国际学校高中数学期中试卷(美高几何)

海南省海南枫叶国际学校2021-2021学年高二数学上学期期中试题时间：120分钟总分值;150分〔考试范围：必修2第二章，选修2-1第二章2.2，第三章3.1.5,3.2〕一、选择题(本大题共12小题，每题5分，共60分,在每题给出的四个选项中，只有一项为哪一项符合题目要求的.)1. 以下说法中正确的选项是( )A. 经过两条平行直线,有且只有一个平面B. 如果两条直线平行于同一个平面,那么这两条直线平行C. 三点确定唯一一个平面D. 如果一个平面内不共线的三个点到另一平面的距离相等,那么这两个平面相互平行2.如下图，用符号语言可表达为〔〕A. α∩β=m，n⊂α，A⊂m，A⊂nB. α∩β=m，n∈α，A∈m，A∈nC. α∩β=m，n⊂α，m∩n=AD. α∩β=m，n∈α，m∩n=A3. 是不同的直线,是不同的平面,以下结论成立的个数是〔〕①②③④A. 1B. 2C. 3D. 44.设α，β为两个不重合的平面，l，m，n为两两不重合的直线，给出以下四个命题：①假设α∥β，l⊂α，那么l∥β；②假设m⊂α，n⊂α， m∥β，n∥β，那么α∥β；③假设l∥α，l⊥β，那么α⊥β；④m⊂α，n⊂α，且l⊥m，l⊥n，那么l⊥α；其中真命题的序号是〔〕A. ①③④B. ①②③C. ①③D. ②④5.如图是一个正方体的平面展开图，那么在正方体中直线AB与CD的位置关系为〔〕A. 相交B. 平行C. 异面而且垂直D. 异面但不垂直6.如图，在正方体ABCD —A 1B 1C 1D 1中，E ，F 分别是C 1D 1，CC 1的中点，那么异面直线AE 与BF 所成角的余弦值为( ) A.B. C. D.7.假设ABC ∆的三个顶点的坐标分别为)4,1,6(),3,2,4(),1,2,1(--C B A ,那么ABC ∆的形状是〔 〕 A.锐角三角形B. 直角三角形C. 钝角三角形D. 等边三角形8.空间向量)2,1,2(),2,,1(-==b n a ，假设b a -2与b 垂直，那么a 等于〔 〕A.B.C.D.9.向量),,3(),5,4,2(y x b a ==，分别是直线21,l l 的方向向量，假设21//l l ，那么〔 〕A.，B.，C.，D.，10.假设椭圆C ：的短轴长等于焦距,那么椭圆的离心率为〔 〕A. B .C.D.11.假设曲线表示椭圆,那么k 的取值范围是 ( )．A.B.C.D.或12.椭圆1922=+x y 中，过点)21,21(P 的直线与椭圆相交于B A ,两点，且弦AB 被点P 平分，那么直线AB 的方程为〔 〕A. 049=--y xB. 059=-+y xC. 022=-+y xD. 05=-+y x 二、填空题〔本大题共4小题，每题5分，共20.0分〕13.a (2,1,2),(1,1,4),2a 3)(__________)_b b a b =--=--⋅+=已知向量则（1m,,___________,2n l m n l αα〈〉=-14.已知分别是直线的方向向量和平面的法向量，若cos 则与所成的角为．22122221310343___________x y C a b F F F a b l C A B AF B C +=15.已知椭圆：（＞＞）的左、右焦点为、，离心率为，过的直线交于、两点，若的周长为，则的方程为．16.点P 是椭圆＋＝1)0(>>b a 上的一点，F 1，F 2分别为椭圆的左、右焦点，∠F 1PF 2＝120°，且|PF 1|＝3|PF 2|，那么椭圆的离心率为___________．三、解答题〔本大题共6小题，17题10分，其余每题12分，共70分〕 17.求适合以下条件的椭圆标准方程：〔1〕与椭圆有相同的焦点，且经过点〔2〕经过两点18. 如图，在四棱锥P -ABCD 中，底面是正方形，侧面PAD ⊥底面ABCD ，且PA =PD =AD ，假设E 、F 分别为PC 、BD 的中点．〔1〕 求证：EF ∥平面PAD ；〔2〕 求证：EF ⊥平面PDC ．19.如图：在三棱锥P -ABC 中，PB ⊥面ABC ，△ABC 是直角三角形，∠B =90°，AB =BC =2，∠PAB =45°，点D 、E 、F 分别为AC 、AB 、BC 的中点．〔1〕求证：EF⊥PD；〔2〕求二面角E-PF-B的正切值．20.如图，在四棱锥P-ABCD中，底面ABCD为正方形，平面PAD⊥平面ABCD，点M在线段PB 上，PD∥平面MAC，PA=PD=，AB=4．〔1〕求证：M为PB的中点；〔2〕求二面角B-PD-A的大小；〔3〕求直线MC与平面BDP所成角的正弦值．21.如图1，四边形BCDE为直角梯形，∠B=90°，BE∥CD，且BE=2CD=2BC=2，A为BE的中点．将△EDA沿AD折到△PDA位置〔如图2〕，连结PC，PB构成一个四棱锥P-ABCD．