.her她的;8.hate讨厌,憎恨;9.hide藏;

10.head头;11.hold拿,抓住,举行;12.husband丈夫;13.hotel旅馆;14.hope希望;15.happy高兴的,愉快的;16.hurry匆忙,赶快

【8,15】

1.introduction介绍;2.instruction指示,命令,说明;3.in在……里;4.idea主意,想法;5.immediately立即,马上;6.interesting有趣的;7.interestingly有趣地;8.importantly重要地;9.imagine想象,假设;10.information消息;

11.jump跳 12.keep保持;保留;13.knock敲;14.know知道,认识,了解

1.low低的;2.leave离开,落下;3.little小的,少许,一点,几乎没有;4.land土地,国家,着陆;5.live居住;6.large大的,巨大的;7.leg腿8.loser失主,失败者;9.line线,行列,路线;10.lost丢失;11.listen(to) 听;12.lead领导,带领,过……生活;13.lay摆,放,下蛋;14.long长的;15.last持续,最后

1.make(使)让;2.meet遇见;3.move移动;4.memory记忆;5.more更多;6.mark标记;7.management管理;8.married结婚;9.much十分,非常;10.mention提到;

11.many许多

1.near附近;2.nod点头;3.nothing什么也没有;4.nervous紧张的;5.notice注意;6.never从不;7.news新闻;8.natural自然的;9.mind介意;10.order命令,订购;11.out外面;12.over在……上方,结束;13.or或者;14.opinion观点;15.old

老的;16.of……的

1.program节目;2.pleased高兴的;3.progress进步;4.put放置;5.problem问题;6.patient耐心的;7.poor贫穷的;8.parents父母;9.place地点;10.push推;11.pull拉;12.pride骄傲,傲气;13.possible可能的;14.plan计划,打算;

15.pass通过,经过;16.proud自豪的;17.people人民,人们;18.peace和平

19.question问题;20.quiet安静的

1.relaxed放松的;2.raise举起,抬起;3.return返回,还;4.report报告;5.refuse拒绝;6.record记录;7.reach到达,抓到;8.realize认识到,了解;9.recognize认出

1.sometimes有时;2.some一些,若干;3.something有些事情;4.so因此;5.soon不久;6.straight直的,平的;7.sickness疾病;8.show给……看;9.sadness伤心;10.shake摇,摇动;11.satisfied满意的;12.sun太阳;13.sad伤心的;14.serious严重的;15.sudden突然;16.similar相似的;17.sense意义;18.stop停;19.swimmer游泳者;20.shy害羞的;21.slow慢的;22.strange陌生的;23.study学习,书房;

24.speak说话;25.special特殊的;26.surprise惊讶;27.soften使软,变软;

28.spend花费,度过;29.sport运动;30.seriously严肃地;31.successfully成功地;32.surprisingly惊讶地

1.take乘,花费;2.touch触摸;3.test测试;4.turn变化;5.tell告诉,讲;6.their他们的;7.terrible恐怖的;8.think想;9.thought想法;10.task任务;11.trouble麻烦;12.though即使;13.talk about谈论关于

1.up向上;2.to 3.under在……下面;4.until直到;5.understand理解,明白;

6.use使用;7.unfair不公平;8.uncertain不确定;9.unsafe不安全的;10.undoubted毫不怀疑的 11.value价值

1.while当……时候,然而;2.without没有;3.wish愿望;4.wide宽的;5.worry

担忧;6.worried担忧的;7.wound受伤;8.warn警告;9.wind风;10.winner获胜者;11.wall墙;12.walk走,散步;13.wife妻子;14.word单词;15.wonder好奇的;16.want想,想要;17.warm暖和的;18.war战争19.yet还;20.young年轻的,年少的

8,15 第五篇_大宗商品8.11-8.15走势

大宗商品一周走势及分析

(8.11-8.15)

核心提示

周内中国公布数据不及预期,欧元区和德国公布数据低迷,俄乌等地缘政治危机层出不穷,基本金属受压,其中跌幅最大的是铅和锌。①:伦铝虽也有抗跌迹象,但仍顶不住大环境的下压氛围,下跌0.71%。②:伦铜破位性下跌,虽有逢低接货,但空头氛围下还是表现供大于求,跌1.86%。③:螺纹钢持续下跌,周跌1.95%。④:动力煤,稳中有升,周内创下反弹以来新高,周涨0.097%。 一、 铜 (一) 价格表

