必修①1-2-1-1
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新人教版高一数学必修一目录
一、第一章函数
1. 基本概念
2. 函数的表示法
3. 函数的图象
4. 函数的性质
二、第二章曲线
1. 曲线的表示法
2. 曲线的切线
3. 兰联形曲线
4. 椭圆曲线
5. 双曲线
三、第三章相关与回归
1. 相关系数
2. 线性回归与回归直线
四、第四章初等函数
1. 指定法求方程的根
2. 二次函数及加减乘除法
3. 牛顿迭代法求方程的根
五、第五章指数函数
1. 指数函数的基本性质
2. 常用指数函数
3. 对数函数及其应用
六、第六章对数函数及其应用
1. 对数函数的基本性质
2. 对数函数及其应用
七、第七章几何极限
1. 无穷小分析法
2. 无穷量极限
3. 二元函数极限
4. 级数的极限
八、第八章函数的微分
1. 导数的概念
2. 定义型微分
3. 导数的性质及应用
九、第九章函数的积分
1. 定积分及其应用问题
2. 微积分的应用ii
3. 曲线的积分性质。
江苏高中数学目录全 WTD standardization office【WTD 5AB- WTDK 08- WTD 2C】高一上:必修一、二高一下:必修三、四高二上:必修五、选修1-1(文)、选修2-1(理)高二下:文选修1-2,理选修2-2、2-3高一数学上数学1第1章集合集合的含义及其表示子集、全集、补集交集、并集第2章函数概念与基本初等函数Ⅰ函数的概念和图象函数的概念和图象函数的表示方法函数的简单性质映射的概念指数函数分数指数幂指数函数对数函数对数对数函数幂函数函数与方程二次函数与一元二次方程用二分法求方程的近似解函数模型及其应用数学2第3章立体几何初步空间几何体棱柱、棱锥和棱台圆柱、圆锥、圆台和球中心投影和平行投影直观图画法空间图形的展开图柱、锥、台、球的体积点、线、面之间的位置关系平面的基本性质空间两条直线的位置关系直线与平面的位置关系平面与平面的位置关系第4章平面解析几何初步直线与方程直线的斜率直线的方程两条直线的平行与垂直两条直线的交点平面上两点间的距离点到直线的距离圆与方程圆的方程直线与圆的位置关系圆与圆的位置关系空间直角坐标系空间直角坐标系空间两点间的距离高一数学下数学3第5章算法初步算法的意义流程图基本算法语句算法案例第6章统计抽样方法总体分布的估计总体特征数的估计线性回归方程第7章概率随机事件及其概率古典概型几何概型互斥事件及其发生的概率数学4第8章三角函数任意角、弧度任意角的三角函数三角函数的图象和性质第9章平面向量向量的概念及表示向量的线性运算向量的坐标表示向量的数量积向量的应用第10章三角恒等变换两角和与差的三角函数二倍角的三角函数几个三角恒等式高二数学上数学5第11章解三角形11.1正弦定理11.2余弦定理11.3正弦定理、余弦定理的应用第12章数列12.1等差数列12.2等比数列12.3数列的进一步认识第13章不等式13.1不等关系13.2一元二次不等式13.3二元一次不等式组与简单的线性规划问题 13.4基本不等式文科数学选修系列11-1(上)第1章常用逻辑用语1.1命题及其关系1.2简单的逻辑联结词1.3全称量词与存在量词第2章圆锥曲线与方程2.1圆锥曲线2.2椭圆2.3双曲线2.4抛物线2.5圆锥曲线与方程第3章导数及其应用3.1导数的概念3.2导数的运算3.3导数在研究函数中的应用3.4导数在实际生活中的应用1-2(下)第1章统计案例1.1假设检验1.2独立性检验1.3线性回归分析1.4聚类分析第2章推理与证明2.1合情推理与演绎推理2.2直接证明与间接证明2.3公理化思想第3章数系的扩充与复数的引入3.1数系的扩充3.2复数的四则运算3.3复数的几何意义第4章框图4.1流程图5.2结构图理科数学选修系列22-1(上)第1章常用逻辑用语1.1命题及其关系1.2简单的逻辑连接词1.3全称量词与存在量词第2章圆锥曲线与方程第3章空间向量与立体几何2-2(上)第1章导数及其应用第2章推理与证明第3章数系的扩充与复数的引入 2-3(下)第1章计数原理第2章概率第3章统计案例。
参数方程是必修几高一数学必修有5本,必修1到必修5。
高一上必修1、必修2、必修4、必修5。
高二上必修3和选修。
必修1主要是集合与函数;必修2主要是空间几何体,点与直线平面的关系,直线与方程,圆与方程;必修4主要是三角函数和平面向量;必修5主要是解三角形,数列和不等式。
高中数学共学习11本书,其中必修5本,选修6本。
必修课本为必修1、2、3、4、5,选修课本为选修2-1,2-2,2-3,4-1(几何证明选讲),4-4(坐标系与参数方程),4-5(不等式选讲)。
高考范围的书:高考范围为必修1、2、3、4、5,选修课本为选修2-1,2-2,2-3,而选修4-1(几何证明选讲),4-4(坐标系与参数方程),4-5(不等式选讲),三选二,共10本。
就教学进度来说,各个学校可根据实际情况安排。
就我们学校来说,先学习高考考察的主干知识,再学习零散知识,速度由慢到快,深度有难到易,难度自始至终与广东高考理科数学难度相当。
高一第一学期刚开学不讲上述11本书的内容,而是对初、高中的知识进行衔接,继续深入探讨二次函数的性质和应用,韦达定理,二次根式,因式分解等。
接着进入必修1的学习,然后是选修2-2的导数部分。
本学期学习的核心是函数与导数。
高一第二学期学习必修5的数列部分,必修4,核心是数列、三角与平面向量。
高二第一学期先学习选修4-1,再学习必修2的立体几何部分,然后是必修2和选修2-1的解析几何部分的直线、圆和椭圆,核心是平面几何、立体几何和解析几何。
高二第二学期继续必修2和选修2-1的解析几何部分的双曲线、抛物线的学习,接着是隶属与解析几何的选修4-4,再学必修5的线形规划部分,再学选修2-3的其余部分(包括排列组合与二项式定理、概率与统计)。
接着完成选修2-2的其余部分(包括定积分、数学归纳法、复数),选修2-1其余部分(包括常见逻辑用语、空间向量),必修5和选修4-5的不等式部分,必修3(算法)等零散知识的学习,结束高中理科数学课程。
高中英语北师大版必修一英语单词Unit1topic Talk1.senior /ˈsiːniə/adj.较高的,高级的2.secondary /ˈsekəndəri/adj.中等教育的;中级的;次要的3.stressful /ˈstresfəl/adj.充满压力的,紧张的4.challenging /ˈtʃæləndʒɪŋ/adj.富有挑战性的5.differ /ˈdɪfə/vi.不同,不一样,有区别6.previous /ˈpriːviəs/adj.以前的,先前的7.dynamic /daɪˈnæmɪk/adj.充满活力的;精力充沛的8.campus /ˈkæmpəs/n.校园9.schedule /ˈʃedjuːl/n.日程表,计划表10.expectation /ˌekspekˈteɪʃən/n.期待;预料,预期11.confidence /ˈkɒnfɪdəns/n.自信,信心;信赖petence /ˈkɒmpɪtəns/n.能力,胜任13.chapter /ˈtʃæptə/n.一段时期;章节14.all in all 总而言之,总的来说15.apartment /əˈpɑːtmənt/n.公寓套房16.am /ˌeɪˈem/(ante meridiem)午前,上午17.shift /ʃɪft/n.(工厂、医院等轮班制的)当班时间18.pressure /ˈpreʃə/n.压力19.leisure /ˈleʒə/n.空闲,空暇,业余时间20.recover /rɪˈkʌvə/vi.恢复健康,康复21.injury /ˈɪndʒəri/n.伤,损害22.plus /plʌs/adj.有利的,好的prep.加23.unfortunately /ʌnˈfɔːtʃənətli/adv.不幸地;令人遗憾地24.challenge /ˈtʃæləndʒ/n.挑战;具有挑战性的事物vt.向……挑战25.arise /əˈraɪz/vi.(问题或困难)出现,发生Lesson 126.lifestyle /ˈlaɪfstaɪl/n.生活方式27.chat /tʃæt/vi. &n.闲谈,聊天28.surf /sɜːf/vi. &vt.冲浪29.surf the Internet 网上冲浪,浏览因特网30.voluntary /ˈvɒləntəri/adj.志愿的;服务的;自愿的31.engine /ˈendʒɪn/n.引擎32.search engine 搜索引擎33.definitely /ˈdefɪnɪtli/adv.确切地,肯定地34.teen /tiːn/adj.青少年的,十几岁孩子的ptop /ˈlæptɒp/n.笔记本电脑,便携式电脑36.digital /ˈdɪdʒətl/adj.数字的,数码的37.native /ˈneɪtɪv/n.本地人38.range /reɪndʒ/n.一系列;范围39.various /ˈveəriəs/adj.各种各样的;多种(类型)的40.hardware /ˈhɑːdweə/n.