一道高考题的本质揭示与教学启示

2012年高考数学四川卷理科第12题:设函数f(x)=2x-cosx,{an}是公差为π/8的等差数列,f(a1)+f(a2)+…+f(a5)=5π,则[f(a3)]2-a1a5=().A.0B.1/16π2C.1/8π2D.13/16π21试题概况笔者最初是在《数学通迅》的网页上见到此题的,有老师在该杂志的网页论坛上寻问     

Epitaxial α″-Fe_(16)N_2 Films Grown on NaCl (001) by Facing Target Sputtering

In 1972 ,KimandTakahashi[1] observedagiantsaturatedmagneticfluxdensity (Bs=2 .5 8T)whichwas 17%strongerthanthatofpureiron .BelievingthattheFe NfilmwasapolycrystallinemixtureofFeandα″ Fe16 N2 ,theydeducedthattheBsofα″ Fe16 N2 wouldbe2 .83Tfromthevolumeratioofα″ Fe16 N2 inthefilm .Sincethelargesaturatedfluxdensityisofimportance ,boththeoreticallyandfromthepointofviewofpracticalapplications,manyresearchershavemadegreateffortsandusedavarietyofmethodstosynthesizeα″ Fe16 N2 intobulkmat…     

一共有多少只小鸡

万义， 曝 讯 慈 f 7 3.小鸭问小甘鸡: 黔学 } 第32页“卡通数学”参考答案: 黑鸡:3 5二8(只); 花鸡:8 5=13(只); 黄鸡:8 8=16(只); 一共有8 13 16=37(只)lj、鸡。一共有多少只小鸡@木子 @王媛林~~     

比较实数大小的几种方法

C．在7和8之间 D．在8和9之间 分析：因为16〈24〈25,所以、√16〈、√24〈、√25,即4〈√24〈5,所以4＋3〈√24＋3〈5＋3,即7〈√24＋3〈8．     

我“发现”了一个有用的公式(初三)

我在解题过程中,偶然发现了一个有用的公式.题目已知抛物线y=-12x2+5/2x-2的顶点为A,与x轴交于B、C两点,求△ABC的面积.当时我是这样解的:(?)顶点A(5/2,9/8),所以AD=9/8.(?)所以S△ABC=1/2BC·AD=1/2·3·9/8=27/16.     

多思善想 巧求分数

<正>【例1】果园里有桃树、梨树和苹果树,其中桃树和梨树占总面积的13/16,苹果树和梨树占总面积的5/8。梨树占总面积的几分之几？解法一：根据桃树和梨树占总面积的13/16,可以先求出苹果树占总面积的1-13/16=3/16,再根据苹果树和梨树占总面积的5/8,就可以求出梨树占总面积的5/8-3/16=7/16。     

Beyond冷光美白漂白有色牙疗效观察

Beyond冷光美白是外漂白治疗有色牙的一种新技术,它的特点是无痛苦、见效快、对牙齿无损伤.本院采用此技术对45例有色牙患者进行治疗,结果在原来基础上提高5～8个色阶的最多,达58%左右;提高8个色阶以上占16%;提高3-4个色阶为11%;原来颜色小于C4,无法确定原来颜色,治疗后在C4左右的占16%.     

不同练习频率影响定位投篮技能形成的比较研究

采用每轮次1次、3次、5次、10次四种不同的练习频率,对没有投篮技术基础的3组(每组男8名,女16名)大学一年级学生进行8周16次课的定位授篮分组对比实验.结果显示:与8周一直以每轮次连续投篮5次和以每轮次投蓝1次的练习频率相比,第1-2周以每轮次连续投篮3次、第3-6用以每轮次连续投篮5次、最后2周以每轮次连续投篮10次的练习频率进行定位投篮练习最有利于形成定位投篮技能、提高投篮命中率.     

数学二年级上学期期末测试卷

()×()=()()×()=()口诀:我踢的既不是25下,也不是16下。我踢了16下。?一、填一填,你能行1.2 2 2 2 2改写成乘法算式是()。2.一个角有()个顶点,有()条边。3.4×5=20,读作(),其中()和()是因数,()是积。4.1米=()厘米14厘米-8厘米=()厘米40米-5米=()米。5.七八()六()四十二()九四十五6.看图列式7.在○里填上 、-、×、>、<或=4○6=2425 8○352×6○1230○6=2415○20=355×7○328.()里最大能填几?()×4<297×()<509.根据六九五十四这句口诀写出两道乘法算式分别是()、()。10.3个同学踢毛毽子,他们分别踢了16下、20下、25个。1.小平踢了()下。2.…     

小学数学一年级(上)期末测试题

一、看图写数。(每空2分,共6分)()▲▲▲▲▲▲▲▲▲▲▲▲()()十位个位二、先观察,再填数。(每空1分,共10分)1.找规律填数。12151827()10()2025()2.在□里填数。3 □=7□ 8=130 □=5□ 7=16三、直接写出得数。(每题1分,共28分)4 8=2 9=7 9=7 5=4 7=6 5=7 9=10-4=9-4=19-10=8 10=6 2=16-4=10-7=5 8=4 9=9 9=6 10=13-0=17-4=6 6=7 8=10 9=9 6=8 8=5 8-3=4 6 8=19-9-7=四、填空。(每空2分,共16分)(1)16里面有()个十和()个一。(2)1个十和7个一合起来是()。(3)个位上是0,十位上是2,这个数是()。(4)十位上是1,个位上的数字比十位上的数字大4,这…     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

风的曲线

Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose.     

团图为数的图中的闭团贯数

Given a graph G,a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and |C|≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as TC (G), is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K (G), is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F={G|K(G) is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus TC (G)/|G|≤1/2 for all G ∈ F.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.