(二) 现货、期货走势对比图

(三)分析

【期货走势】国内沪期铜表现较外盘抗跌,沪伦比值始终维稳在7.12附近,虽然跟随外盘回调,失守49000元关口,低位48620元/吨,完全承压60日均线,持仓量激增4万余手,抛压力量激增,呈现技术性破位态势。

【现货市场】 现货市场,期铜破位下跌,保值盘流出增加,加之交割前隔月价差保持在500元/吨左右,持货商逢高换现意愿强,供应压力增,现货升水难维,周初铜在5万元附近接货量虽有增加,但现铜跌破5万元后市场对后市看跌心态趋浓,底部位置进一步下降,观望情绪提升,暂停补货,周内虽逢低补货增加,但整体成交先扬后抑。

二、铝 (一)价格表【8,15】

(二) 现货、期货走势对比图

(三)分析

【期货走势】 国内沪期铝主力周初滞涨抗跌,甚至盘整区间稍有抬升,但随着伦铝跌破2000美元/吨关口,国内恐慌抛盘情绪出现,主力迅速跌破14000元/吨至13900元/吨低点,

并丧失30日均线支撑,但收盘再度顽强收于14000元/吨附近,周内成交量增加41.6万手至88.9万手,持仓量减少1.9万手至12.8万手。

【现货市场】周初现货波动区间进一步缩窄,SMM现货价格在14000-14070元/吨之间窄幅波动,中间商一方面对未来铝锭价格走势不明,另一方面本周现货成交贴水稳定在贴水100元/吨附近,套利交易区间也有限,参与市场积极性依旧不高,下游消费无起色,价格低端接货稍好,但持货商在14000元/吨关口挺价意愿较强,成交一度陷入拉锯状态,周末期铝大跌,SMM现货价格跌至13900元/吨,低价持货商惜售,出货减少,市场打破拉锯,呈现供不应求状态。 三 、 螺纹钢 (一) 价格表

(二)现货、期货走势对比图

(三)分析

【期货走势】期货方面,:螺纹钢持仓上空头延续增仓打压、部分旧空减仓,多头小幅补仓,多空分歧较大,空头抛压仍较大。短期盘面破位下探、空头延续压盘,做多资金偏小,行情跟风煤炭小幅反弹,3020-3050区或震荡反复波动,关注此区资金增减异动以防变盘大波动。

【现货市场】本周成都市场售价小幅上涨后陷入震荡状态。周初在本地主要钢厂的推动下,成都市场售价小幅拉升,部分规格依然短缺。但因处于传统淡季,销售情况偏淡,龙港钢材市场螺纹钢出库量在8000-10000吨之间,加之外围

8,15 第六篇_离婚协议书2016年8月15日

离婚协议书

男方:王**,男,汉族,19**年07月04日生,住址:

潍坊市**区**东街****号楼4单元202,身份证号码:3707**************,联系电话:137****2132。

女方:宋**,女,汉族,19**年01月29日生,住址:

潍坊市**区**西街****小区5号楼1单元501号,身份证号码:3707**************,联系电话:152****9123。

男方与女方于2015年07月28日在**区民政局登记结

婚,2016年1月16日,生育儿子***。现因夫妻感情彻底破裂,已无和好可能,自愿离婚。经双方商定达成一致意见,对有关事项达成以下协议:

一、子女抚养、抚养费及探望权

男方与女方的婚生儿子***由男方抚养。儿子***的抚养

费(生活费)男女双方平摊,由女方支付每月 元,支付给男方,由男方用于儿子***的生活消费,支付至18周岁,支付方式 (支付方式:1.现金2.银行、支付宝等电子转账,男方收到现金应当出具收到条确认数额和时间,收到银行、支付宝等电子转账应当发短信确认数额和时间);由男方负担每月 元,支付至18周岁。

儿子***的教育费、医疗费等费用由双方各负担一半,

生活中先由男方垫付,后凭发票、收据等票据找女方报销。

在不影响孩子学习、生活的情况下,双方都具有探视孩

子的权利,另一方应当积极配合,不得阻扰,否则按照本协议第四条每阻扰一次视为一次违约。

二、夫妻共同财产的处理

1.双方确认无共同财产,亦无需分割;

2.双方各自名下的其它财产归各自所有;