(计算机)硬件41.necessity /nəˈsesəti/n.必需品42.convenient /kənˈviːniənt/adj.方便的,便利的43.quality /ˈkwɒləti/n.质量,品质44.from time to time 有时;偶尔;间或45.living room 起居室46.addict /ˈædɪkt/n.对……着迷的人47.according to 按……所说,根据48.in person 亲自49.media /ˈmiːdiə/n.新闻媒体,大众传播媒介(总称)50.social media 社交媒体51.actually /ˈæktʃuəli/adv.实际上,事实上52.drag /dræɡ/vt.拖,拉53.tend to do sth. 易于做某事54.goal /ɡəʊl/n.目标,目的55.aim /eɪm/n.目的,意图vi.力求达到56.target /ˈtɑːɡɪt/n.目标57.update /ʌpˈdeɪt/vt.更新58.* meanwhile /ˈmiːnwaɪl/adv.与此同时59.distance /ˈdɪstəns/n.距离,间距60.volunteer /ˌvɒlənˈtɪə/vi. &vt.自愿;志愿n.志愿者61.revise /rɪˈvaɪz/vi. &vt.复习62.saying /ˈseɪɪŋ/n.格言,谚语63.ahead /əˈhed/adv.在前面;向前64.get ahead 取得进步,获得成功Lesson 265.café /ˈkæfeɪ/n.咖啡馆,小餐馆66.downtown /ˌdaʊnˈtaʊn/adv.向/在城镇商业中心区67.stress /stres/n.压力;忧虑;紧张68.suffer /ˈsʌfə/vi. &vt.遭受(痛苦)69.suffer from(身体或精神上)遭受……(痛苦)70.reduce /rɪˈdjuːs/vt.减少;降低;缩小71.expert /ˈekspɜːt/n.专家,行家72.frank /fræŋk/adj.坦率的,坦诚的73.to be frank 坦白说,坦率地说74.editor /ˈedɪtə/n.编辑,主编75.remove /rɪˈmuːv/vt.移走;去掉76.entirely /ɪnˈtaɪəli/adv.完全地,彻底地77.position /pəˈzɪʃən/n.职位;位置itary /ˈmɪlɪtəri/n.军队,武装力量79.due to 因为80.absolutely /ˈæbsəluːtli/adv.正是,当然81.stressed /strest/adj.焦虑的,紧张的82.extent /ɪkˈstent/n.程度83.thus /ðʌs/adv.因此,因而,从而84.tension /ˈtenʃən/n.紧张;焦虑anise /ˈɔːɡənaɪz/vt.组织,筹划86.in other words 换句话说87.function /ˈfʌŋkʃən/n.功能88.seek /siːk/vt.寻求;请求89.professional /prəˈfeʃənəl/adj.专业的,职业的Lesson 390.feature /ˈfiːtʃə/vt.以……为特色,是…的特征91.typical /ˈtɪpɪkəl/adj.平常的,一贯的;典型的92.province /ˈprɒvins/n.省93.graduate /ˈɡrædʒueɪt/vi.毕业94.graduate from 从……毕业95.certificate /səˈtɪfɪkət/n.合格证书96.inspire /ɪnˈspaɪə/vt.鼓励,激励97.apply /əˈplaɪ/vi.申请;请求98.apply for 申请99.eager /ˈiːɡə/adj.热切的;渴望的100.s ort /sɔːt/n.种,类;类型101.s ort of 有几分,有点102.i ndependently /ˌɪndəˈpendəntli/adv.独立地,自立地103.p ower /ˈpaʊə/n.电,电力;力量104.s upply /səˈplaɪ/n.供应,供给105.u nstable /ʌnˈsteɪbəl/adj.不稳定的106.d usty /ˈdʌsti/adj.布满灰尘的107.m uddy /ˈmʌdi/adj.泥泞的,多泥的108.t ough /tʌf/adj.困难的,难办的109.f lash /flæʃ/vi. &vt.闪现,闪过n.照相机闪光灯110.g ive up 放弃111.d eal with 对付,应付,处理112.r esponsible /rɪˈspɒnsəbəl/adj.负责的;有责任心的113.b e responsible for 对……负责114.a ttractive /əˈtræktɪv/adj.有吸引力的;好看的,美观的115.a s well as ……以及……116.l aughter /ˈlɑːftə/n.笑;笑声117.c onfident /ˈkɒnfɪdənt/adj.自信的118.* besides /bɪˈsaɪdz/adv.除此之外,而且119.c ontact /ˈkɒntækt/n.联系,联络vt.(写信,打电话)联系(某人)120.c harity /ˈtʃærəti/n.慈善机构,慈善团体121.o rganisation /ˌɔːɡənaɪˈzeɪʃən/n.组织,团体,机构122.c ontribution /ˌkɒntrɪˈbjuːʃən/n.贡献123.i ntend /ɪnˈtend/vt.计划,打算,想要124.W riting Workshop125.j unior /ˈdʒuːniə/adj.低年级的126.f ormal /ˈfɔːməl/adj.正式的,官方的127.i nformal /ɪnˈfɔːməl/adj.非正式的128.a dapt /əˈdæpt/vi.(使)适应129.a dapt to sth. 适应某事130.g ym /dʒɪm/n.体育馆,健身房131.m oment /ˈməʊmənt/n.某一时刻132.a t the moment 此刻,目前,眼下133.p resentation /ˌprezənˈteɪʃən/n.报告;陈述,说明134.s lide /slaɪd/n.幻灯片135.f orward /ˈfɔːwəd/adv.向前;进展136.l ook forward to(doing)sth. 期待,盼望137.R eading Club 1138.d igestion /daɪˈdʒestʃən/n.消化Reading Club 2139.r ecreation /ˌrekriˈeɪʃn/n.娱乐,消遣140.e ntertainment /ˌentəˈteɪnmənt/n.娱乐141.r ural /ˈrʊərəl/adj.农村的,乡村的,田园的Unit 2142.a thlete /ˈæθliːt/n.运动员143.f requency /ˈfriːkwənsi/n.发生的频率,发生率144.p refer /prɪˈfɜː/vt.更喜欢145.r ather than 而不是146.b adminton /ˈbædmɪntən/n.羽毛球147.g olf /ɡɒlf/n.高尔夫148.g ymnastics /dʒɪmˈnæstɪks/n.体操149.j og /dʒɒɡ/vi. &n.慢跑150.c ycle /ˈsaɪkəl/vi.骑自行车151.b owling /ˈbəʊlɪŋ/n.保龄球152.s kateboard /ˈskeɪtbɔːd/n.滑板vi.用滑板滑行153.t rack /træk/n.跑道154.i n good / bad shape 健康状况良好/不佳155.b alanced /ˈbælənst/adj.均衡的156.d iet /ˈdaɪət/n.日常饮食157.s tair /steə/n.楼梯;梯级158.r egularly /ˈreɡjələli/adj.经常;定期地159.n et /net/n.(网球等的)球网;网160.c ourt /kɔːt/n.(网球等的)球场161.w ithin /wɪðˈɪn/prep.在……之内Lesson 1162.u nderdog /ˈʌndədɒɡ/n.处于劣势的人(队);弱方163.d efeat /dɪˈfiːt/vt.(在比赛、战争中)战胜,打败164.c ompany /ˈkʌmpəni/n.公司;一群人165.g uy /ɡaɪ/n.(非正式)男人,家伙166.c hampion /ˈtʃæmpiən/n.冠军,第一名167.* shot /ʃɒt/n.投球,击球168.i nspiration /ˌɪnspəˈreɪʃən/n.激励,鼓舞;给人以灵感的人/物;灵感169.t ry out for sth. 争取成为;参加选拔170.* bench /bentʃ/n.