〔Ⅰ〕求证AD⊥PB；〔Ⅱ〕假设PA⊥平面ABCD．①求二面角B-PC-D的大小；②在棱PC上存在点M，满足)10(≤≤=λλPCPM，使得直线AM与平面PBC所成的角为45°，求λ的值．22.椭圆C：)0(12222>>=+baaybx的离心率为,椭圆C的长轴长为4．求椭圆C的方程；直线l：与椭圆C交于A,B两点,是否存在实数k使得以线段AB为直径的圆恰好经过坐标原点O？假设存在,求出k的值；假设不存在,请说明理由．海南枫叶国际学校2021-2021学年度第一学期高二年级数学学科期中考试试卷答案一．选择题1-6.ACACDD 7-12.ABDCDB 二．填空题13.-45 14.030 15.12322=+y x 16.413三．解答题 17.解：〔1〕椭圆的焦点坐标为〔，0〕，∵椭圆过点，∴=+=4，∴a =2，b =，∴椭圆的标准方程为；〔2〕设所求的椭圆方程为，m ＞0，n ＞0，m ≠n ．把两点代入，得： ， 解得m =8，n =1，∴椭圆方程为．18.证明：〔Ⅰ〕连接AC ，那么F 是AC 的中点，在△CPA中，EF∥PA，且PA⊂平面PAD，EF⊊平面PAD，∴EF∥平面PAD〔Ⅱ〕因为平面PAD⊥平面ABCD，平面PAD∩平面ABCD=AD，又CD⊥AD，所以CD⊥平面PAD，∴CD⊥PA又PA=PD=AD，所以△PAD是等腰直角三角形，且∠APD=，即PA⊥PD而CD∩PD=D，∴PA⊥平面PDC，又EF∥PA，所以EF⊥平面PDC.19.连接BD、在△ABC中，∠B=90°．∵AB=BC，点D为AC的中点，∴BD⊥AC．又∵PB⊥面ABC，即BD为PD在平面ABC内的射影，∴PD⊥AC．∵E、F分别为AB、BC的中点，∴EF∥AC，∴EF⊥PD．〔2〕〔仅供参考，建议建系做〕过点B作BM⊥PF于点M，连接EM，∵AB⊥PB，AB⊥BC，∴AB⊥平面PBC，即BM为EM在平面PBC内的射影，∴EM⊥PF，∴∠EMB为二面角E-PF-B的平面角．∵Rt△PBF中，，∴．20.〔1〕证明：如图，设AC∩BD=O，∵ABCD为正方形，∴O为BD的中点，连接OM，∵PD∥平面MAC，PD⊂平面PBD，平面PBD∩平面AMC=OM，∴PD∥OM，那么，即M为PB的中点；〔2〕解：取AD中点G，∵PA=PD，∴PG⊥AD，∵平面PAD⊥平面ABCD，且平面PAD∩平面ABCD=AD，∴PG⊥平面ABCD，那么PG⊥AD，连接OG，那么PG⊥OG，由G是AD的中点，O是AC的中点，可得OG∥DC，那么OG⊥AD．以G为坐标原点，分别以GD、GO、GP所在直线为x、y、z轴距离空间直角坐标系，由PA=PD=，AB=4，得D〔2，0，0〕，A〔-2，0，0〕，P〔0，0，〕，C〔2，4，0〕，B 〔-2，4，0〕，M〔-1，2，〕，，．设平面PBD的一个法向量为，那么由，得，取z=，得．取平面PAD的一个法向量为．∴cos＜＞==．∴二面角B-PD-A的大小为60°；〔3〕解：，平面BDP的一个法向量为．∴直线MC与平面BDP所成角的正弦值为|cos＜＞|=||=||=．21.证明：〔Ⅰ〕在图1中，∵AB∥CD，AB=CD，∴ABCD为平行四边形，∴AD∥BC，∵∠B=90°，∴AD⊥BE，当△EDA沿AD折起时，AD⊥AB，AD⊥AE，即AD⊥AB，AD⊥PA，又AB∩PA=A，AB、PA平面PAB，∴AD⊥平面PAB，又∵PB⊂平面PAB，∴AD⊥PB．〔Ⅱ〕①以点A为坐标原点，分别以AB，AD，AP为x，y，z轴，建立空间直角坐标系，那么A〔0，0，0〕，B〔1，0，0〕，C〔1，1，0〕，D〔0，1，0〕, P〔0，0，1〕，=〔1，1，-1〕，=〔0，1，0〕，=〔1，0，0〕，设平面PBC的法向量为=〔x，y，z〕，那么，取z=1，得=〔1，0，1〕，设平面PCD的法向量=〔a，b，c〕，那么，取b=1，得=〔0，1，1〕，设二面角B-PC-D的大小为θ，那么cosθ=-=-=-，∴θ=120°．∴二面角B-PC-D的大小为120°．②设AM与面PBC所成角为α，=〔0，0，1〕+λ〔1，1，-1〕=〔λ，λ，1-λ〕，平面PBC的法向量=〔1，0，1〕，∵直线AM与平面PBC所成的角为45°，∴sinα=|cos＜＞|===，解得λ=0或．22.解：〔1〕设椭圆的半焦距为c，那么由题设，得：，解得，所以b2=a2-c2=4-3=1，故所求椭圆C的方程为+x2=1.〔2〕存在实数k使得以线段AB为直径的圆恰好经过坐标原点O．理由如下：设点A〔x1，y1〕，B〔x2，y2〕，将直线l的方程y=kx+代入+x2=1，并整理，得．〔*〕那么x1+x2=， x1x2=．因为以线段AB为直径的圆恰好经过坐标原点O，所以•=0，即x1x2+y1y2=0．又，于是+3=0，解得k=±，经检验知：此时〔*〕式的＞0，符合题意．所以当k=±时，以线段AB为直径的圆恰好经过坐标原点O．。

