高三上学期第十一次周练数学试题
1.化简416x 8y 4
(x ＜0，y ＜0)得( )
A ．2x 2y
B ．2xy
C ．4x 2y
D ．－2x 2y
2.化简[(－2) 6
]1
2－(－1)0
的结果为( )
A ．－9
B ．7
C ．－10
D ．9
3.(2014·朝阳区期末)函数y ＝?
???
?x 2
（x ＜0）2x －1（x ≥0）的图象大致是 ( )
4．函数y ＝(a 2
－3a ＋3)a x
是指数函数，则有( ) A ． a ＝1或a ＝2 B ．a ＝1 C ．a ＝2 D ．a ＞0且a ≠1
5．函数f (x )＝1－2x
的定义域是( ) A ．(－∞，0] B ．[0，＋∞) C ．(－∞，0) D ．(－∞，＋∞)
6．(教材改编)函数y ＝3x
与y ＝－3－x
的图象的对称图形为( ) A ． x 轴 B ．y 轴 C ．直线y ＝x D ．原点
7. (2014·山东高考优化卷)设函数f (x )＝2x
1＋2x －1
2，[x ]表示不超过x 的最大整数，
则函数y ＝[f (x )]＋[f (－x )]的值域为( )
A ．{0}
B ．{－1，0}
C ．{－1，0，1}
D ．{－2，0}
8．函数y ＝a x
－1a
(a ＞0，且a ≠1)的图象可能是( )
9．已知一元二次不等式f (x )＜0的解集为??????x ?
??x ＜－1或x ＞12，则f (10x
)＞0的解集为
( )
A ．{x |x ＜－1或x ＞－lg 2}
B ．{x |－1＜x ＜－lg 2}
C ．{x |x ＞－lg 2}
D ．{x |x ＜－lg 2}
10．函数f (x )的图象向右平移1个单位长度，所得图象与曲线y ＝e x
关于y 轴对称，则
f (x )＝( )
A ．e
x ＋1
B ．e
x －1
C ． e
－x ＋1
D ．e
－x －1
11．方程4x
－2
x ＋1
－3＝0的解是________．
12．若函数f (x )＝a x
(a ＞0，a ≠1)在[－1，2]上的最大值为4，最小值为m ，且函数g (x )＝(1－4m )x 在[0，＋∞)上是增函数，则a ＝________．
13.化简下列各式．
(1)031)6
7()23(-?-+ 44128?+6
3)32(?－32
)32(-＝________；
(2)
4
3
5
35
2
3
a
b b
a ?
＝________．
14.计算下列各式： (1)3
3
133
73
32
9
a
a a a ?÷
?--；
(2)5
.021
20)01.0()4
12(2)532(-?+--.
15.(2014·佛山模拟)已知定义域为R 的函数f (x )＝－2x
＋b 2x ＋1＋a 是奇函数．
(1)求a ，b 的值；
(2)若对任意的t ∈R，不等式f (t 2－2t )＋f (2t 2
－k )＜0恒成立，求k 的取值范围． 答案： 1. D 2. B 3. B 4.C 5.A 6.D 7. B 8.D 9．D 10． D 11．log 23 12． 14
13.(1)110 (2)a 4
a 14.计算下列各式： (1)3
3
133
7
3
3
2
9a
a
a
a ?÷
?--；
(2)5
.021
20)01.0()4
12(2)532(-?+--.
