6679 2012年05月Edexcel A-leve 数学试题

2012年管理类联考综合能力测试数学真题一、问题求解：第1~15小题，每小题3分，共45分。

下列每题给出的,,,,A B C D E五个选项中，只有一项是符合试题要求的。

请在答题卡上将所选项的字母涂黑。

1、某商品定价200元，受金融危机影响，连续2次降价20%后的售价为（）.114 B.120 C.128 D.144 E.160A2、如图2，三个边长为1的正方形所组成区域（实线区域）的面积（）A. 3B.3C.3D.3E.33、在一次捐赠活动中，某人将捐赠的物品打包成件，其中帐篷和食品共320件，帐篷比食品多80件，则帐篷的件数是（）A.180B.200C.220D.240E.260a b c分别是为，，4、如图2，三角形ABC是直角三角形，，，为正方形，已知,,的边长，则：（）222222333333 =+=+=+=+=+ ...22.22A a b cB a b cC a b cD a b cE a b c5、如图3，一个储物罐的下半部分是底面直径与高均是20m的圆柱体，上半部分（顶部）是半球形的，已知底面与项部的造价是400元/，侧面的造价是300元/，该储物罐的造价是（）万元A.56.52B.62.8C.75.36D.87.92E.100.486、在一次商品促销活动中，主持人出示了一个9位数，让顾客猜测商品的价格，商品的价格是该9位数中从左到右面相邻的3个数字组成的3位数，若主持人出示的是的513535319，则一顾客猜中价格的概率是（）11121.....A B C D E965727、某商店经营15种商品，每次在橱窗内陈列5种，若每两次陈列的商品不完全相同，则最多可陈列（）次A.3000 B.3003 C.4000 D.4003 E.43008、甲、乙、丙三个地区公务员参加一次测评，其人数和如下表：三个地区按平均分从高到低的排列顺序为（）A.乙、丙、甲B. 乙、甲、丙C. 甲、丙、乙D.丙、甲、乙E. 丙、乙、甲9、经统计，某机构的一个安检口每天中午办理安检手续的乘客人数及对应的概率如下表：.0.2.0.25 .0.4 .0.5E. 0.75A B C D10、某人在保险柜中存放了M 元现金，第一天取出它的，以后每天取出的前一天所取的，共取了7天，保险柜中剩余的现金为（ ）77766222.....[1()]33333MM M M A B C D E M- 11、在直角坐标系中，若平面区域D 中虽有的点的坐标（x,y ）均满足：，，，则面积是（ ）999.(14).9(4).9(3).(2).(1)44444A B C D E πππππ+--++ 12、某单位春季植树100棵，前2天安排乙组植树，其余任务由甲、乙两组共用3天完成，已知甲组每天比乙组多植树4棵，则甲组每天植树（ ）棵A.11B.12C.13D.15E.1713、有两队打羽毛球，每队派出3男2女参加5局单打比赛，第二局和第四局为女生，那么每队派队员出场的方式有几种？（ ）A. 12B.10C.8D.6E.414、若能被整除，则（ ）.4,4.4,4.10,8.10,8.2,0A a b B a b C a b D a b E a b ===-=-==-=-==-=15.某公司计划运送180台电视机和110台洗衣机下乡，现有两种货车，甲种货车每辆最多可载40台电视机和10台洗衣机，乙种货车每辆最多可载20台电视机和20台洗衣机，已知甲、乙两种货车的租金分别是每辆400元和360元，则最少的运费是（ ）元A. 2560B.2600C.2640D.2680E.2720二、充分性条件判断：第16～25小题小题，每小题3分，共30分。

