广东省深圳市耀华实验学校2018_2019学年高二数学上学期期中试题国际班.docx

广东省深圳市耀华实验学校2018-2019 学年高二数学上学期期中试题（国际班）1. What is the midpoint of the line segment joining ( 1, 7) and (0, 9)?A)1 , 1B)1 ,822C)4, 7D)10, 722wE) ( 1, 16)2. What is an equation of the parabola withvertex at (0, 0) and directrixx = 3?A)y2 = 3xB)x2 = 3yC)y2 = 1 xD)x2 = 12 y3E)y2 = 12 x3. An equation for a cross section of aflashlight s parabolic reflector can be modelled byy2= 6 x. The light bulb is atthe focus of the parabolic reflector. What is the focus?A)3,0B)0,322C)3D)0,3,022E) (0, 0)4. What is the radius of the circle 9x2 + 9 y2 = 63?A)1B)7C) 7D)63E)63- 1 - / 135. What is an equation of the line tangent tothe circlex2 +y2 = 32 at (4, 4)?A)y = x 8B)y = x + 8C)y = x + 8D)y = xE) y = x + 46. What is an equation of the ellipse withcenter at the origin, a vertex at ( 5, 0),and a focus at ( 2, 0)?x2y2A)12125x2y2C)1254x2y2E)12521x2y21B)521x2y2D)12157. What are the co-vertices of the ellipse 3x2 + 2 y2 = 72?A)( 2, 0)B)(0, 6)C)( 6, 0)D)( 2 6 , 0)E)(0, 2 6 )8. What are the asymptotes of the hyperbola 9x2 16 y2 = 576?A)y = 3 xB) y = 4 x43C)y =3xD)y = 4xE) y = 3 x5- 2 - / 139. Which line is a line of symmetry for theparabola ( x 1)2y 1)?= 4(A)y= 1B)y=1C)x= 1D)x=1E) x = 010.Which equation represents a hyperbola?A) x2 + 9 y2 + 6 x 90 y + 225 = 0B) x2 9 y2 + 6 x + 90 y 225 = 0C)x2 +y2 + 6 x 10 y + 25 = 0D) x2 + 6 x 4 y + 14 = 0E) x2 + 3 y2 + 6 x 30 y + 78 = 011. Which ordered pair is a solution of the system below?x2 + y2 8 x 9 = 0 3x + 4 y 13 = 0A)(4, 1)B)(4, 5)C)(5, 7)D)(7,4)E)(1, 4)12.How many solutions does the systemconsisting of the equationsx2 + y2 = 16andx2 + 4 y2 = 36 have?A)0B)1C)2D)3E)413.How many solutions does the systemconsisting of the equations 2x y 9 = 0and 4 x2+ 9 y2 18 x 27 = 0 have?A)0B)1C)2D)3E)4- 3 - / 1314. A ship s LORAN system locates the ship on the hyperbolas with the equations givenbelow. Find the ships location if it is northand east of the origin.x2 y2 12 x + 24 = 0 x2 + y2 9 = 0A)(0, 3)B)(0, 3)C)5 ,13D)5 ,1344445 1E) ,2 2In Exercises 15-17, refer to the spinnershown. The spinner is divided into sections with the same area.15.You spinthe spinner12 times.It stops on 19 two times. What is the experimentalprobability of stopping on 19?A)1B)1C)11264D)1E)5312- 4 - / 1316.You spin the spinner 20 times. It stops onan odd number 8 times. What is the experimental probability of stopping on an odd number?A)1B)1C) 2455D)3E)35417.What are the odds against stopping on a number greater than 1?A) 5 : 1B) 6: 1C) 1 : 2D) 1 : 6E) 1 : 518.There are 10 cheerleading squads performing in a competition. The order of theperformancesis determinedat random. What is the probabilitythatyour squad performsfirst and your friends squad performs second?A)1B)1C) 190185D)1E)410519. You are planting flowers in a large pot. There are 6 types of flowers to choose from andyou would like to use 2 different types. How many combinations of flowers are possible?A) 2 B) 6C) 10D) 15E) 2020.A vase holds 4 red tulips, 2 yellow tulips,and 3 pink tulips. You randomly choose a tulip, place it in a different vase, thenrandomlychoose another tulip.What is the probabilitythat you choose a yellow tulip,then a red tulip?A)8B)1C) 18196D)2E)13318- 5 - / 1321.A survey asked students how manyemails they receive each day. The results are shown in the bar graph. What is the experimental probability (rounded to three decimal places) that a randomly selected student receives at most 20 emails a day?A) 0.086B) 0.221C) 0.282D) 0.500E) 0.78622.A card israndomlyselectedfroma standard deck of 52 cards. What is theprobability of drawing a face cardora red card?A)3B)1C)826213D)19E)21262623.Events A and B are dependent, withP( A) = 0.3 andP( A and B) = 0.24. What isP( B| A)?A) 0.06B) 0.08C) 0.54D) 0.72E) 0.8024. Out of the 50 students on student council,29 are either on the honor rollor write for the school paper. There are 38 studentscouncilmembers who are on thehonor rolland 5 that write for the school paper. Whatis the probability that a randomly selected student council member is both on thehonor rolland writes for the school paper?