上海中学2017-2018学年第学期高一英语试题 Choice 21.The impact__________ high technology draws worldwide attention. A.on 22.________________,the more expansive gestures you should employ when you deliver a speech. A.The more audience there is B.The more the audience are C.As much audience as there is D.The larger the audience is 23.John is really an independent boy and he tries his best to settle every problem_______. A.of his own his own C,for his own his own 24.The queen,__________ an old woman, made a poisonous apple and came to the cottage to tempt Snow White to eat it. A,dressed in was dressing like like had clothes on as 25.It is reported that __________schools in the west of China are improving their study environment. A.a great many of large number of B..a great amount of large number of you really mean_________a basketball player? Do you know that training to be a basketball player means_____________at least eight hours every day? ,practicing be,practicing be,to practice ,to practice the workload of a _________job alongside a course of study can be difficult, so there is an increasing tendency for people to give up work and go back to school. 28. I couldn't resist having another piece of cake ____________I was supposed to be on a diet and lose weight. if 29. Your children will not follow your advice to ____________business management as his major if you ___________. up,force him to up,force him on,force him to on,force him 30.The students of class 8____________a farewell party for their retired class teacher
II.Grammar and Vocabulary Section B Recently,I flew to Las Vegas to attend a meeting.As we were about to arrive,the pilot announced with apology that there would be a slight delay before setting down.High desert winds had forced the airport to close all but one runway.He said that we would be circling the city for a few minutes waiting to land.We were also told to remain in our seats meanwhile with our seat belts(21)________(fasten) because there might be a few bumps.Well,that few minutes turned into about forty-five minutes, including a ride that would make a roller coaster(22)________(pale)by comparison. The movement was so sudden(23)________several passengers felt sick and had to use airsickness bags.(24)________you might guess,that’s not good thing to happen in a narrow space because it only serves to increase the discomfort of the situation. About twenty minutes into the adventure,the entire airplane became very quiet.There was now a sense of anxiety and fear that could be distinctly noticed.Every passenger simply held on for dear life… (25)________one.A baby was having a good time!With each bump of the aircraft,he(26)________let out a giggle of happiness.As I observed this,I realized that he didn’t know he was supposed to be afraid and worried about his safety.He(27)________thought about the past nor about the future.Those are (28)________we grown-ups have learned from experience.He was enjoying the ride because he (29)________(not teach)to fear it.(30)________(understand)this,I took a deep breath and sat back into my seat,pretending I was really on a roller coaster.I smiled for the rest of the flight.I even managed to giggle once or twice,which is much to the chagrin of the man sitting next to me holding the airsickness bag. C Section People become quite illogical when they try to decide what can be eaten and what cannot be eaten.If you lived in the Mediterranean,for instance,you would consider octopus a great__31__.You would not be able to understand why some people find it repulsive.On the other hand,your stomach would__32__ at the idea of frying potatoes in animal