高二上学期期中考试试卷国际 SAT2数学Section One: Multiple Choice1.What is the midpoint of the line segmentjoining (–1, 7) and (0, 9)?A)1,12⎛⎫--⎪⎝⎭B)1,82⎛⎫-⎪⎝⎭C)74,2⎛⎫⎪⎝⎭D)710,2⎛⎫⎪⎝⎭wE) (–1, 16)2.What is an equation of the parabola with vertex at (0, 0) and directrix x = –3?A) y2 = –3x B) x2 = –3yC) y2 =13x D) x2 = 12yE) y2 = 12x3.An equation for a cross section of aflashlight’s parabolic reflector can be modelled by y2 = 6x. The light bulb is at the focus of the parabolic reflector. What is the focus?A)3,02⎛⎫⎪⎝⎭B)30,2⎛⎫⎪⎝⎭C)3,02⎛⎫-⎪⎝⎭D)30,2⎛⎫-⎪⎝⎭E) (0, 0)4.What is the radius of the circle 9x2 + 9y2 = 63?A) 1C) 7E) 635.What is an equation of the line tangent to the circle x2 + y2 = 32 at (4, 4)?A) y = x –8 B) y = x + 8C) y = –x + 8 D) y = xE) y = –x + 46.What is an equation of the ellipse with center at the origin, a vertex at (–5, 0), and a focus at (–2, 0)?A)2212125x y+=B)2215x=C)221254x y+=2215y+=E)221 2521x y+=7.What are the co-vertices of the ellipse 3x2 + 2y2 = 72?A) (±2, 0)B) (0, ±6)C) (±6, 0)D) , 0)E)8.What are the asymptotes of the hyperbola 9x2– 16y2 = 576?A) y = ±34x B) y = ±43xC) y = ±3x D) y = ±4xE) y = ±3 5 x9.Which line is a line of symmetry for the parabola (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 the system below?x2 + y2– 8x – 9 = 0–3x + 4y – 13 = 0A) (4, 1)B) (4, 5)C) (5, 7)D) (7, –4)E) (1, 4)12.How many solutions does the system consisting of the equations x2 + y2 = 16and x2 + 4y2 = 36 have?A) 0 B) 1C) 2D) 3 E) 413.How many solutions does the system consisting of the equations 2x –y – 9 = 0 and 4x2 + 9y2– 18x – 27 = 0 have?A) 0 B) 1 C) 2D) 3 E) 414. A ship’s LORAN system locates the shipon the hyperbolas with the equations given below. Find the ship’s location if it is north and east of the origin.x2–y2– 12x + 24 = 0–x2 + y2– 9 = 0A) (0, 3) B) (0, –3)C)513,44⎛⎫⎪⎝⎭D)513,44⎛⎫-⎪⎝⎭E)51, 22⎛⎫ ⎪⎝⎭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)112B)16C)14D)13E)51216.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)14B)15C)25D)35E)3417.What are the odds against stopping on a number greater than 1?A) 5 : 1 B) 6: 1 C) 1 : 2D) 1 : 6 E) 1 : 518.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 first and your friend’s squad performs second?A)190B)118C)15D)110E)4519.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 combinations of flowers are possible?A) 2 B) 6 C) 10D) 15 E) 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)881B)19C)16D)23E)131821. 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) 0.221 C) 0.282D) 0.500E) 0.78622. A card is randomly selected from a standard deck of 52 cards. What is the probability of drawinga face card or a red card?A)326B)12C)813D)1926E)212623.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) 0.08 C) 0.54D) 0.72 E) 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)225B)725C)2150D)2950E)335025.What is the probability of the spinner landingon 5, then landing on an even number?A) 0.05 B) 0.3 C) 0.5D) 0.6 E) 0.9526.If P(A) = 0.36, what is P(A)?A) 0.06B) 0.54 C) 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 and2 science fiction novels can you read?A) 521 B) 3201 C) 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 combinations of yard sales can you attend?A) 386 B) 638 C) 848D) 1286E) 9,858,24029.Which is the coefficient of x3 in theexpansion of (4x – 1)10 ?A)–7680 B) 120 C) 840D) 7680E) 13,44030.What is the probability of tossing a numbercube 30 times and getting the number fiveexactly 8 times?A) 0.02 B) 0.04 C) 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) 0.05 B) 0.15 C) 0.20D) 0.80E) 0.9532.The city council of a small town wantsto survey the town’s residents about whether they think the local sales tax should be 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) 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 miles east 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 company conducts a poll for a governor’s election. How many people did the company 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 is the probability (round to three decimal places) that he makes at least one free throw? Justify your result.高二期中考试国际 SAT2数学试卷答案Section One (每题2分，共68分)1B11E21E31E2 E 12 E 22 C 32 D3 A 13 C 23 E 33 A4 B 14 C 24 B 34 E5 C 15 B 25 A6 E 16 C 26 D7 D 17 E 27 C8 A 18 A 28 B9 C 19 D 29 A10 B 20 B 30 CSection Two (每题3分，共18分)35 736 937 21038 0.1 or 1/1039 250040 30Section 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 complement of missing both freethrows, or 1 – 0.22(0.48) = 0.8944.。