替补队员席171.r eplacement /rɪˈpleɪsmənt/n.替换的人(物)172.d esire /dɪˈzaɪə/n.渴望173.c rash /kræʃ/vi. & vt.猛撞174.c rash into 猛撞,猛击175.g ather /ˈɡæðə/vi. &vt.聚集,聚合176.g ather around 聚集177.n ot...anymore 不再……178.p ack /pæk/n.包,包裹vi. &vt.把……包起来179.s harply /ˈʃɑːpli/adv.严厉地,毫不客气地180.l et sb. down 使失望,辜负(别人的信任或期望)181.o nto /ˈɒntʊ/prep.到……上,向……上182.e xtra /ˈekstrə/adj.额外的,另外的183.p ay off 取得成功;奏效184.k eep up with 跟上,保持同步185.e nergy /ˈenədʒi/n.力量,活力186.c rowd /kraʊd/n.人群187.c lap /klæp/vi. &vt.鼓掌,拍手188.e arn /ɜːn/vt.赢得;博得Lesson 2189.b oxing /ˈbɒksɪŋ/n.拳击(运动)190.b ounce /baʊns/vi. &vt.(使)弹起,(使)反弹191.b elt /belt/n.腰带,皮带192.a nnouncement /əˈnaʊnsmənt/n.通告,公告193.d efence /dɪˈfens/n.防守队员,后卫194.a udience /ˈɔːdiəns/n.观众;听众195.r emind /rɪˈmaɪnd/vt.使(某人)想起,提醒196.b ite /baɪt/vi. &vt.咬197.p rohibit /prəˈhɪbɪt/vt.禁止198.c ase /keɪs/n.状况,场合;事例,实例199.i n case 以防万一200.s ign up 报名201.a nnual /ˈænjuəl/adj.一年一度的,每年的202.a pplication /ˌæplɪˈkeɪʃən/n.申请书203.w arm-up 热身运动,准备活动204.q uit /kwɪt/vi. &vt.停止(做某事)205.h alfway /ˌhɑːf ˈweɪ/adv.半途地206.t ip /tɪp/n.建议,忠告,窍门207.o ught to aux.应该,应当208.o ccupy /ˈɒkjupaɪ/vt.占用,占去(时间)209.d isappointment /ˌdɪsəˈpɔɪntmənt/n.失望;扫兴;沮丧210.a mazingly /əˈmeɪzɪŋli/惊人地,了不起地Lesson 3211.r elieve /rɪˈliːv/vt.减轻,缓解212.s trengthen /ˈstreŋθən/vi. &vt.(使)强健213.* immune /ɪˈmjuːn/adj.免疫的;有免疫力的214.s ystem /ˈsɪstɪm/n.系统215.i mmune system 免疫系统216.c heer up(使)高兴起来,(使)振作起来217.w eekly /ˈwiːkli/adj.一周一次的,每周的218.b e fed up with 厌烦的,不满的无法再忍受的219.a wkward /ˈɔːkwəd/adj.令人尴尬的220.p articular /pəˈtɪkjələ/n.尤其,特别adj.特定的221.i n particular 尤其,特别222.b enefit /ˈbenɪfɪt/n.好处,益处223.m embership /ˈmembəʃɪp/n.会员身份224.e quipment /ɪˈkwɪpmənt/n.设备,装备225.c apable /ˈkeɪpəbəl/adj.能干的;能力强的226.b e capable of 有能力做227.p revent /prɪˈvent/vt.预防;阻止,阻挡228.d isease /dɪˈziːz/n.疾病229.u pper /ˈʌpə/adj.较上的,上面的230.f low /fləʊ/vi.流,流动n.流动231.o xygen /ˈɒksɪdʒən/n.氧232.r elief /rɪˈliːf/n.减轻,缓解233.a che /eɪk/n.隐痛234.g uideline /ˈɡaɪdlaɪn/n.指导方针,指导原则235.c lick /klɪk/vi. &vt.点击(鼠标)236.d etail /ˈdiːteɪl/n.细节237.p rinciple /ˈprɪnsəpəl/n.原则,基本的观念238.a mount /əˈmaʊnt/n.数量,数额239.s hortcut /ʃɔːtkʌt/n.捷径,近路240.o vernight /ˌəʊvəˈnaɪt/adv.突然,一下子241.a chievable /əˈtʃi:vəbəl/adj.可完成的;做得成的242.m ake sure 确保243.m uscle /ˈmʌsəl/n.肌肉244.b one /bəʊn/n.骨头,骨245.s atisfaction /ˌsætɪsˈfækʃən/n.满足,满意246.s weat /swet/n.汗水247.o verdo /ˌəʊvəˈdu/vt.把……做得过火248.W riting Workshop249.s ight /saɪt/n.视野250.c yclist /ˈsaɪklɪst/n.骑自行车者,自行车运动员251.o vertake /ˌəʊvəˈteɪk/vt.超过252.a mazed /əˈmeɪzd/adj.大为惊奇的,惊讶的253.s portsmanship /ˈspɔːtsmənʃɪp/n.体育精神254.* bronze /brɒnz/n.铜255.m edal /ˈmedl/n.奖牌;勋章256.r esponse /rɪˈspɒns/n.回答,答复257.* gesture /ˈdʒestʃə/n.姿态;手势;姿势258.t ake advantage of sth. 利用某物Reading Club 1259.d efend /dɪˈfend/vi. & vt.保护,保卫260.R eading Club 2261.f lexibility /ˌfleksəˈbɪləti/n.灵活性。
Book1Unit1add v / æd /1.add put with sth else [T] to put something with something else or with a group of other things(1)If the mixture seems dry, add water.(2) add sth to sth Do you want to add your name to the list?2. add up phr v .to calculate the total of several numbers(1)I can add up in my head quite easily.(2) add sth ←→up Specialized software adds up the statistics.3.add up to sth: phr produce a particular total or resultRising prison population and overcrowding add up to a real crisis.ignore to behave as if you had not heard or seen someone or something(1)The phone rang, but she ignored it. (2)Sam rudely ignored the question.REGISTER In everyday British English, people often say take no notice of something or not take any notice of something rather than ignore something.There are signs telling you not to smoke, but people don’t take any notice of them.upset: to make someone feel unhappy or worried: Don’t do anything that would upset him.calm (1) a place, period of time, or situation is calm, there is less activity, trouble etc than there ometimes is, or than there has been recently : The financial markets are calm at the moment.