sat2数学level2知识点【篇一：sat2数学level2知识点】考试中，突破level2 知识点后，level1的知识点就不是难题了，下面来看下sat2数学level2知识点介绍。
sat2数学考试中，level2 知识点总结： algebra (代数)部分根据考试方的官方分类，algebra大概占math2考试所有问题的18%，代数是math2的基础，没有对它熟练的掌握很难拿到高分，当然这点对于中国学生来说，简直是小菜一碟。
对代数部分，kaplan的介绍分为四个方面 expressions and exponents (表达式和指数)operations with polynomials and factoring (多项式和因数分解的应用) the golden rule of equations (等式的黄金规则) quadratic equations (二次方程式) 练习时的时间控制在：12分钟10道题plane geometry (平面几何部分)sat2数学考试，中国高中没有涉及的知识点：求分数函数的渐近线，概率论部分圆桌型概率模型，线性代数中的简易矩阵，多项式函数的零点。
以上是sat2数学level2知识点介绍，更多sat考试信息可以关注新航道频道。
【篇二：sat2数学level2知识点】2考试期间注意：休息期间考生可有秩序地前往洗手间，或于考场外(不得在座位内或考场内饮食)每一节休息时间后，监考员会再次核对每位考生的身份证明文件，请考生将身份证明文件放在台面，以便监考员检查l如考生要增加、减少或更改所报考的科目，你毋须向监考人员提出询问或申请，因为所有科目的试卷将会印在同一本试题簿内，你只需在考试时作答你想应考的科目便可，考试后你应自行联络美国大学理事会缴交因增加科目需额外的费用考试科目的次序考生可自行决定，但每一节只能应考一门考生必须出示身份证明文件(香港或澳门身份证、有效未到期的港澳通行证或护照) (注意：中国居民身份证因没有英文姓名，不可用作考试的身份证明文件)准考证上的英文姓名及出生日期，必须与身份证明文件上的信息完全相同【篇三：sat2数学level2知识点】下面为大家总结的是sat2数学知识点中关于level 2的部分，后面都附有例题解析。
Math Section------------------------------------------------------------------------------------------------------------ Q1:The table above gives the coffee consumption in 1994 for five countries. If the total coffee consumption of these countries was 40 percent of the world’s coffee consumption, what was the world’s coffee consumption, in millions of kilograms, in 1994?A.4,320B.4,470C.5,400D.6,480E.6,700Answer:------------------------------------------------------------------------------------------------------------ Q2:When positive integer x is divided by positive integer y, the remainder is 9. If x/y =96.12, what is the value of y?A.96B.75C.48D.25E.12Answer:------------------------------------------------------------------------------------------------------------ Q3:Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?(1) The average (arithmetic mean) salary of Company Y’s employees is greater thanthe average salary of Company Z’s employees.(2) The median salary of Company Y’s employees is greater than the median salaryof Company Z’s employees.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q4:What is the value of v3– k3?(1) v k > 0(2) v – k = 6A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q5:In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?(1) AB = 3 and BC =2(2) CD =1 and DE = 4A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q6:tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?A.5½ ftB.7½ ftC.8 ½ ftD.9½ ftE.10 ftAnswer:------------------------------------------------------------------------------------------------------------ Q7:Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?A.6πB.12πC.3√2 πD.6√2 πE.12√2 πAnswer:------------------------------------------------------------------------------------------------------------ Q8:The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?I.x ⊗ xy = x(1 ⊗ y)II.x ⊗ y = -(y ⊗ x)III.1/x ⊗ 1/y = y ⊗ xA. I onlyB. II onlyC. III onlyD. I and IIE. II and IIIAnswer:------------------------------------------------------------------------------------------------------------ Q9:What was the price at which a merchant sold a certain appliance?(1) The merchant’s gross profit on the appliance was 20 percent of the price atwhich the merchant sold the appliance.(2) The price at which the merchant sold the appliance was $50 more than themerchant’s cost of the appl iance.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q10:An attorney charged a fee for estate planning services for a certain estate. The attorney’s fee was what percent of the accessed value of the estate?(1) The accessed value of the estate was $1.2 million.(2) The attorney charged $2,400 for the estate planning services.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q11:Is the sum of the integers x and y a prime number?(1) x is an even prime number.(2) y is a prime number between 10 and 20.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q12:There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?A.120B.720C.1,060D.1,520E.1,980Answer:------------------------------------------------------------------------------------------------------------ Q13:An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?(1) The tens digit of n is a factor of the units digit of n.(2) The tens digit of n is 2.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q14:C(m,n) = m! / [(m-n)! n!] for nonnegative integers m and n, m ≥ n. If C(5,3) = C(5,x) and x ≠3, what is the value of x?A.0B. 1C. 2D.4E. 5Answer:------------------------------------------------------------------------------------------------------------ Q15:If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?A.7B.11C.14D.21E.42Answer:------------------------------------------------------------------------------------------------------------ Q16:The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?A.1,104B.972C.672D.294E.192Answer:------------------------------------------------------------------------------------------------------------ Q17:If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?