- 6 - / 13A)2B)7C) 21252550D)29E)33505025.What is the probability of the spinner landingon 5, then landing on an even number?A) 0.05B) 0.3 C) 0.5D) 0.6E) 0.9526.If( ) = 0.36, what isP( A )?P AA) 0.06B) 0.54 C) 0.60D) 0.64E) 0.7227.For your literature class, you are to read5 different novels. Your teacher gave you a list of 27 novels, of which 15 arehistoricalnovelsand 12 are sciencefictionnovels.Howmany differentsetsof exactly3 historical novels and 2 science fiction novels can you read?A) 521B) 3201C) 30,030D) 52,100E) 360,360- 7 - / 1328.There are 10 houses in your neighborhoodhaving a yard sale. You want to go to at least 5 of the houses having a yard sale.How many different combinations of yard sales can you attend?A) 386B)638C) 848D) 1286E)9,858,24029. Which is the coefficient ofx3 in theexpansion of (4x 1) 10 ?A) 7680B)120C) 840D)7680E)13,44030. What is the probability of tossing a number cube 30 times and getting the number five exactly 8 times?A) 0.02B)0.04C) 0.06D) 0.08E)0.0931.The histogram shows a probabilitydistribution for a random variableX. What is the probability thatX isat most4?- 8 - / 13A) 0.05B)0.15C) 0.20D) 0.80E)0.9532.The city council of a small town wantsto survey the towns residents about whether they thinkthe local sales tax shouldbe raised.The citycouncilcalledevery 12thresidentfrom the telephonecompanysdatabase. Identify the type of sample described.A) Convenience sampleB) Random sampleC) Self-selected sampleD) Systematic sampleE) None of these33. In a survey of 1200 teenagers, 48% said they are involved in an extracurricular activity. What is the margin of error for the survey?A) 2.9%B) 3.3%C) 3.9%D) 4.2%E) 4.8%34. A survey about favorite Olympic sports reported a margin of error 3.5%. Howmany people were surveyed?A)400B)525C) 724D)800E)816Section Two: Gridded Answer35.What is the radius of the circlex2 10x + y2 + 4y 20 = 0?36. A cellular phone tower services a 20-mile radius. A rest stop on the highway is5 miles- 9 - / 13east and 12 miles north of the tower. If you continue driving due east, for how manymore miles will you be in range of the tower?37. There are 10 finalists for a game show. The producer of the show wants to choose4 of the finalists to appear on the show. In how many ways can the producer choose the finalists?38. Let n be a randomly selected integer from 1 to 40. What is the probability thatn is prime given it is greater than 25?39.A company conducts a poll for a governors election. How many people did thecompany poll if the margin of error is2%?40. 4 children are selected from 2 boys and 5 girls. How many different ways if at least one boy and one girl are chosen?Section Three: Extended Response41.When shooting two consecutive free throwsduring the regular season, a basketball player makes the first free throw 78% of the time. If he makes the first free throw, he makes the second one 88% of the time, buthe only makes the second free throw 52% of the time after missing the first one.a. Make a probability tree diagram to model this situation.b.When he shoots a pair of free throws in the teams first playoff game, what isthe probability(roundto threedecimalplaces)thathe makes at leastone freethrow?Justify your result.- 10 - / 13- 11 - / 132018 年秋季期中考试高二国际SAT2 数学试卷答案Section One (每题 2 分，共 68分 )1B11E21E31E2E12E22C32D3A13C23E33A4B14C24B34E5C15B25A6E16C26D7D17E27C8A18A28B9C19D29A10B20B30CSection Two (每题 3 分，共 18 分 )35 736 937 21038 0.1 or 1/1039 250040 30- 12 - / 13Section Three (Part A 10分， Part B 4分，共 14 分 )a.b. The probability of making at least one of the two freethrows is the complementof missing both freethrows, or 1 0.22(0.48) = 0.8944.- 13 - / 13