(2) to become quiet and relaxed after you have been angry, excited, nervous, or upset, or to make someone become quiet and relaxed : He tried to calm the frightened children. Calm down and tell me what happened(3) remain/stay/keep calm I tried to stay calm and just ignore him.(4) calm yourself (down) She lit a cigarette to calm herself down.(5) calm down.if a situation calms down, it becomes easier to deal with because there are fewer problems and it is not as busy as it was before It took months for things to calm down after we had the baby.concern v [T] (1) [not in passive ] if a story, book, report etc concerns someone or something, it is about themThis study concerns couples’expectations of marriage.(2)to make someone feel worried or upset Issues like food additives do concern me.(3).[not in passive ] if an activity, situation, rule etc concerns you, it affects you or involves you The tax changes will concern large corporations rather than small businesses.concern n / kən'sɜːn ; kənˋsɝn(1) [U] a feeling of worry about something important .In her last days the poet expressed concern for her father. [+ for ]our concern for human rights [ + about/over/with ] the rise of concern about the environment(2) [C,U] something that is important to you or that involves you His main concern is to be able to provide for his family. [+ about ]She is concerned about how little food I eat. [+ for ] He called the police because he was concerned for Gemma’safetygo through phr v go through sth to experience a difficult or unpleasant situation, feeling etcWhen you’re going through a crisis, it often helps to talk to someone. He’s going through a divorce at the moment.set sth/sb ←→down phr v1to write about something so that you have a record of itI wanted to set my feelings down on paper.series of sth several events or actions of a similar type that happen one after the otherthe series of events that led to the outbreak of warThe police are investigating a series of attacks in the area.out‧doors adv / ‚aʊt'dɔːz ; ͵autˋdɔrz / outside, not in a buildingSYN out of doors OPP indoors It’s warm enough to eat outdoors tonight. He likes to work outdoors.do sth on purpose PHRASE If you do something on purpose, you do it intentionally.You make it sound as if I did it on purpose! Was it an accident or did David do it on purpose?at duskThe street lights go on at dusk. We arrived home at dusk.Thunder (1) [U] the loud noise that you hear during a storm, usually after a flash of lightningWe were woken in the night by thunder.(2) V-I When it thunders, a loud noise comes from the sky after a flash of lightning.The day was heavy and still. It would probably thunder later.entire (1) ADV Entirely means completely and not just partly. ...an entirely new approach.…It was the worst day in my entire life. Our situation is entirely different.power ABILITY (1) [C,U] a natural or special ability to do something[+ over ] People should have more power over the decisions that affect their lives.After the accident she lost the power of speech (= ability to speak ) .(2) Nuclear power is cleaner than coal.draw/close/pull the curtains Ella drew the curtains and switched the light on.draw back/open the curtains Shall I open the curtains?covered with dust Adrian cycled along the dusty road. Everything’s really dusty.partnerHe's a partner in a Chicago law firm.suf‧fer v / 'sʌfə; ˋsʌfɚ/ PAIN [I,T] to experience physical or mental painAt least he died suddenly and didn’t suffer. She’s suffering a lot of pain.