(1) a = 2b(2) a + b > 1A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q18:On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?A.33 1/3%B.40%C.50%D.60%E.66 2/3%Answer:------------------------------------------------------------------------------------------------------------ Q19:If x is an integer, which of the following must be an odd integer?A.2x + 2B.4x + 3C.12x - 6D.13xE.14xAnswer:------------------------------------------------------------------------------------------------------------ Q20:A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.(2) The sum of the numbers on the remaining 35 cards is 176.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q21:If xy 0, is x/y = 1?(1) x2 = y2(2) xy > 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q22:A construction company was paid a total of $500,000 for a construction project. The company’s only costs for the project were for labor and materials. Was the company’s profit for the project greater than $150,000?(1) The company’s total cost was three times its cost for materials.(2) The company’s profit was greater than its cost for labor.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q23:Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?A.12.0B.12.1C.12.2D.12.3E.12.4Answer:------------------------------------------------------------------------------------------------------------ Q24:The value of (9⨯107)(9⨯108) is closest to which of the following?A.1016B.1017C.1056D.1057E.1058Answer:------------------------------------------------------------------------------------------------------------ Q25:A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?A.0B.1/9C.2/9D.1/3E. 1Answer:------------------------------------------------------------------------------------------------------------ Q26:There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this self include at least one paperback?A.40B.45C.50D.55E.60Answer:------------------------------------------------------------------------------------------------------------ Q27:In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?A.3/5B.2/3C.3/4D.4/5E.5/6Answer:------------------------------------------------------------------------------------------------------------ Q28:Of the goose eggs laid at a certain pond, 2/3 hatched, and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?A.280B.400C.540D.600E.840Answer:------------------------------------------------------------------------------------------------------------ Q29:If 1050– 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?A. 424B. 433C.440D.449E.467Answer:------------------------------------------------------------------------------------------------------------ Q30:EIn the figure, each side of square ABCD has length 1, the length of line segment CE is 1, and the length of line segment BE is equal to the length of line segment DE. What is the area of the triangular region BCE?A.1/3B.(√2)/4C.1/2D.(√2)/2E.3/4Answer:------------------------------------------------------------------------------------------------------------ Q31:There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?A.1/2B.2/3C.32/35D.11/12E.13/14Answer:------------------------------------------------------------------------------------------------------------ Q32:What is the remainder when the two digit, positive integer x is divided by 3?(1) The sum of the digits of x is 5.(2) The remainder when x is divided by 9 is 5.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q33:In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?A.16%B.25%C.32%D.40%E.52%Answer:------------------------------------------------------------------------------------------------------------Q34:If k = -1, which of the following is (are) true?I. k k = kII.∣k∣ = -kIII. k0 = -kA. I onlyB. I and II onlyC. I and III onlyD. II and III onlyE. I, II, and IIIAnswer:------------------------------------------------------------------------------------------------------------Q35:Is the sum of p2 and q2 greater than 1?(1) p is greater than 1/2.(2) q is greater than 1/2.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q36:What is the median number of employees assigned per project for the projects at Company Z?(1) 25 percent of the projects at Company Z have 4 or more employees assigned toeach project.(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned toeach project.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q37:What is the sum of the integers from -190 to 195, inclusive?A.0B. 5C.375D.875E.965Answer:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Answers:EBEED, BDECC, EEACB, BBCBD, CCABC, DDDCB, EDBEE, CE。