美国高中生数学试题及答案一、选择题（每题2分，共20分）1. 下列哪个数是无理数？A. 3.14159B. πC. 0.33333...D. √22. 如果一个函数f(x) = 2x^2 + 3x - 5，那么f(-2)的值是多少？A. -1B. 1C. 3D. 53. 一个直角三角形的两条直角边分别为3和4，斜边的长度是多少？A. 5B. 6C. 7D. 84. 以下哪个方程没有实数解？A. x^2 + 4x + 4 = 0B. x^2 - 4x + 4 = 0C. x^2 + 4x - 5 = 0D. x^2 - 9 = 05. 一个圆的半径是5，那么它的面积是多少？A. 25πC. 75πD. 100π6. 以下哪个是二次方程的根？A. x = 2B. x = -2C. x = 3D. x = -37. 如果一个数列是等差数列，且前三项为2, 5, 8，那么第10项是多少？A. 23B. 24C. 25D. 268. 一个函数g(x) = 3x - 2，当x = 4时，g(x)的值是多少？A. 10B. 12C. 14D. 169. 以下哪个是线性方程的解？A. x = 0B. x = 1C. x = 2D. x = 310. 一个正方体的体积是27立方单位，它的边长是多少？A. 3C. 9D. 12二、填空题（每题3分，共15分）11. 一个圆的周长是2πr，其中r是______。