[+ from ] I’m suffering from a bad back. Mary’s suffering from ill health at the moment.recover to get better after an illness, accident, shock etcAfter a few days of fever, she began to recover. [+ from ] He’s in hospital, recovering from a heart attack.tiredso tired (that) I’m so tired I could sleep for a week.tired of (doing) sth bored with something, because it is no longer interesting, or has become annoyingI’m tired of watching television; let’s go for a walk.I was getting tired of all her negative remarks.pack[+ of ]a pack of three T-shirtspack sth ←→up I gave her a hand packing up her clothes and stuff.pack up phr v1to put things into cases, bags etc ready for a trip somewhereMost of the holidaymakers had packed up and gone.towerEach corner had a guard tower, each of which was exactly ten metres in height.swap [I,T] to give something to someone and get something in return SYN exchange Do you want to swap umbrellas? swap sth for sth He swapped his watch for a box of cigars.swap sth with sb The girls chatted and swapped clothes with each other.dis‧like v [T not in progressive ] / dɪs'laɪk ; dɪsˋlaɪk / 1to think someone or something is unpleasant and not like them OPP like Why do you dislike her so much?dislike doing sth I dislike being the centre of attention.Unit2elevator n [C] S3 W3 / 'elɪveɪtə'eləveɪtə; ˋɛlə͵vetɚ/ a machine that takes people and goods from one level to another in a building SYN liftWe’ll have to take the elevator. We took the elevator to the fourteenth floor.officialan official investigation into the causes of the explosion the official policy on educationthe Queen’s performance of official dutiesan official visit/engagement etc The President was leaving for a four-day official tour of Mexico.voyageThe voyage from England to India used to take six months.Writing a biography is an absorbing voyage of discovery.He aims to follow Columbus's voyage to the West Indies.native (1) COUNTRY [only before noun ] your native country, town etc is the place where you were born →home They never saw their native land again. He spent most of his professional life outside his native Poland.(2) SYN first language English is not the native language for almost half of our overseas visitors.(3)the native traditions of Peru Dr. Aubin is a native of St. Louis. Joshua Halpern is a native Northern Californian. She spoke not only her native language, Swedish, but also English and French.(4) ADJ Plants or animals that are native to a particular region live or grow there naturally and were not brought there. ...a project to create a 50 acre forest of native Caledonian pines.…The coconut palm is a native of Malaysia.Singapore has many native species of palm.[+ to ]These fish are native to North America.come up phr v (1) if someone comes up to you, they come close to you, especially in order to speak to youOne of the teachers came up and started talking to me.(2) [+ to ] A man came up to him and asked for a light.(3)if a subject comes up, people mention it and discuss it SYN arise His name came up in the conversation.The subject of salaries didn’t come up.(4)if the sun or moon comes up, it moves up into the sky where you can see it SYN riseIt was six o’clock, and the sun was just coming up.(5) if a plant comes up, it begins to appear above the ground The first spring bulbs are just coming up. apartment n [C] S2 W3 / əˈpɑːtmənt ; əˋpɑrtmənt / a set of rooms on one floor of a large building, where someone lives She lives in a small apartment.actually adv S1 W1 / ˈæktʃuəli, -tʃəli ; ˋæktʃu əlɪ/ (1) [sentence adverb ] used to add new information to what you have just said, to give your opinion, or to start a new conversation spokenI’ve known Barbara for years. Since we were babies, actually.Actually, on second thoughts, I don’t think I want to go out tonight.(2)used to emphasize the real or exact truth of a situation, rather than what people may thinkWhat time are you actually leaving? Labor costs have actually fallen.—‘Disappointed?’—‘No, actually I’m rather glad.’(3) ADV You can use actually when you are politely expressing an opinion that other people might not have expected from you.