fat---the__33__accepted practice in many northern countries.The sad truth is that most of us have been brought up to eat certain foods and we__34__to them all our lives. No creature has received more praise and abuse than the common garden snail.Cooked in wine, snails are a great luxury in various parts of the world.There are countless people who,ever since their early years,have learned to__35__snails with food.My friend,Robert,lives in a country where snails are despised.As his flat is in a large town,he has no garden of his own.For years he has been asking me to collect snails from my garden and take them to him.The idea never appealed to me very much,but one day,after a heavy__36__,I happened to be walking in my garden when I noticed a huge number of snails taking a stroll on some of my__37__plants.Acting on a sudden impulse,I collected several dozen,put them in a paper bag,and took them to Robert.Robert was delighted to see me and__38__pleased with my little gift.I left the bag in the hall and Robert and I went into the living room where we talked for a couple of hours.I had forgotten all about the snails when Robert suddenly said that I must stay to dinner. 第1页/共8页
上海市上海中学高一数学上学期期中试卷（含解析） 一、选择题（本大题共4小题） 1.已知集合，则中元素的个数为 A. 9 B. 8 C. 5 D. 4 【答案】A 【解析】 分析：根据枚举法，确定圆及其内部整点个数. 详解：， 当时，； 当时，； 当时，； 所以共有9个，选A. 点睛：本题考查集合与元素关系，点与圆位置关系，考查学生对概念理解与识别. 2.已知实数x，y，则“”是“”的（） A. 充要条件 B. 充分而不必要条件 C. 必要而不充分条件 D. 既不充分也不必要条件 【答案】B 【解析】 【分析】 找出与所表示的区域，再根据小范围推大范围可得结果． 【详解】表示的区域是以为顶点的正方形及内部， 表示的区域是以为圆心，1为半径的圆及内部， 正方形是圆的内接正方形， ，推不出， “”是“”的充分而不必要条件． 故选：B． 【点睛】本题主要考查充分条件和必要条件的判断，考查了不等式组表示的区域，考查了推理能力，属于中档题． 3.设，，且，则（）
A. B. C. D. 以上都不能恒成立 【答案】A 【解析】 【分析】 利用反证法可证得，进而由可得解. 【详解】利用反证法： 只需证明， 假设， 则： 所以：， 但是， 故：，，． 所以：与矛盾． 所以：假设错误， 故：， 所以：， 故选：A． 【点睛】本题考查的知识要点：反证法的应用，关系式的恒等变换，主要考查学生的运算能力和转化能力，属于中档题型． 4.对二次函数（为非零常数），四位同学分别给出下列结论，其中有且仅有一个结 论是错误的，则错误的结论是（） A. 是的零点 B. 1是的极值点 C. 3是的极值 D. 点在曲线上 【答案】A 【解析】 若选项A错误时，选项B、C、D正确，，因为是的极值点，是的极值，所以，即，解得：，因为点在曲线上，所
上海中学高一周练数学试卷10 2019.12 一. 填空题 1. 函数2lg(23)y x x =--的定义域为 ，单调递减区间为 2. 函数2413x x y -+-=的单调递增区间为 ，值域为 3. 若函数1()21 x f x a =+ -是奇函数，则a 的值为 4. 若lg lg 2x y +=，则1100x y +的最小值为 5. 若log 2a x =，log 3b x =，log 4c x =，则log abc x 的值为 6. 已知幂函数2()(57)m f x m m x =-+是R 上的增函数，则m 的值为 7. 若关于x 的方程3 23()25x a a +=-有负根，则实数a 的取值范围为 8. 已知偶函数()f x 是以2为周期的周期函数，且当(0,1)x ∈时，()21x f x =-，则 2(log 10)f 的值为 9. 已知13()1 x f x x -=+，函数()y g x =的图像与1(1)y f x -=+的图像关于直线y x =对称， 则(3)g 的值为 10. 已知0x >，定义()f x 表示不小于x 的最小整数，若1(3())(6)31x f x f x f +=+ +，则 正数x 的取值范围为 11. 对于函数1()42x x f x m +=-?，若存在实数0x ，使得00()()f x f x -=-成立，则实数m 的取值范围为 12. 设函数()f x =a ∈R ，e 为自然对数的底数），若曲线221x y +=上存在00(,)x y 使得00(())f f y y =，则a 的取值范围为 二. 选择题 13. 函数|24|()x f x a -=（0a >且1a ≠），满足1(1)9 f =，则()f x 的单调递减区间为（ ） A. (,2]-∞ B. [2,)+∞ C. [2,)-+∞ D. (,2]-∞- 14. 奇函数()y f x =的反函数为函数1()y f x -=，函数1()y f x -=在[0,)+∞上是减函数， 则函数()y f x =-在(,0)-∞上为（ ） A. 增函数 B. 减函数 C. 非单调函数 D. 不能确定
上海中学高一期中数学卷 2016.11 一. 填空题 1. 设集合{0,2,4,6,8,10}A =，{4,8}B =，则A C B = 2. 已知集合{|||2}A x x =<，{1,0,1,2,3}B =-，则A B =I 3. “若1x =且1y =，则2x y +=”的逆否命题是 4. 若2211()f x x x x +=+ ，则(3)f = 5. 不等式9x x >的解是 6. 若不等式2(1)0ax a x a +++<对一切x R ∈恒成立，则a 的取值范围是 7. 不等式2(3)30x --<的解是 8. 已知集合{|68}A x x =-≤≤，{|}B x x m =≤，若A B B ≠U 且A B ≠?I ，则m 的 取值范围是 9. 不等式1()()25a x y x y ++ ≥对任意正实数,x y 恒成立，则正实数a 的最小值为 10. 设0a >，0b >，且45ab a b =++，则ab 的最小值为 11. 已知二次函数22 ()42(2)21f x x p x p p =----+，若在区间[1,1]-内至少存在一个 实数c ，使()0f c >，则实数p 的取值范围是 12. 已知0a >，0b >，2a b +=，则22 21 a b a b +++的最小值为 二. 选择题 1. 不等式||x x x <的解集是（ ） A. {|01}x x << B. {|11}x x -<< C. {|01x x <<或1}x <- D. {|10x x -<<或1}x > 2. 若A B ?，A C ?，{0,1,2,3,4,5,6}B =，{0,2,4,6,8,10}C =，则这样的A 的个数 为（ ） A. 4 B. 15 C. 16 D. 32 3. 不等式210ax bx ++>的解集是11 (,)23 -，则a b -=（ ） A. 7- B. 7 C. 5- D. 5 4. 已知函数2 ()f x x bx =+，则“0b <”是“(())f f x 的最小值与()f x 的最小值相等” 的（ ）条件 A. 充分不必要 B. 必要不充分 C. 充要 D. 既不充分也不必要