12. 一个二次方程ax^2 + bx + c = 0的判别式是______。

13. 一个数的平方根是4，那么这个数是______。

14. 如果一个数列是等比数列，且首项为2，公比为3，那么第5项是______。

15. 一个函数h(x) = kx + b，当k不等于0时，这个函数是______函数。

三、解答题（每题5分，共25分）16. 解方程：3x + 5 = 14。

17. 证明：如果一个三角形的两边长分别为a和b，且a + b > c，那么这个三角形是存在的。

Unit Two Test Choose:(20’)1.What would be the next two number in the following set?{5, 7, 9, 11}( ).A)10, 12 B)13, 14 C)12, 13 D)13, 152.What shape and how many of this shape will be next in the pattern below?( ).A)1 Circle B)3 Circles C)1 Triangle D)3 Triangles3.Identify the if-then form of the given statement."A regular polygon has all its sides equal."( )A)If a polygon is regular, then it has all its sides equal. B)A polygon is regular, if it has all its sides equal.C)A regular polygon has all its sides equal. D)If a polygon has all its sides equal, then it is regular.4.Which of the following connectors is the logical disjunction?( ).A)OR B)AND C)BUT D)Both 5.Which of the following is a counterexample of the conjecture below?Conjecture: The product of two positive numbers is always greater than either number( ).A)2,2 B)21,2 C)3,10 D)2,-1 6.If ∠CFE is an obtuse angle,what is true.( ).A)∠CFE is greater than 90 degrees and less than 180 degrees. B)∠CFE is supplementary.C)∠CFE is less than 90 degrees. D)∠CFE can not be 110 degrees.7.What s a conjecture?( ).A) a guess B) unproven statement based on observationsC) switching the hypothesis and conclusion D)a false statement8.A specific case of when a conjecture is false is called a(n)?( )A)Counterexample B)Inverse C)Wrong answer D)Negation9.write the converse of the statement in symbolic form.( )A ) p → qB ) t → ~ wC ) ~ m → pD ) q → p 10.write the contrapositive of the statement in symbolic form.( )A ) p → qB ) t → ~ wC ) ~ m → pD ) ~ q → ~ pFor the following problems, Find the hypothesis and conclusion in each conditional statement.(8’)1. If today is Monday, then tomorrow is Tuesday.Hypothesis:_________________________; Conclusion:_________________________.2.If a truck weighs 2 tons, then it weighs 4000 pounds.Hypothesis:_________________________; Conclusion:_________________________.3.All chimpanzees love bananas.Hypothesis:_________________________; Conclusion:_________________________.4.Collinear points lie on the same line.Hypothesis:_________________________; Conclusion:_________________________.Determine if each statement is true or false. If false, provide a counterexample. (4’)1、If an animal can swim, then it is a fish.___________________________________________________________________________.2、If two angles are congruent, then they are right angles.___________________________________________________________________________.Write the contrapositive of the statement in words. (6’)1)If you care enough to send the best, then you send Trademark cards.___________________________________________________________________________.2)If you use Trickle deodorant, then you won’t have body odor.___________________________________________________________________________.Supply the word,phrase or symbol that can be placed in each blank to make the resulting statement true.(6’)(1)When p is true and q is false ,then p^~q is _____________.(2)When p ˅~q is false ，then p is ___________ and q is ______.(3)If the conclusion q is true ,then p→q must be ______.Use the following to answer questions 1-5:(10’)p: I love Geometry q:Mrs. Davis is a great teacherr: Mr. Tucker likes Algebra s:Algebra stinksWrite the symbolic representation.1、If I love geometry, then algebra stinks2、If Mrs. Davis is a great teacher or Mr. Tucker does not like Algebra, then I love Geometry.3、Algebra stinks if I love Geometry and Mrs. Davis is not a great teacher if Mr. Tucker likes Algebra.Write the words for each.4、r p →~5、q r s →∧)(Write the inverse of the statement in words.(6’) 1) If you buy Goal toothpaste, then your children will brush longer.___________________________________________________________________________2) When you serve imported sparkling water, it shows that you have good taste.___________________________________________________________________________ 3) The man who wears Curtis clothes is well dressed.___________________________________________________________________________Inductive or Deductive Reasoning(6’)1、Marcus learns in Social Studies that a presidential election happens every four years. He knows that the last presidential election was in 2004, so he concludes that the next presidential election will be in 2008.2、The United States Census Bureau collects data on the earnings of American citizens. Using data for the three years from 2001 to 2003, the bureau concluded that the national average median income for a four-person family was $43,527.3、Every cross country practice begins with a warm-up jog and stretching. Practice is about to start and the team assumes they will jog 2 warmup laps and stretch before their workout starts.Extra Questions(15’)Point O is the center of the regular octagon ABCDEFGH , and X is the midpoint of the side AB What fraction of the area of the octagon is shaded?One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?。

