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 midpo int of the line segme ntjoining ( —1,7) and (0, 9)?f 1 J f 1 c)A) , -1 B) ,82 丿V 2 )C) 4,7D) 10,7I 2丿I 2丿wE) ( - 1, 16)2. What is an equati on of the parabola withvertex at (0, 0) and directrix x = - 3?2 2A) y = - 3x B) x = - 3y2 1 2C) y = —x D) x = 12 y32E) y = 12 x3. An equati on for a cross secti on of aflashlight ' s parabolic reflector can be modelled by the focus of the parabolic reflector. What is the focus?A) 0 i B) '0-1)2,0 ) 0, 2『3 ) 『3丨C)-畀D) 0二E) (0, 0)4. What is the radius of the circle29x 2+ 9 y = 63?A) 1 B) 7 C) 7D) 63 E) 632y = 6 x. The light bulb is at5. What is an equation of the line tangent to the circle 2、 2 x + y=32 at (4, 4)? A) y = x - 8B) y = x + 8 C) y = -x + 8D) y = xE) y = —x + 46. What is an equation of the ellipse with cen ter at the origi n, a vertex at (and a focus at (- 2, 0)? -5, 0),2 2 A) 21C) 2 2 —1 25 4D) 2 L 1 E) 2 2 x y ‘125 21 2 2 3x + 2 y = 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 9x 2 — 2 16y = 576?,3,4 A) y =± x B ) y = ± - x 43 C) y =±3x D) y =±4 xE) y = ± 3x 52 27. What are the co-vertices of the ellipse9. Which line is a line of symmetry for the parabola ( x 2- 1) 2= 4( y - 1)?A) y = 1 B) y = - 1C) x = 1 D) x = - 1E) x = 010. Which equation represents a hyperbola?22A) x + 9y + 6x - 90y+ 225 = 022B) x - 9y + 6 x + 90y - 225 = 022C) x2+ y2+ 6 x - 10 y + 25 = 02D) x + 6 x - 4 y + 14 = 02211. Which ordered pair is a solution of the system below?22x2+ y2- 8x - 9 = 0- 3x + 4y - 13 = 0A) (4, 1) B) (4, 5)D) (7, - 4) E) (1, 4)C) (5, 7)12. How many solutions does the systemconsisting of the equations22 and x + 4 y = 36 have?22x + y = 16A) 0 B) 1 C) 2D) 3 E) 413. How many solutions does the system consisting of the equations 222and 4 x + 9 y - 18 x - 27 = 0 have?A) 0 B) 1 C) 2D) 3 E) 4A)1 12 C)D) 12 14. A ship ' s LORAN system locates the ship on the hyperbolas with the equati ons give n below. Find the ship ' s location if it is northand east of the origi n. 2 2x — y - 12 x + 24 ==0 2 2 小—x + y - 9 = 0A)(0, 3) B) (0, -3)5 135 13 C) 1 ，— D) ,4' 4 4 4E)In Exercises 15-17, refer to the spinnershow n. The spinner is divided into secti ons with the same area.15. You spin the spinner 12 times. It stops on 19 two times. What is the experimentalprobability of stopp ing on 19?A)D) 8 81 23 C)18 16. You spin the spinner 20 times. It stops onan odd number 8 times. What is the experimental probability of stopping on an odd nu mber?11 2 A) B) C)- 455 D) 3E)- 5 4 17. What are the odds against stopping on a number greater than 1?A) 5 : 1B) 6: 1 C) 1 : 2D) 1 : 6 E) 1 : 5 18. There are 10 cheerleading squads performing in a competition. The order of the performances is determined at random. What is the probability that your squad performs's squad performs second? 19. You are planting flowers in a large pot. There are 6 types of flowers to choose from and you would like to use 2 differe nt types. How many comb in ati ons of flowers are possible?A) 2 B) 6C) 10 D) 15 E) 2020. A vase holds 4 red tulips, 2 yellow tulips, and 3 pink tulips. You ran domly choose a tulip, place it in a differe nt vase, the n randomly choose another tulip. What is the probability that you choose a yellow tulip,then a red tulip?first and your friendA)D)丄 90 丄 10C)21. A survey asked students how manyemails they receive each day. The results are show n in the bar graph. What is the experime ntal probability (roun ded to three decimal places) that a ran domly selected stude nt receives at most 20 emails a day?Emails received23. Events A and B are dependent, withP (A ) = 0.3 andP ( A and B ) = 0.24. What is P ( B | A )? A) 0.06B) 0.08 D) 0.72E) 0.80 24. Out of the 50 students on student council,29 are either on the honor rollor write for the school paper. There are 38 studentscouncil members who are on the honor roll and 5 that write for the school paper. What is the probability that a ran domly selected stude nt council member is both on thehonor roll andwrites for the school paper?544332211E c p p n l lrl -」主 A) 0.086D) 0.500 B) 0.221 E) 0.786 C) 0.282 22. A card is ran domly selected from a standard deck of 52 cards. What is the probability of draw ing a face card or a red card? A) 26C) 813 D) 1926E) 21 26 C) 0.5425. What is the probability of the spinner landingA) D) 225 29 50 B)— 25 50C) 2150A) 0.05 B) 0.3 C) 0.5D) 0.6 E) 0.9526. If RA ) = 0.36, what is P( A )?A) 0.06 B) 0.54 C) 0.60D) 0.64 E) 0.7227. For your literature class, you are to read5 differe nt no vels. Your teacher gave you a list of 27 no vels, of which 15are historical novels and 12 are scienee fiction novels. Howmany differentsets of exactly A) 521 B) 3201 C) 30,030D) 52,100 E) 360,3603 historical novels and 2 scienee fiction novels can you read?28. There are 10 houses in your neighborhoodhavi ng a yard sale. You want to go to at least 5 of the houses havi ng a yard sale.How many differe nt comb in ati ons of yard sales can you atte nd?A) 386 B) 638 C) 848D) 1286 E) 9,858,240x3in the29. Which is the coefficient of10expansion of (4 x - 1) ?C) 840A) - 7680 B) 120D) 7680 E) 13,44030. What is the probability of tossing a number cube 30 times and getting the number five exactly 8 times?A) 0.02 B) 0.04 C) 0.06D) 0.08 E) 0.0931. The histogram shows a probabilityA) 0.05 B) 0.15 C) 0.20D) 0.80 E) 0.9532. The city council of a small town wantsto survey the town ' s residents about whether they think the local sales tax shouldbe raised. The city council called every 12th resident from the telephone company' s 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) 400 B) 525 C) 724D) 800 E) 816Section Two: Gridded Answer35. What is the radius of the circle22x - 10x + y + 4y - 20 = 0?36. A cellular phone tower services a 20-mile radius. A rest stop on the highway is5 mileseast 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 governor ' s election. How many people did thecompany 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 throw, he makes the second one 88% of the time, but he 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 team ' s first playoff game, what isthe probability (round to three decimal places) that he makes at least one free Justify yourthrow? result.2018年秋季期中考试高二国际SAT2数学试卷答案Section Two （每题3 分，共18 分）a.b. The probability of making at least one of the two freethrows is the complement of miss ing both freethrows, or 1Sectio n Three (Part A 10 分，Part B 4 分，共14分）-0.22(0.48) = 0.8944.。