3.婚姻存续期间的男女双方工资、奖金等收入存放在一

起,后该共同财产用于男方父亲名下房子的装修上,男女双方确认对该共同财产不再分割,互不追索。

三、债务处理

双方确认在婚姻关系存续期间共同债务(截止到离婚

前,该笔债务用于儿子***看病、生活等) 元,男女双方各承担一半,离婚时女方按照本协议第二条约定的方式支付男方 元。

四、违约责任

任何一方不按本协议约定期限履行支付义务的,应支付

违约金一万元给对方。

五、生效条款

【8,15】

甲乙双方签字后生效;本协议一式三份,甲乙双方各执

一份,交婚姻登记机关存档备案一份。

六、争议解决方式

甲乙双方在履行本协议过程中发生争议,由**区人民法

院管辖。

七、补充条款 。

男方 (签字):

女方(签字):

2016年 月 日

8,15 第七篇_典范英语8-15

Here comes trouble

Chapter 1

On Friday afternoon Class Seven had an Art lesson. It was their favourite lesson of the week. Everyone looked forward to it.

Everyone except Trudy Hubble.

Trudy had elbows that stuck out and knocked things over. Her hands were large and clumsy. Her feet were so big she was always tripping over things.

When she came into the classroom Rob Mason said, ‘Look out, here comes Trouble!’【8,15】

This was Rob’s idea of a joke. He called her ‘Trouble’ because it sounded like her two names—Trudy Hubble—put together. The other kids laughed. Trudy had to smile and pretend she didn’t mind.

But she did mind. She minded a lot.

Mrs Weston said, ‘Sit down, Trudy. Let Lisa bring you a water jar and some paints.’

Trudy knew why Mrs Weston wanted her to sit down. Mrs Weston had been her teacher for three months now. She had seen what happened when Trudy tried to do Art. It was always a disaster!

Lisa Gibbs fetched paper and paint and brushes.

She put them on the table she shared with Trudy. Next, she filled a jar with water and took that to Trudy. Before she sat down she moved her chair as far away from Trudy as possible.

Trudy wished she could be more like Lisa. Lisa never knocked things over. She had small hands and feet and wavy brown hair. Trudy’s hair was as straight as straw.

‘Now, today,’ Mrs Weston said, ‘I’d like you to paint me a monster. The scariest monster you can think of.’

‘Oh, great!’ Class Seven loved painting monsters.【8,15】

Trudy decided to start with the eyes. The eyes were the scariest part of any monster. She dipped her brush in red paint. Then she made two large red circles on the paper.

Then two large yellow circles.

Then two large green circles.

But it didn’t look much like a monster. It looked more like two sets of traffic lights.

She glanced at Lisa’s picture. Lisa had painted a beautiful green dragon with flames coming out of its mouth.

Trudy sighed. She reached out to dip her brush in some black paint and-oh, no!

She knocked over the jam jar. Dirty water spread in a pool across the table. It drowned Lisa’s dragon.

‘Oops, sorry,’ Trudy muttered.

Lisa started down at her soggy picture. Tears came into her eyes.

Rob Mason came over to look. ‘Hey, Mrs Weston!’ he called. ‘Come and see what Trudy’s done now.’

Trudy went red in the face. ‘I’ll get a cloth,’ she muttered.

She jumped to her feet-and-

Her chair fell over backwards.

She turned round and her paintbrush caught Rob Mason across the face. It gave him a droopy black moustache.

He was so surprised that he staggered back against a wire bookstand. The bookstand came crashing down and books went all over the floor.

‘Oh, no!’ Mrs Weston came hurrying over. She caught her leg on Trudy’s chair and laddered her tights.

Chapter 2

I hate Art, Trudy thought as she went home on the bus. And I hate school! She wished she never had to go to school again.

The bus stopped outside her house. She jumped up from her seat. Her elbow knocked a woman’s hat right over her eyes. She got off the bus and ran indoors.

As soon as she opened the door she knew something was wrong. The house was too quiet. Not a sound from the kitchen. Not a sound in the hall.

‘Mum?’ she called.

‘I’m upstairs, Trudy.’ Mum’s voice sounded strange, all hoarse and croaky.

Trudy went upstairs two-at-a-time. She opened the bedroom door.

Mum lay in bed, holding a box of paper hankies. ‘I’ve got an awful cold,’ she said. ‘Don’t come too close or you might catch it.’