I ∙ ChOiCe questions (20 POintS )1.If the POIynOmial √r^4 -3x+4 in X has a degree Of 2 With three terms, the n equals ( )A. 3B. 4C. 5D. 62.In the following CalCUIatiOnS the COrreCt One is ( )∕∖.b4 b4=2b A B.A-4+X4=X8 C. (-a2b)5 = -a2b5 D. 3-(X-Y) = 4-x3.In the following equations, the One WhOSe transformation from Ieft Side to right Side is factorization is ( )A. 4∕-4b2=(2" + 2b)(2α-2∕?)B. (x + 2)? =F+4r + 4C. (d-%)' =a2 -2ab + b2D. Cr+ α + l = α(c + l) + l4.In the following expressiOnS the One Where a PerfeCt SqUare formulacan be applied to CalCUlate is ( )A. (2x + y)(2x + y)B. (2x一y)(2x + y)C. (-2x _ y)(-2x + y)D. (2x _ y)(-2x - y)5.If Onefactor of √-16y2 is X-^y, the Other factor is ( )A. x-yB. x + yC. x-4y D・ x + 4y6.In the following CalCUIatiOnS the COrreCt One is ( )A. 3X2+ 2√ =5√B. 2Λ2 + 3x2 = 5x2C. 2x2 + 3x2 = 5Λ4D. 2x2 + 3x3 = 6x57.If the PrOdUCt Of the POlynOmials 5x+4 Qnd 5x-a does not COntaina term Of x, then the ValUe of a is ( )A. 3B. -3C. 4 D・-48.If the VaIUe Of the algebraic expression 3a1一4“ + 1 is 6, then the VaIUeOf 6∕-8d + 5is( )A. 17B. 15C. 20 D・ 259.In the following statements, the incorrect One is ( )2A.The COeffiCient Of -—-is -24B.7ΛJ is a monomial With degree 3C.Ix3-Ixy2 + y3 is a POlynOmial Of degree 3 With three termsD.O is a monOmiel10.When factorizing the POlynOmial 5x2y + ∖0xy2-∖5xy , the COmmOnfactor to extracted is ( )A. 5xB. 5yC. 5x2y2D. 5xyII ・ FiII in the blanks (20 POintS)e an algebraic expression to represent "the SqUare Of the SUrn Of 3 times Xand y": _____________________2.Arrange the POlynOmial 5xy3 -6y4 +x3y-4x2 in descending POWerS Ofy：__________________3.CalCUIate: 二___________________________________________4.CalCUlate: x(5x-3)= _____________________5.CalCUlate： (x-2)(x + 5)= _______________6.FaCtOriZe : x-16y2= ____________________7.The difference Of SqUareS formula: _________________________8.The PerfeCt SqUare formula:⑴(M= ________________⑵(心)2 = _______________________ ・9・ If 〃7 + 丄=3 , (/W + —)2= __ , (〃2 _ —)2 = _______In m InIIL ShOrt answer questions ( 40 POintS )1. CalCUIate:(4) 36-4X 4Hl ∙ QUeStiOnS that require SOlUtiOnS (20 POintS)⑴(α + 3)~ 一(d + 2)(α-2)(3)(-4f∕)2+(-2^3)3∙6/ ⑷(X 一 2)(X + 7) — (3 — x)(2 + x) 2. FaCtOriZe :(1) 6α-12√+18/ (2) 7(x — 3) + 4(3 — x)(5) -X 2 +16y 2(6) 3@-疔 +27(G-Zo1∙GiVen A = 2λ^3^5^+8x+6 and—討+4+, find the EUeofA-2B and the ValUe Of A+B2. GiVen x+y = 2 end χy = ∖, find the ValUe Of the algebraic expressiOn (x2+iχ∕+l).3.GiVen χ2 -8x+y2-16y + 80 = 0, find the ValUeS OfX end y.4.FirSt simplify, and then evaluate:x-3(-x--y2)÷3(-2Λ + y2), for χ = 2 Qnd y = -2。