九天教育——英美中小学辅导领导品牌 扫码获取更多免费资料Time allowed● 1 hour 15 minutesInstructions●Use black ink or black ball-point pen.●Fill in the boxes at the top of this page.●Answer all questions.●You must answer the questions in the spaces provided.●Do not write outside the box around each page in margins or on blankpages.●You may ask for extra paper. Extra paper must be secured to thisbooklet.●Do all rough work in this book. Cross through any work you do notwant to be marked.Information●The maximum mark for this paper is 60.●You are expected to use a calculator, where appropriate.●The marks for questions are shown in brackets.●Quality of Written Communication will be assessed in all answers.●You will be marked on your ability to:- use good English- organise information clearly- use scientific vocabulary accurately.1(c)The scientists used a transmission electron microscope to study the structure of the amoeba. Explain why.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2 marks)Turn over for the next questionTurn overᮣ2Scientists compared the results of three investigations, A, B and C. These investigations were into the effect of drinking different amounts of alcohol onthe risk of developing heart disease.The graph shows the results of these investigations.2(b)All the volunteers who took part in investigation C were aged between 40 and50 years old. Explain how choosing volunteers of a similar age improved thisinvestigation.....................................................................................................................................................................................................................................................................................................................................................................................................................................(1 mark)2(c) A newspaper headline used the information in the graph to claim ‘Alcohol is good for you.’ Evaluate this claim.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)(Extra space) .................................................................................................................................................................................................................................................................6 ............................................................................................................................................Turn over for the next questionTurn overᮣ3The diagram shows the position of the diaphragm at times P and Q.P Q3(b)Air moves into the lungs between times P and Q. Explain how the diaphragm causes this.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)(Extra space) .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3(c)Describe how oxygen in air in the alveoli enters the blood in capillaries.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2 marks)7Turn over for the next questionTurn overᮣ4 A scientist investigated the effect of cyanide on the uptake of sodium ions byanimal tissue. He set up two beakers, J and K .He put equal volumes of a solution containing sodium ions and equal masses of an animal tissue in each beaker.●He added cyanide to beaker J .●He did not add cyanide to beaker K .He measured the concentration of sodium ions remaining in the solution ineach beaker, for 80 minutes. The graph shows his results.4(b)Adding cyanide affects the uptake of sodium ions by the tissue. Use thegraph to describe how.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2 marks)4(c)Cyanide is a substance which affects respiration.Use information in the question to explain the effect of cyanide on the uptakeof sodium ions by the tissue.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)7 (Extra space) .............................................................................................................................................................................................................................................................................................................................................................................................................Turn over for the next questionTurn overᮣ5(a)What is a pathogen?............................................................................................................................................(1 mark) 5(b)When a pathogen enters the body it may be destroyed by phagocytosis.Describe how.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4 marks)(Extra space) .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................5(c)When a pathogen causes an infection, plasma cells secrete antibodies whichdestroy this pathogen.Explain why these antibodies are only effective against a specific pathogen.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2 marks)7Turn over for the next questionTurn overᮣ6 A student investigated the effect of pH on the activity of the enzyme amylase.She set up the apparatus shown in the diagram.Turn over ᮣ76(b)After 30 minutes, the solution in tube B was higher than the solution in tube A .6(b)(i)Explain why the solution in tube B was higher.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)(Extra space) .............................................................................................................................................................................................................................................................................................................................................................................................................6(b)(ii)The student concluded from her investigation that the optimum pH of amylasewas pH8. Is this conclusion valid? Explain your answer....................................................................................................................................................................................................................................................................................................................................................................................................................................(1 mark)Turn over for the next question7Read the following passage.Gluten is a protein found in wheat. When gluten is digested in the small intestine,the products include peptides. Peptides are short chains of amino acids. Thesepeptides cannot be absorbed by facilitated diffusion and leave the gut in faeces.Some people have coeliac disease. The epithelial cells of people with coeliac disease do not absorb the products of digestion very well. In these people, some of the peptides from gluten can pass between the epithelial cells lining the small intestineand enter the intestine wall. Here, the peptides cause an immune response that leads to the destruction of microvilli on the epithelial cells.Scientists have identified a drug which might help people with coeliac disease.It reduces the movement of peptides between epithelial cells. They havecarried out trials of the drug with patients with coeliac disease.Use the information in the passage and your own knowledge to answer thefollowing questions.7(a)Name the type of chemical reaction which produces amino acids from proteins.............................................................................................................................................(1 mark)7(b)The peptides released when gluten is digested cannot be absorbed byfacilitated diffusion (lines 2–3). Suggest why.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)(Extra space) .............................................................................................................................................................................................................................................................................................................................................................................................................5107(c) The epithelial cells of people with coeliac disease do not absorb the products of digestion very well (lines 4 –5). Explain why.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3 marks)(Extra space) ............................................................................................................................................................................................................................................................................................................................................................................................................. 7(d)Explain why the peptides cause an immune response (lines 7–8).....................................................................................................................................................................................................................................................................................................................................................................................................................................(1 mark) 7(e)Scientists have carried out trials of a drug to treat coeliac disease (lines 10–11).Suggest two factors that should be considered before the drug can be used onpatients with the disease.1 .....................................................................................................................................................................................................................................................................................2 .........................................................................................................................................(2 marks)Turn over for the next questionTurn overᮣ8(a)The heart controls and coordinates the regular contraction of the atria and ventricles.Describe how.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5 marks)(Extra space) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8(b)T he diet of a person can increase the risk of coronary heart disease.Explain how.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5 marks)10 (Extra space) .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................END OF QUESTIONSDO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDEDDO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED。