上海中学高一周练数学卷 2017.3.2 一. 填空题 1. 若角α的终边过点(12,35)-，则s i n α= ；cos α= ； tan α= ； cot α= ；sec α= ；csc α= ； 2. 已知20tan 21 α=，且α是第三象限角，则sin α= ；cos α= ； cot α= ；sec α= ；csc α= ； 3. 角度制与弧度制互化：大小为105?的角的弧度数是 ；大小为3?的角的弧度数是 ；弧度数为20 π的角，其大小用角度制表示是 ； 4. 在一个半径为2的圆中，两条半径将圆周分成一段劣弧和一段优弧，其中劣弧长为2，则 劣弧所在的扇形与优弧所在的扇形的面积之比为 5. 若sin |cos ||sin |cos αααα=，则α的取值范围是 6. 已知02απ≤<，(cos 4,sin 4)--是角α终边上的一点，则α = 7. 已知集合{|,}3m A m Z παα==∈，集合{|,}4 n B n Z πββ==∈，则A B = 8. 已知sin cos αα-=，(0,)απ∈，则tan α= 9. 在下列四个命题中，正确命题的序号是 ① 若α角与β角的终边关于原点对称，则sin sin 0αβ+=，cos cos 0αβ+=； ② 若α角与β角的终边关于x 轴对称，则sin sin 0αβ+=，cos cos 0αβ+=； ③ 若α角与β角的终边关于y 轴对称，则sin sin 0αβ+=，cos cos 0αβ+=； ④ 若cos cos αβ=且sin sin αβ=，则α角与β角的终边相同； 10. 化简：sin(31)tan(747)cos(684)tan(27)cos(36)sin(329) αααααα??????++-=++- 11. 已知AB 是平面Γ内一条长度为2的线段，集合{|M M ψ=∈Γ且至少存在一个半径 为2的圆，使得M 、A 、B 中的每一点，都是或者在此圆内，或者在此圆周上}，则ψ中 的点形成的平面区域的面积为 二. 选择题 1. 记cos(100)k ?=，那么tan 80?=（ ） A. B. C. D.
2016高三英语模拟考试 II. Grammar and Vocabulary Section A Directions:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank. (A) Once just a science fiction idea, VR has now become more accessible than ever. (25) _________ (wear) a pair of VR goggles connected to your computer and you can experience a lot of things without stepping out of the room. From climbing (26) _________ (high) mountain in the world to flying a spacecraft, the things you can experience with VR are limitless. This new 'reality ' is starting to takeover China. The Report on Chinese VR Users' Behavior was released on March 18 during the 12th TFC Global Mobile Game Conference & Intelligent Entertainment Expo held in Beijing. The report is based on a survey of 5,626 people, (27) _________ (age) between 15 and 39, from across the country. It shows that up to 68.5 percent of people have heard of or are interested in VR products. But surprisingly, it isn't new technology that has made VR so popular. 'VR has been (28) _________ for many years, but it will stick this time because there's enough computer power and the price will just keep going down,' Todd Richmond, a VR group member with the Institute of Electrical and Electronic Engineers in the US, told USA Today. VR (29) _________ (expect) to change various different fields. For example, VR could be used to train pilots and miners before they had to actually risk their lives in highly dangerous working environments, or to treat patients with acrophobia(恐高症）by making them think they were standing on top of a high building. 'If you have perfect virtual reality, (30) _________ you'll be able to simulate everything that a human can experience or imagine experiencing,it's hard to imagine where you go from there,' Palmer Luckey, 23 inventor of the Oculus VR goggles, told NPR. But the technology is still far from perfect. Users report experiencing motion sickness, headaches and other discomfort while wearing VR goggles. Also, (31) _________ more and more tools are flooding the market, the software that runs VR games and simulators has yet to catch up with all the new advancements. It could take (32) _________ while for VR to be widely accepted. When every new technology is first introduced, the technology (33) _________ is the driving force. But for it to really blend into people's lives, meeting basic and practical needs should be the main aim. (B) It has become the talk of the town: A stranger allegedly attacked a woman in a Beijing hotel at night on April 3. The man is said to have clutched her by the neck and attempted to drag her into the elevator. Lodgers passed by, but no one tried to intervene until one woman did. Her actions are believed to (34) _________ (save) the victim from whatever was going to happen to her. The incident has pushed the risks of solo traveling into the spotlight. Online forums like Sina Weibo (35) _________ (flood) with advice for how women (36) _________ protect themselves