—"Do you think it's a good idea to socialize with one's patients?" —"Actually, I do, I think it's a great idea."“base 1 v S1 W1 / beɪs ; bes / 1[T usually passive ] to have your main place of work, business etc in a particular place The paper had intended to base itself in London.be based in sth The new organization will be based in Dallas.base 2n (1) lowest part [C usually singular ]1) the lowest part or surface of something SYN bottoma frozen dessert with a biscuit base a wine glass with a heavy base [+ of ] There is a door at the base of the tower. the base of a triangle(2) the lowest point on a plant or part of your body, where it joins another part SYN bottom [+ of ]a hole in the base of the treebase 3 knowledge/ideas [C] the most important part of something, from which new ideas develop SYN foundation India has a good scientific research base.at presentat this time SYN now The item you want is not available at present.At present, the airport handles 110 flights a day.make use of sth to use something that is available in order to achieve something or get an advantage for yourselfWe will make use of her vast experience.There is an answering machine for you to make use of. Try to make good use of your time.It’s no use complaining.latterWhere unemployment and crime are high, it can be assumed that the latter is due to the former.Celebrations are planned for the latter part of November.identity (1) [C,U] someone’s identity is their name or who they areThe identity of the killer is still unknown.(2) N-V AR The identity of a person or place is the characteristics that distinguish them from others.I wanted a sense of my own identity.fluent adj / 'fluːənt ; ˋfluənt / (1) able to speak a language very well [+ in ]She was fluent in English, French, and German.(2) fluent French/Japanese etcsomeone who speaks fluent French etc speaks it like a person from that countryHe spoke in fluent Italian.(3) fluent speech or writing is smooth and confident, with no mistakesHe was a fluent and rapid prose writer.(3)Someone who is fluent in a particular language can speak the language easily and correctly. You can also say that someone speaks fluent French, Chinese, or some other language.She studied eight foreign languages but is fluent in only six of them.fluency. N-UNCOUNTHis son was praised for speeches of remarkable fluency.frequent 1 adj W3 / 'friːkwənt ; ˋfrikwənt / happening or doing something often OPP infrequentTrains rushed past at frequent intervals . She was a frequent visitor to the house.usage n / 'juːsɪdʒ, 'juːz- ; ˋjusɪdʒ/ /1[C,U] the way that words are used in a languagea book on modern English usage2[U] the way in which something is used, or the amount of it that is usedWater usage is increasing.command (1) ORDER [C] an order that should be obeyed Shoot when I give the command .(2) N-UNCOUNT Your command of something, such as a foreign language, is your knowledge of it and your ability to use this knowledge. His command of English was excellent.(2)at your command if you have a particular skill at your command, you are able to use that skill well and easily a pianist with the keys at his commandcommand v (1) CONTROL [T] to control somethingThe party that commands a majority of seats in Parliament forms the government.(2) ORDER He commanded his troops to attack.request (1) n [C] S3 W2 / rɪ'kwest ; rɪˋkwɛst / a polite or formal demand for something[+ for ] They have made an urgent request for international aid.