‘Okay.’ Trudy stayed near the door. ‘Shall I make you a mug of tea?’

Mum said quickly, ‘No, thanks. I’ll wait till your dad gets home.’

Trudy sighed. She knew why Mum didn’t want her to make any tea. She was afraid Trudy would spill it coming up the stairs.

‘What’s that?’ Trudy asked eagerly.

‘Take a message to Mrs Willow. Tell her I shan’t be well enough to come to work tomorrow.’ Mum blew her nose into a paper hanky. ‘She’s a very old lady. I don’t want to give her my cold.’

Trudy turned to the door.

‘Thanks. Oh, but Trudy-‘

Trudy stopped. ‘Yes, Mum?’

‘Mrs willow’s house is full of beautiful things. I have to be very, very careful not to break anything. So, if she asks you to come in, you’d better say no.’

Trudy sighed. ‘Yes, Mum.’

She went downstairs again and ran along the crowded street. ‘Oops, sorry,’ she said as she bumped into a passer-by. Luckily she didn’t have far to go.

Mrs willow lived in a tall, graceful old house. Trudy knocked on the door and waited. She heard the tap-tap of a stick coming from inside.

The door opened.

There stood an old lady with white hair and sharp blue eyes. Although she walked with a stick, she was tall and graceful, like her house.

‘Hello, Mrs Willow,’ said Trudy. ‘I’m Trudy Hubble. My mum’s your home help. She won’t be able to come tomorrow. She’s got a cold.

‘I’m sorry to hear that. What she needs is my special cold cure. Come inside and I’ll give you some.’ Mrs Willow opened the door wider.

Trudy remembered her mother’s warning, I’ll wait here,’ she said.

‘Nonsense, you can wait in my sitting room.’ Mrs Willow turned and started to walk down the hall, her stick tap-tapping on the floor.

Oh, help! thought Trudy. What should she do?

‘come in, come in,’ called Mrs Willow.

Trudy took a deep breath and stepped inside.

Chapter 3

Trudy looked round Mrs Willow’s sitting room.

She saw at once why Mum had been worried. There were beautiful things everywhere-pretty china figures and little glass animals, delicate tea sets and glass bowls. But the most beautiful thing of all stood alone on a little table. It was a large green-and-white vase with a dragon painted on the side.

Trudy stood very, very still. She was afraid to move in case she knocked something over. Stiff as a statue, she kept her

elbows pressed to her sides.

Mrs Willow came back into the room. ‘Ah, I see you’re looking at my Chinese vase,’ she said. ‘It’s very, very old. Do you like it?’

Trudy nodded.

Mrs Willow held out a small brown bottle. ‘Here’s my cold cure,’ she said. ‘Don’t ask me what’s in it. It’s an old family secret. But it always works.’

Trudy took the bottle. She couldn't speak because she was holding her breath.

Mrs Willow looked hard at her. ‘Is something wrong?’

Trudy shook her head.

‘But you’ve gone quite red in the face. Are you sure you’re all right?’

Trudy could hold her breath no longer. She let it out in a long, long sigh. ‘I’m fine,’ she said. ‘Thanks for the cold cure, Mrs Willow. I must go home now.’

Mrs Willow looked sad. ‘Can’t you stay for a cup of tea?’

‘No, I-I have to go.’

Trudy couldn't wait to get away. The room was too full of beautiful things. Any minute now there would be a disaster, she felt sure. She turned to the door.

Something furry brushed against her leg. Trudy jumped backwards.

The furry thing gave a loud ‘YEOWLL!’ It leaped on to the piano.

Trudy jumped again, sideways. Her elbow hit the green-and-white vase. It began to sway. She watched in horror as it rocked from side to side……to side to side……to side to side and…

It fell to the floor and broke into little pieces. DISASTER.

Nobody moved. The cat-who had caused all the trouble-sat on top of the piano. It swished its tail.

Then Trudy said, ‘Oh, I’m sorry. I’m really sorry. It’s because I’m clumsy. That’s why I didn't want to came into your house. I knew something would get broken. It always does when I’m around.’

‘It’s all right,’ Mrs Willow said calmly.

Surprised, Trudy stared at her.

‘Not a bit. You see, that vase has been broken before. It had to be mended then. And do you know who broke it?’ Mrs Willow smiled. ‘I did, when I was just about your age. Yes, I used to be clumsy too.’