2012数学高考试题及答案[一、选择题]1. 已知函数 f(x) = x^2 + bx + c 的图像与 x 轴交于 A, B 两点，且 A、B 两点的横坐标之和为 -1，则该函数 f(x) 的表达式为：A) f(x) = x^2 + x + 1 B) f(x) = x^2 + x - 1C) f(x) = x^2 - x + 1 D) f(x) = x^2 - x - 1答案：D2. 已知等差数列 {an} 的公差为 2，若 a1 + a2 + ... + a10 = 100，则a1 + a4 + a7 + ... + a28 =A) 252 B) 260 C) 268 D) 276答案：C3. 已知几何体的一个棱长为 2，且该几何体的其它各边长全都大于1，则这个几何体可以是：A) 正四面体 B) 正六面体 C) 正八面体 D) 正十二面体答案：C4. 已知函数 f(x) = log[size(base a)](3x - 2)，其中 a > 1，则 f^(-1)(3) =A) (a^3 - 2) / 3 B) a^3 - 2 C) a^3 + 2 D) (a^3 + 2) / 3答案：A[二、填空题]1. 某地区市场调查表明，70% 的家庭有电话，80% 的家庭有电视，60% 的家庭有汽车。

调查结果表明至少有一种物品的家庭占总数的百分之几？答案：90%2. 设 a = log[size(base 2)]7，b = log[size(base 3)]7，c = log[size(base 7)]2，则 a × b × c =答案：13. 在甲、乙两列数中，甲列为等差数列，乙列为等比数列，甲、乙两列的首项均为 1，且甲列的前 100 项的和等于乙列的前 100 项的积，则公比 q =答案：104. 设函数 f(x) = a^x + b^x + c^x + d^x，其中 a、b、c、d 为正数，且a > 1，b > 1，c > 1，d > 1，则 f(1) =答案：4[三、解答题]1. 已知函数 f(x) = x^2 + bx + c，若其图像在直线 y = 3x 上方，则函数 f(x) 的图像与直线 y = 3x 交于一个实数解 x，求 b 的取值范围。