UNIVERSITY OF CAMBRIDGE INTERNA TIONAL EXAMINA TIONSGeneral Certificate of Education Advanced LevelMATHEMATICS9709/03Paper3Pure Mathematics3(P3)May/June20061hour45minutes Additional Materials:Answer Booklet/PaperGraph paperList of Formulae(MF9)READ THESE INSTRUCTIONS FIRSTIf you have been given an Answer Booklet,follow the instructions on the front cover of the Booklet.Write your Centre number,candidate number and name on all the work you hand in.Write in dark blue or black pen on both sides of the paper.Y ou may use a soft pencil for any diagrams or graphs.Do not use staples,paper clips,highlighters,glue or correctionfluid.Answer all the questions.Give non-exact numerical answers correct to3significantfigures,or1decimal place in the case of angles in degrees,unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected,where appropriate.Y ou are reminded of the need for clear presentation in your answers.The number of marks is given in brackets[]at the end of each question or part question.The total number of marks for this paper is75.Questions carrying smaller numbers of marks are printed earlier in the paper,and questions carrying larger numbers of marks later in the paper.At the end of the examination,fasten all your work securely together.This document consists of4printed pages.©UCLES2006[Turn over1Given that x =4 3−y ,express y in terms of x .[3]2Solve the inequality 2x >|x −1|.[4]3The parametric equations of a curve are x =2θ+sin 2θ,y =1−cos 2θ.Show that d y d x =tan θ.[5]4(i)Express 7cos θ+24sin θin the form R cos (θ−α),where R >0and 0◦<α<90◦,giving theexact value of R and the value of αcorrect to 2decimal places.[3](ii)Hence solve the equation7cos θ+24sin θ=15,giving all solutions in the interval 0◦≤θ≤360◦.[4]5In a certain industrial process,a substance is being produced in a container.The mass of the substancein the container t minutes after the start of the process is x grams.At any time,the rate of formation of the substance is proportional to its mass.Also,throughout the process,the substance is removed from the container at a constant rate of 25grams per minute.When t =0,x =1000and d x d t=75.(i)Show that x and t satisfy the differential equationd x d t=0.1(x −250).[2](ii)Solve this differential equation,obtaining an expression for x in terms of t .[6]6(i)By sketching a suitable pair of graphs,show that the equation 2cot x =1+e x ,where x is in radians,has only one root in the interval 0<x <12π.[2](ii)Verify by calculation that this root lies between 0.5and 1.0.[2](iii)Show that this root also satisfies the equation x =tan −121+e x .[1](iv)Use the iterative formula x n +1=tan −1 21+e x n,with initial value x 1=0.7,to determine this root correct to 2decimal places.Give the result of each iteration to 4decimal places.[3]©UCLES 20069709/03/M/J/067The complex number2+i is denoted by u.Its complex conjugate is denoted by u*.(i)Show,on a sketch of an Argand diagram with origin O,the points A,B and C representing thecomplex numbers u,u*and u+u*respectively.Describe in geometrical terms the relationship between the four points O,A,B and C.[4](ii)Express uu*in the form x+i y,where x and y are real.[3](iii)By considering the argument ofuu*,or otherwise,prove thattan−1 43=2tan−1 12.[2]8The diagram shows a sketch of the curve y=x12ln x and its minimum point M.The curve cuts the x-axis at the point(1,0).(i)Find the exact value of the x-coordinate of M.[4](ii)Use integration by parts tofind the area of the shaded region enclosed by the curve,the x-axis and the line x=4.Give your answer correct to2decimal places.[5]9(i)Express10(2−x)(1+x2)in partial fractions.[5](ii)Hence,given that|x|<1,obtain the expansion of10(2−x)(1+x2)in ascending powers ofx,up toand including the term in x3,simplifying the coefficients.[5]©UCLES20069709/03/M/J/06[Turn over10The points A and B have position vectors,relative to the origin O,given by−−→OA= −135and−−→OB=3−1−4.The line l passes through A and is parallel to OB.The point N is the foot of the perpendicular from B to l.(i)State a vector equation for the line l.[1](ii)Find the position vector of N and show that BN=3.[6] (iii)Find the equation of the plane containing A,B and N,giving your answer in the form ax+by+c =d.[5]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible.Every reasonable effort has been made by the publisher(UCLES)to trace copyright holders,but if any items requiring clearance have unwittingly been included,the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate(UCLES),which is itself a department of the University of Cambridge.©UCLES20069709/03/M/J/06。