[+ from ] request from customers for more information(2) v request sb to do sth All club members are requested to attend the annual meeting.dialect N- COUNT A dialect is a form of a language that is spoken in a particular area.Chinese/Yorkshire etc dialect The people up there speak a Tibetan dialect .It is often appropriate to use the local dialect to communicate your message.expression n / ɪk'spreʃən ; ɪkˋsprɛʃən /STRONG FEELINGS/THOUGHTS [C,U] something you say, write, or do that shows what you think or feelStudent leaders are demanding greater freedom of expression[+ of ] I decided to go to the meeting as an expression of support.The letter was a genuine expression of sympathy.expressionThere was a blank expression on her face . A pained expression crossed her face.eastern adj ( Eastern ) ( written abbreviation E ) / 'iːstən ; ˋistɚn /in or from the east of a country or areathe eastern shore of the island farmers in eastern EnglandEastern religions Eastern EuropeIn many Eastern countries massage was and is a part of everyday life.African /ˈæfrɪkən/ ADJ African means belonging or relating to the continent of Africa, or to its countries or people. ...the African continent. ...African countries. ...traditional African culture.Fish is a staple in the diet of many Africans.play a big/important part in sth Pictures play an important part in publishing.Health education will play a part in preparing us for old age.have a part to play (in sth)to have a particular job or be responsible for somethingThe church used to have a more important part to play in the community.recognize v [T] ( also -ise BrE ) / 'rekəɡnaɪz, / [not in progressive ](1) to know who someone is or what something is, because you have seen, heard, experienced, or learned about them in the pastI didn’t recognize you in your uniform.It was malaria, but Dr Lee hadn’t recognized the symptoms.(2) to officially accept that an organization, government, document etc has legal or official authority British medical qualifications are recognized in Canada.recognize sth as sth The World Health Organization has recognized alcoholism as a disease since 1951.The receptionist recognized him at once.(3) V-T If someone says that they recognize something, they acknowledge that it exists or that it is true. I recognize my own shortcomings.lorry /ˈlɒrɪ/ CET4 TEM41N-COUNT A lorry is a large vehicle that is used to transport goods by road.Now and then they heard the roar of a heavy lorry.My dad is a lorry driver.accent n [C] / ˈæks ənt / (1) the way someone pronounces the words of a language, showing which country or which part of a country they come from →dialect He had a strong Irish accent(2) the part of a word that you should emphasize when you say it SYN stress[+ on ] In the word ‘dinner’the accent is on the first syllable.dinner .lightning/ˈlaɪtnɪŋ/ N-UNCOUNT Lightning is the very bright flashes of light in the sky that happen during thunderstorms.One man died when he was struck by lightning.Another flash of lightning lit up the cave.straight adv / stret / IN A STRAIGHT LINE in a line or direction that is not curved or bentShe was looking straight at me.Terry was so tired he couldn’t walk straight.straight adj ( comparative straighter , superlative straightest )NOT BENDING OR CURVING something that is straight does not bend or curvea long, straight road Try to keep your legs straight..block n [C] / blɒk / (1) solid material , a piece of hard material such as wood or stone with straight sidesa wall made of concrete blocks(2) streets/area 1) the distance along a city street from where one street crosses it to the next Head for 44th Street, a few blocks east of Sixth Avenue.The church is down the block.the four city streets that form a square around an area of buildingsLet’s walk round the block.She grew up playing with the other kids on the block.cab n [C] / kæb/ 1a taxiNew York’s yellow cabsRalph tried to hail a cab (= wave to get a cab to stop for you ) .take/get a cab I took a cab to the airport.call (sb) a cab (= telephone for a taxi)Could I use your phone to call a cab?Unit 3We need to get rid of the idea that we must be liked all the time in order to be worthwhile.我们需要摆脱那种必须一直受人爱戴才有价值的观念。
1.2函数及其表示
1.2.1 函数的概念
基础达标
1.下列对应法则是集合M 上的函数的有( ).