III. Reading Comprehension Section B Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read. B Kettlebells do not hurt people. People do. A kettlebell will get your respect – the easy way or the hard way. Here is the easy way. 1. Get a medical clearance. Get clearance, especially from an orthopedist and a cardiologist. The latter is no joking matter, since kettlebell training can be extremely intense. 2. Always be aware of your surroundings. Find a training area with a non-slippery surface on which you are not afraid to drop a kettlebell. The area must be clear of objects you might trip over – including other kettlebells – or that you might hit with a kettlebell. There should be no people or animals in a radius where you could injure them. 3. Train barefoot or wear shoes with a flat, thin sole and room for the toes to spread. Training barefoot is superior for health and performance reasons. If you must wear shoes, wear Converse Chuck Taylors, Vibram Five Fingers, or similar shoes that have thin soles and do not pinch the toes together. You have sensory receptors on the bottoms of your feet that make you stronger and improve balance and coordination. Wearing traditional shoes diminishes the ability of these receptors to work properly, and therefore inhibits performance and can increase the risk of injury. Go native. 4. Never contest for space with a kettlebell. Do not try to save a rep that has gone wrong. Guide the kettlebell to fall harmlessly, and move out of the way if necessary. And remember, quick feet are happy feet. 5. Practice all safety measures at all times. Respect every kettlebell, even the lightest one. Always use perfect form picking up and setting down a kettlebell. The set is not over until the bell is safely parked.
微信号：JW2215874840或ross950715或Soulzbb 上海中学 2019-2020 学年高一下期中考试 一、填空题（每空3分,共30分） 1.已知点A (2,-1)在角α的终边上,则sin α=__________. 2.函数sin(2)y x π=+的最小正周期是________. 3．一个扇形半径是2,圆心角的弧度数是2,则此扇形的面积是________. 4.已知函数[]()sin (0,)f x x x π=∈和函数1()tan 2 g x x = 的图像交于A 、B 、C 三点,则△ABC 的面积为________. 5.在平面直角坐标系xoy 中,角α与角β都以x 轴正半轴为始边，它们的终边关于y 轴对称.若1sin 3 α= ,则cos()αβ-=__________.6.已知3sin()45x π-=,则sin 2x =__________.7.设(),0,x y π∈，且满足2222sin cos cos cos sin sin 1sin() x x x y x y x y -+-=+，则x y -=_____.8.我国古代数学家秦九韶在《数学九章》中记述了“三斜求积术”,用现代式子表示即为：在△ABC 中，A ∠、B ∠、C ∠的对边分别是a 、b 、,c 则△ABC 的面积 S =.根据此公式，若cos (3)cos 0a B b c A ++=,且2222a b c +-=,则△ABC 的面积为_______. 9.若函数()2sin(2)1()6f x x a a R π=++-∈在区间0,2π?????? 上有两个不同的零点12,x x ,则12x x a +-的取值范围是__________. 10.已知函数sin ()cos m f ααα-=在(0,2 π上单调递减,则实数m 的取值范围是________.二、选择题（每题4分,共24分） 1.已知cos ,(1,1),(,)2k k πααπ=∈-∈,则sin()πα+=( ) A. C. D.1k -
上海中学高一数学周练卷 一. 填空题 1. 已知实数0a <与G ，G ，依次成等 比数列，则G = 2. 项数为k 的数列{}n a 的各项不是0就是1，而且此数列既不是只有0，也不是只有1，所 有的0相连且所有的1相连，这样的数列有 个 3. 数列{}n a 满足11a =，且11n n a a n +-=+（*n N ∈），则数列1{}n a 的前n 项和为 4. 已知数列{}n a 对任意的*n N ∈都有21n n n a a a ++=-，而11a =，23a =，则数列{}n a 的 前n 项和n S 能取得的最大值为 5. 将一条长度为1的线段三等分，抹去中间的一段，以此作为第一次操作，将第一次操作后留下的两条线段的每一条都三等分，并各自将中间的一段抹去，以此作为第二次操作，此后的每次操作都按上述方式进行，如果这样的操作进行了八次，则剩余的所有线段的长度和 为 6. 制作如图所示的一个“3步”的楼梯用了18根牙签， 如果要做成一个“10步”楼梯，还需要增加的牙签的 根数是 7. 算式9291 2(2(22(2(2(2(2(21)1)1)1)1)1)1)1)1????????+++++++++个个的值是 8. 若三角形的三边长是公差为1的等差数列，最大角是最小角的两倍，则最小角的余弦值为 9. 已知数列{}n a 和{}n b 的通项公式分别为2n a n =和2n n b =，数列{}n a 的前m 项构成集合A ，数列{}n b 的前k 项构成集合B ，且m k a b =，任取x A B ∈，则用k 表示x A B ∈的 概率为 10. 已知实数x 使得1sin a x =，2cos a x =，3tan a x =的数列{}n a 为等比数列，若 1cos n a x =+，则n = 11. 如图，互不相同的点12,,,,n A A A ??????和12,,,,n B B B ?????? 分别在角O 的两条边上，所有n n A B 相互平行，且所有梯形 11n n n n A B B A ++的面积均相等，设n n OA a =，若11a =， 22a =，则数列{}n a 的通项公式是n a = 12. 在自然数数列中，保留前4个数，划去1个数，保留5个数，划去2个数，保留6个数，