第 1 页 共 3 页2012高考数学试题（全国卷Ⅱ） 一．选择题：（共12个小题，每小题5分，满分60分）1. 复数131ii -++= (A) 2+i(B) 2i(C) 1+2i(D)12i2.已知集合A={1，3，m }，B ={1，m}，A ∪B =A ，则m = (A) 0或3(B) 0或3(C) 1或3(D) 1或33.椭圆的中心在原点，焦距为4，一条准线为x = 4，则该椭圆的方程为(A)221612y +x =1(B)22168y +x =1(C)2284y +x =1(D)22124y +x =14.已知正四棱柱ABCD A1B1C1D1中，AB = 2，CC1 = 22，E 为CC1的中点，则直线AC1与平面BED 的距离为： (A) 2(B) 3(C) 2(D) 15.已知等差数列{an}的前n 项和为Sn ，a5 = 5，S5 =15，则数列{11n n a a +}的前100项和为(A) 100101(B) 99101(C) 99100(D) 1011006.△ABC 中，AB 边的高为CD ，CB = a ，CA = b ，a •b = 0，| a | = 1，| b | = 2，则AD =(A)13a 13b(B) 23a 23b(C) 35a 35b(D)45a45b7.已知 为第二象限的角，sin +cos =33，则cos2 =(A) 53(B) 59(C) 59(D) 538.已知F1、F2为双曲线C ：x 2y2 =2的左、右焦点，点P 在C 上，|PF1|=2|PF2|，则cos ∠F1PF2 =(A) 14 (B) 35 (C) 34 (D) 45第 2 页 共 3 页9.已知x = ln ，y =log 5 2，z =12e-，则(A) x < y < z (B) z < x < y (C) z < y < x (D) y < z < x10.已知函数y =x 33x + c 的图像与x 轴恰有两个公共点，则c =(A) 2或2 (B) 9或3 (C) 1或1 (D) 3或111.将字母a, a, b, b, c, c 排成三行两列，要求每行的字母互不相同，每列的字母也互不相同，则不同点排列方法共有(A) 12种 (B) 18种 (C) 24种 (D) 36种12.正方形ABCD 的边长为1，点E 在边AB 上，点F 在边BC 上，AE = BF =37，动点P 从E 出发沿直线向F 运动，每当碰到正方形的边时反弹，反弹时反射角等于入射角，当点P 第一次碰到E 时，P 与正方形的边碰撞的次数为(A) 16 (B) 14 (C) 12 (D) 10二．填空题：（共4个小题，每小题5分，满分20分）13.若x 、y 满足约束条件 ，则z =3x y 的最小值为14.当函数y = sinx cosx (0≤x <2 )取得最大值时，x =15.若(x +1x ) n 的展开式中第三项与第七项的二项式系数相等，则该展开式中21x 的系数为16. 三棱柱ABC A1B1C1中，底面边长和侧棱长都相等，∠BAA1=∠CAA1= 60o ，则异面直线AB1与BC1所成的角的余弦值为二．解答题：（共6个小题，满分70分）17.（本小题满分10分）△ABC 的内角A 、B 、C 的对边分别为a 、b 、c ，已知cos(A C) + cosB = 1，a = 2c ，求C .18. （本小题满分12分）如图，四棱锥P －ABCD 中，底面ABCD 为菱形，PA ⊥底面ABCD ，AC = 22，PA = 2， E 是PC 上的一点，PE = 2EC . (Ⅰ)证明：PC ⊥平面BED ；(Ⅱ)设二面角A PB C 为90o ，求PD 与平面PBC 所成的角的大小.x - y +1≥0x + y -3≤0x + 3y -3≥0 E AB CDP19. （本小题满分12分）乒乓球比赛规则规定：一局比赛，双方比分在10平前，一方连续发球2次后，对方再连续发球2次，依次轮换. 每次发球，胜方得1分，负方得0分. 设再甲、乙的比赛中，每次发球，发球方得1分的概率为0.6，各次发球的胜负结果相互独立. 甲、乙的一局比赛中，甲先发球.(Ⅰ)求开始第四次发球时，甲、乙的比分为1比2的概率；(Ⅱ) 表示开始第四次发球时乙的得分，求 的期望.20. （本小题满分12分）设函数f (x ) = ax + cosx , x∈[0, ] .(Ⅰ)讨论f (x )的单调性；(Ⅱ)设f (x ) ≤1 + sinx ，求a的取值范围.21. （本小题满分12分）已知抛物线C：y = (x +1) 2与圆M：(x 1) 2 +( y 12) 2 = r 2 (r > 0)有一个公共点A，且在A处两曲线的切线为同一直线l.(Ⅰ)求r ；(Ⅱ)设m、n是异于l且与C及M都相切的两条直线，m、n的交点为D，求D到l的距离.22. （本小题满分12分）函数f (x ) = x 2 2x 3 .定义数列{x n}如下：x 1= 2，x n+1是过两点P(4, 5)、Qn(x n, f (x n ))的直线PQn与x轴的交点的横坐标.(Ⅰ)证明：2≤x n < x n+1<3 ；(Ⅱ)求数列{x n}的通项公式.答案C 2.B 3.C 4.C 5.A 6.D 7.A 8.C 9.D 10.A 11.A 12.B13. -1 14. 15. 56 16. ………………第 3 页共3 页。