海南省海南枫叶国际学校2021-2021学年高一数学上学期期中试题一、选择题、(本大题共12小题，每题5分，共60分,在每题给出的四个选项中，只有一项为哪一项符合题目要求的.)1.集合U={1，2，3，4，5，6}，S={1，4，5}，T={2，3，4}，那么S∩〔∁U T〕等于〔〕A. 4,5,B.C.D. 2,3,4,2.假设f〔x〕是定义在R上的奇函数，当x＞0时，f〔x〕=x2x，那么f〔2〕=〔〕A. 2B. 6C.D.3.集合A={x∈N|∈N}的真子集的个数是〔〕A. 4B. 7C. 8D. 164.函数的定义域为〔〕A. B.C. D.5.，函数的最小值是A. 5B. 4C. 6D. 86.那么的值等于〔〕A. B. 4 C. 2 D.7.假设a∈R，那么“a2＞a〞是“a＞1〞的〔〕A. 充分而不必要条件B. 必要而不充分条件C. 充分必要条件D. 既不充分也不必要条件8.以下不等式正确的选项是〔〕A. 假设,那么B. 假设,那么C. 假设,那么D. 假设,那么 b9.以下函数中，既是偶函数又在〔0，+∞〕上单调递增的函数是〔〕A. B.C. D.10.假设函数f〔x〕=的定义域为R，那么实数a的取值范围是〔〕A. B. C. D.11.函数f〔x〕是偶函数，且在〔0，+∞〕内是增函数，f〔3〕=0，那么不等式x f〔x〕＜0的解集为〔〕A. 或B. 或C. 或D. 或12.函数y=f〔x〕对于任意x、y∈R，有f〔x+y〕=f〔x〕+f〔y〕1，当x＞0时，f〔x〕＞1，且f〔3〕= 4，那么〔〕A. 在R上是减函数,且B. 在R上是增函数,且C. 在R上是减函数,且D. 在R上是增函数,且二、填空题〔本大题共4小题，每题5分，共20.0分〕13.命题“∃x∈R，x+1≥0〞的否认为______ ．14.f〔2x+1〕=x2+x，那么f〔x〕=______．15.函数的单调增区间是．16.当x＞0时，不等式x2＋mx＋4＞0恒成立，那么实数m的取值范围是________．三、解答题〔本大题共6小题，共70.0分,解容许写出文字说明，证明过程或演算步骤.)17.〔10分〕全集，集合A={x|1≤x<3} ,，〔1〕求；〔2〕假设，且,求实数的取值范围.18.〔12分〕函数．〔1〕求；〔2〕判断函数f〔x〕在〔0，+∞〕上的单调性，并用单调性的定义证明。

【高一】浙江省瑞安中学2021 2021学年高一上学期期中考试（数学）中美班【高一】浙江省瑞安中学2021-2021学年高一上学期期中考试（数学）中美班试卷描述：瑞安中学2021学年第一学期高一国际部期中考试数学试卷一．选择题（本大题共10小题，每小题4分，共40分．在每小题给出的四个选项中，只有一项是符合题目要求的.）1．集合，则集合（▲）a．b．c．d．2．c．d．3.若，则=（▲）a．-1b.0c.2d.14．与函数相等的函数是(▲)a.b.c.d.5．设为函数的反函数,下列结论正确的是（）a．b．c．d．．若函数的图象经过一、三、四象限，则下列结论中正确的是（）a．b．c．d．7.下列函数中,既是偶函数又在区间上单调递增的是（）a．b．c．d．a．c．d．9．已知，则等于（）b．1c．0d．210.函数的图象向平移1个单位长度,所得图象与关于轴对称,则=（）b．c．d．二．填空题（本大题共6小题，每小题4分，共24分）11．已知幂函数图象过点（2，8），则其解析式是12．函数过定点13．函数的值域是14.奇函数时，,则当时，＝15．设函数，，则不等式的解集为___________16．函数的单调递减区间是三.解答题（本大题共4小题，共36分.解答应写出文字说明，证明过程或演算步骤.）17．（本题满分分已知集合．（1）与；（2）.gkstk18．（本小题满分8分）求值：（1）（2）19.（本小题满分10分）已知函数过点（1，5），（）是奇函数；（）在上的单调性，并用定义加以证明.学10分）已知函数（）时，解不等式；（）若在上有最小值9，求的值瑞安中学2021学年第一学期高一国际部期高中入学考试试数学参考答案选择题（10×4=40分）题号答案cadbbddcbc填空题（6×4=24分）11．12.13.14.15.16.三、解答题（8+8+10+10=36分）17．（本题满分分已知集合．（1）与；（2）（1）（2）（本题满分分gkstk（2）解：（1）0---------------4分（2）1.5---------------4分19.（本小题满分10分）已知函数过点（1，5），(1)求函数解析式，并求证:函数是奇函数；(2)判断函数在上的单调性，并用定义加以证明。