Trudy couldn’t believe it. Mrs Willow seemed so tall and graceful. She didn't look the sort of person who would knock things over.

‘You couldn't have been as clumsy as I am,’ she said.

Mrs Willow took a photo from the top of the piano. ‘Do you see this girl playing tennis?’ she asked. ‘Well, that was me.’ Trudy looked at the photo.

The girl playing tennis was tall and thin with untidy hair. She had a wide grin on her face.

Mrs Willow laughed. ‘I was a real ugly duckling, wasn’t I? But do you remember what happened to the ugly duckling?’ Trudy nodded. ‘It grew up to be a swan. But I don't think I shall. I’ll just grow up to been ugly duck.’

‘Not if you do as I did. You have to keep telling yourself that inside, where it matters, you’re really a swan.’

Trudy said doubtfully, ‘I’m a swan.’

‘It does work, you know. It’s a kind of magic. Say it again. This time, as if you really believe it.’

Trudy cleared her throat. She said it louder.

Mrs Willow smiled. ‘Now help me clear up these bits of old vase. Then we’ll have some tea.’

They drank tea from china cups. They ate chocolate cake off delicate plates.

And Trudy didn't break another thing. She ran home muttering, ‘I’m a swan, I’m a swan,’ and she didn't bump into a single person. So perhaps it was a kind of magic, after all.

But what would happen tomorrow, when she went to school.

Chapter 4

Next morning Mum’s cold was much better. ‘That’s because of Mrs Willow’s secret family cure,’ Trudy said.

‘It tastes horrible,’ said Mum. ‘But it seems to work.’

Trudy was glad the cold cure had worked. It proved that Mrs Willow knew what she was talking about. And if the cold cure worked, then the swan cure might work as well. She couldn’t wait to try it out.

On the way to school she tired thinking herself a swan.

She glided on to the bus and sat down slowly. She didn’t trip over anyone’s feet. She didn’t knock anyone’s hat off. When the bus stopped, she rose slowly from her seat.

She stepped on to the pavement.

It was surprising how different she felt, so tall and graceful.

In the school playground some children stood looking up into the chestnut tree.

‘Look out, here comes Trouble!’ called Rob Mason when he saw her.

Trudy pretended not to hear him. She saw that Lisa Gibbs was in tears. ‘What’s the matter?’ she asked.

‘It’s Lisa’s kite,’ said Rob. ‘It’s got stuck up the tree.’

‘Rob did it,’ Lisa said, wiping her eyes. ‘He let go and it flew up into the tree.’

Rob looked a bit ashamed of himself. ‘Stupid old kite,’ he muttered.

‘It’s a beautiful kite!’ said Lisa. ‘I got it for my birthday. It was my best present.’ She began to sob again.

‘Don’t cry,’ Trudy said kindly. I’ll get it down for you. I’m good at climbing trees.’

Lisa looked horrified. ‘No, you’ll tear it! It’s only made of paper. Can’t somebody else get it down?’

But nobody else wanted to climb the tree.

Trudy jumped up and grabbed the lowest branch. She swung herself up and began to climb.

‘Be careful,’ called Lisa. ‘It’s a special Chinese kite. It cost a lot of money.

Like the vase, Trudy though, and nearly stopped. But then she thought of Mrs Willow.

‘I’m a swan, I’m a swan,’ she muttered.

And she started climbing again. She climbed higher and higher until she reached the kite.

The kite was caught on a sharp twig. It was made of thin, silky paper and had a green dragon painted on it. Don’t rush, she told herself. Swans never rush.

At last she managed to free the kite.

But now she had to climb down again using only one hand. It took her ages, but she didn't rush.

She saw that Mrs Weston had joined the crowd below. But she still didn't rush.

Very, very carefully she swung herself down to the ground.

The kite was safe!

‘Thanks, Trudy.’ Lisa showed it to the others. ‘Look, it’s all right!’

Trudy felt very, very proud. But then Mrs Weston said, ‘Trudy Hubble, what a mess you look! Your hands and knees are filthy. Go and wash them ATONCE!’

For a moment Trudy felt like her old clumsy self. But then she remembered what Mrs Willow had said. It didn't matter how she looked outside. Inside, she was really a swan.

Trudy smiled at Mrs Weston. Then she glided swan-like across the playground and into school.

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