①M =Z ,N =N *, 对应法则f :对集合M 中的元素,取绝对值与N 中的元素对应;
②M ={1,-1,2,-2},N ={1,4},对应法则f :x →y =x 2,x ∈M ,y ∈N ; ③M ={三角形},N ={x |x >0},对应法则f :对M 中的三角形求面积与N 中元素的对应.
A .1个
B .2个
C .3个
D .0个
解析 ①M 中的元素0在N 中无对应元素,③M 中的元素不是数集.②是函数.
答案 A
2.(2013·九江高一检测)函数f (x )=x -2+
1x -3的定义域是( ). A .[2,+∞) B .(3,+∞)
C .[2,3)∪(3,+∞)
D .(2,3)∪(3,+∞)
解析 要使函数有意义,需满足⎩⎨⎧
x -2≥0,x -3≠0,
解之得x ≥2,且x ≠3.
答案 C
3.若函数f (x )=ax 2-1,a 为一个正常数,且f [f (-1)]=-1,那么a 的值是( ).
A .1
B .0
C .-1
D .2
解析 f (-1)=a ·(-1)2-1=a -1,
f [f (-1)]=a ·(a -1)2-1=a 3-2a 2+a -1=-1.
∴a 3-2a 2+a =0,
∴a =1或a =0(舍去).
答案 A
4.下列各组函数是相等函数的是________(只填序号).
①f (x )=x -1,g (x )=(x -1)2;
②f (x )=|x -3|,g (x )=(x -3)2;
③f (x )=x 2-4x -2
,g (x )=x +2; ④f (x )=(x -1)(x -3),g (x )=x -1·x -3.
解析 ①③④中两函数定义域不同,②是相等函数.
答案 ②
5.设f (x )=2x 2+2,g (x )=1x +2
,则g [f (2)]=________. 解析 ∵f (2)=2×22+2=10,
∴g [f (2)]=g (10)=
110+2=112. 答案 112
6.如果函数f :A →B ,其中A ={-3,-2,-1,1,2,3,4},对于任意a ∈A ,在B 中
都有唯一确定的|a |和它对应,则函数的值域为________.
解析 由题意知,对a ∈A ,|a |∈B ,
故函数值域为{1,2,3,4}.
答案 {1,2,3,4}
7.求函数f (x )=(x +2)2x +2-2-x 的定义域,并求f ⎝ ⎛⎭⎪⎫34的值. 解 要使f (x )有意义,需使⎩
⎨⎧
x +2≠0,2-x ≥0, 解之得x ≤2,且x ≠-2,
∴原函数的定义域为{x |x ≤2,且x ≠-2}.
又f (x )=x +2-2-x ,x ≤2且x ≠-2,
∴f ⎝ ⎛⎭⎪⎫34=34+2-2-34=11-254
. 能力提升
8.下列函数中,不满足f (2x )=2f (x )的是
( ).
A .f (x )=|x |
B .f (x )=x -|x |
C .f (x )=x +1
D .f (x )=-x 解析 C 中,f (2x )=2x +1,2f (x )=2x +2. ∴f (2x )≠2f (x ),则C 项不满足f (2x )=2f (x ). 答案 C
9.已知函数f (x )的定义域为(-1,1),则函数g (x )=f ⎝ ⎛⎭
⎪⎫x 2+f (x -1)的定义域是________. 解析 由题意知⎩⎪⎨⎪⎧ -1<x 2<1,-1<x -1<1,即⎩⎨⎧
-2<x <2,0<x <2. 从而0<x <2,于是函数g (x )的定义域为(0,2). 答案 (0,2)
10.已知函数f (x )=x 2
1+x 2
. (1)求f (2)与f ⎝ ⎛⎭⎪⎫12,f (3)与f ⎝ ⎛⎭
⎪⎫13; (2)由(1)中求得的结果,你能发现f (x )与f ⎝ ⎛⎭
⎪⎫1x 有什么关系?证明你的发现. 解 (1)由f (x )=x 21+x 2=1-1x 2+1
, ∴f (2)=1-122+1=45,f ⎝ ⎛⎭
⎪⎫12=1-114+1
=15. f (3)=1-132+1=910,f ⎝ ⎛⎭
⎪⎫13=1-119+1
=110. (2)由(1)中发现f (x )+f ⎝ ⎛⎭
⎪⎫1x =1. 证明 f (x )+f ⎝ ⎛⎭⎪⎫1x =x 21+x 2
+1x 21+1x 2 =x 21+x 2+1x 2+1=1.。