2018-2019学年高二数学上学期期中试题(国际班).doc

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 segmentjoining (1, 7) and (0, 9)?A) B) C) D) wE) (1, 16)2. What is an equation of the parabola withvertex at (0, 0) and directrix x = 3?A) y2 = 3xB) x2 = 3yC) y2 =xD) x2 = 12yE) y2 = 12x3. An equation for a cross section of aflashlights parabolic reflector can be modelled by y2 = 6x. The light bulb is at the focus of the parabolic reflector. What is the focus?A) B) C) D) E) (0, 0)4. What is the radius of the circle9x2 + 9y2 = 63?A) 1B) C) 7D) E) 635. What is an equation of the line tangent tothe circle x2 + 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)?A) B) C) D) E) 7. What are the co-vertices of the ellipse3x2 + 2y2 = 72?A) (2, 0)B) (0, 6)C) (6, 0)D) (2, 0)E) (0, 2)8. What are the asymptotes of the hyperbola9x2 16y2 = 576?A) y = xB) y = xC) y = 3xD) y = 4xE) y = x9. Which line is a line of symmetry for theparabola (x 1)2 = 4( y 1)?A) y = 1B) y = 1C) x = 1D) x = 1E) x = 010. Which equation represents a hyperbola?A) x2 + 9y2 + 6x 90y + 225 = 0B) x2 9y2 + 6x + 90y 225 = 0C) x2 + y2 + 6x 10y + 25 = 0D) x2 + 6x 4y + 14 = 0E) x2 + 3y2 + 6x 30y + 78 = 011. Which ordered pair is a solution of thesystem below?x2 + y2 8x 9 = 03x + 4y 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 equations x2 + y2 = 16and x2 + 4y2 = 36 have?A) 0 B) 1C) 2D) 3 E) 413. How many solutions does the systemconsisting of the equations 2x y 9 = 0and 4x2 + 9y2 18x 27 = 0 have?A) 0B) 1C) 2D) 3E) 414. A ships LORAN system locates the shipon the hyperbolas with the equations givenbelow. Find the ships location if it is northand east of the origin.x2 y2 12x + 24 = 0x2 + y2 9 = 0A) (0, 3)B) (0, 3)C) D) E) In Exercises 15-17, refer to the spinnershown. The spinner is divided into sections with the same area.15. You spin the spinner 12 times. It stops on 19 two times. What is the experimental probability of stopping on 19?A) B) C) D) E) 16. 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) B) C) D) E) 17. 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 petition. The order of the performances is determined at random. What is the probability that your squad performs first and your friends squad performs second?A) B) C) D) E) 19. You are planting flowers in a large pot. Thereare 6 types of flowers to choose from andyou would like to use 2 different types. Howmany binations of flowers are possible?A) 2B) 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, then randomly choose another tulip. What is the probability that you choose a yellow tulip, then a red tulip?A) B) C) D) E) 21. 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 is randomly selected from a standard deck of 52 cards. What is the probability of drawing a face card or a red card?A) B) C) D) E) 23. Events A and B are dependent, withP(A) = 0.3 and P(A and B) = 0.24. What is P(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 roll or write for the school paper. There are 38 students council members who are on the honor roll and 5 that write for the school paper. What is the probability that a randomly selected student council member is both on the honor roll and writes for the school paper?A) B) C) D) E) 25. What is the probability of the spinner landingon 5, then landing on an even number?A) 0.05 B) 0.3C) 0.5D) 0.6 E) 0.9526. If P(A) = 0.36, what is P()?A) 0.06 B) 0.54C) 0.60D) 0.64 E) 0.7227. For your literature class, you are to read5 different novels. Your teacher gave you a list of 27 novels, of which 15 are historical novels and 12 are science fiction novels. How many different sets of exactly 3 historical novels and 2 science fiction novels can you read?A) 521B) 3201C) 30,030D) 52,100E) 360,36028. 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 binations of yard sales can you attend?A) 386B) 638C) 848D) 1286E) 9,858,24029. Which is the coefficient of x3 in theexpansion of (4x 1)10 ?A) 7680B) 120C) 840D) 7680E) 13,44030. What is the probability of tossing a numbercube 30 times and getting the number fiveexactly 8 times?A) 0.02B) 0.04C) 0.06D) 0.08E) 0.0931. The histogram shows a probabilitydistribution for a random variable X. What is the probability that X is at most 4?A) 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 think the local sales tax should be raised. The city council called every 12th resident from the telephone panys database. 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%. How many 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 is 5 mileseast and 12 miles north of the tower. If you continue driving due east, for how many more 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 choose 4 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 that n is prime given it is greater than 25?39. A pany conducts a poll for a governors election. How many people did the pany poll if the margin of error is 2%?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 thr