2020-2021学年上海市闵行区七宝中学 高三英语上学期10月月考试卷 I. Listening Comprehension(略) II. Grammar and Vocabulary (20分) Section A Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank. Challenging work that requires lots of analytical thinking, planning and other managerial skills might help your brain stay sharp (21) you age, a study published Wednesday in the journal Neurology suggests. Researchers from the University of Leipzig in Germany gathered more than 1, 000 retired workers who were over age 75 and had the volunteers’ memory and thinking skills (22) (assess)through a battery of tests. Then, for eight years, the scientists asked the same group to come back to the lab every 18 months (23) (take) the same sorts of tests. Those who (24) (hold)mentally stimulating, demanding jobs before retirement tended to do the best on the tests. And they tended to lose cognitive（认知）function (25) a much slower rate than those with the least mentally challenging jobs. The results held true even after the scientists accounted for the participants’ overall health status. “This works just like physical exercise,” says Francisca Then, who led the study. “After a long run, you may feel like you’re in pain, you may feel tired. But it makes you fit. After a long day at work — sure, you will feel tired, (27) it can help your brain stay healthy. ” It’s not just corporate jobs, or even paid work (26) can help keep your brain fit, Then points out. A waiter’ s job, for example, (28) ( require) multitasking, teamwork and decision-making could be just as stimulating as any high-level office work. And “running a family household requires high-level planning and coordinating（协调）,” she says. “You (29) _______ ________organize the activities of the children and take care of the bills and groceries.” Of course, our brains can decline as we grow older for lots of reasons — including other environmental influences or genetic factors. Still, continuing to challenge (30) mentally and keeping your mind busy can only help. 【答案】 21. as 22. assessed23. to take 24.had held25. at26. that 27. but28.requiring 29. have to30. yourself 【难度】中等
2018-2019学年上海中学高三第一学期摸底考试 II.Grammar and Vocabulary 温馨提示：多少汗水曾洒下，多少期待曾播种，终是在高考交卷的一刹尘埃落地，多少记忆梦中惦记，多少青春付与流水，人生，总有一次这样的成败，才算长大。高考保持心平气和，不要紧张，像对待平时考试一样去做题，做完检查一下题目，不要直接交卷，检查下有没有错的地方，然后耐心等待考试结束。 Section A Direction: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the other answer that best completes the sentence. 25.While I was waiting to enter ________ university, I saw advertised in a local newspaper a teaching post at a school in ________ suburb of London. A. /, a B. an, a C. a, the D. the ,the 26.In most cases, ________ a passenger has his ticket and managers to catch his train, he can reach his destination more comfortably than ________ he had to drive himself. A. once, if B. that ,if C. when, while D. where, when 27.The invention of the modern computer is one of the great contributions ________ to man’s efficiency. A. having ever been made B. ever been made C. ever made D. having ever made 28.I was not able to work out the problem ________ my teacher explained it. A. as B. unless C. until D. when 29.For him to be re-elected, what is essential is not that his policy works, but ________ the public believe that it does. A. / B. whether C. that D. if