卜人入州八九几市潮王学校新草桥二零二零—二零二壹高一数学上学期期中试题〔国际部，无答案〕〔考试时间是是：120分钟总分160分〕一、填空题(本大题一一共14小题，每一小题5分，一共70分．请将答案填写上在答题卡相应位置.)1．集合A={}0,1,2,3,4,5，B={}0,1,1,6-那么A B =▲2．集合{2,}Mm =，{2,2}N m =且M N =那么m =▲． 3．函数()23f x x =+它的值域为{}1,2,5,8-那么它的定义域为▲．4．3=，那么1a a -+=____▲__ 5．函数[]2()23,0,3f x x x x =--∈那么()f x 的值域为▲． 6．函数lg(34)y x =-的定义域为▲．7．用不等号连接：1,51()3-▲ 1.91()3- 8．函数2log (2)y x =-在[0,1]上的最大值为_______▲_________. 9．()f x 是定义在R 上的奇函数，且单调递增，假设(2)(1)f x f x >--那么x 的取值范围是__▲_10．函数2, 1()(1), 1x x f x f x x >⎧=⎨+≤⎩，那么1()2f -=_______▲_______ 11．函数()1f x x =-的单调增区间是▲．12．函数()f x 是奇函数，且当0x >时，2()1f x x x =++，那么(1)f -=__▲_____． 13．函数()f x 满足(10)x f x =，那么(5)f =▲14．对于任意实数x ，规定函数()f x 取224, 1, 7x x x ++-三者中的最小者，那么函数()f x 的最大值是▲．二、解答题〔本大题一一共6小题，一共90分.请在答题卡规定区域写出文字说明、证明过程或者演算步骤．〕15．计算:〔1〕ln1ln3(2)25e +．16．集合{}327,x A x x Z =∈，{}|14B x m x m =-<<+． (1)求集合N A ； (2)假设AB =∅，务实数m 的取值范围. 17．函数()2x f x x a =+-．(1)判断该函数的单调性；(2)假设方程20x x a +-=在区间(1,2)上有实数根，求a 的取值范围．18．函数2(1)()2(1)x x f x x x ⎧≤=⎨->⎩， 试解答以下问题：〔1〕求((2))f f -；〔2〕画出函数的图象；〔3〕求方程1()2f x x =的解. 19．函数()lg f x x=． 〔1〕画出函数()f x 的图象； (2)写出()f x 的单调减区间(3)假设存在互不相等的实数,a b 使()(),f a f b =求ab 的值． 20．函数()151x m f x =-+是奇函数． (1)求m 的值；(2)证明：()f x 是R 上的增函数；(3)当[1,2)x ∈-时，求函数()f x 的值域．。

七中实验高一下期国际班期中测试数学一、选择题：(本大题一一共12小题，每一小题5分，一共50分。

只有一个是符合题目要求的，请把正确之答案填入答题卡中。

)1．如图，正六边形ABCDEF 中，BA+CD+FE=( )A ．0B ．BEC ．ADD ．CF2.等边三角形ABC 的边长为1，,a BC =,b CA =c AB =，那么a c c b b a •+•+•等于〔 〕A. 3 B ．-3 C ．23 D ．-233. 在锐角△ABC 中，设.cos cos ,sin sin B A y B A x ⋅=⋅=那么x , y 的大小关系为( )A.y x ≤B.y x >C.y x <D.y x ≥4.假设△ABC 的内角A 、B 、C 所对的边a 、b 、c 满足22a b 4c +-=（）且C=60°那么ab 的值是 ( ).A ．43B ．843-C ．4D ．235．△ABC 的三个内角A ，B ，C 所对的边分别为a ，b ，c ，asinAsinB+bco s 2 A=a 2，那么=a b ( ).〔A 〕23 〔B 〕22 〔C 〕 2 (D)6. A ，B ，C 是单位圆O 上的三点，且→OA ＋→OB ＝→OC ，那么→AB ·→OA ＝( )A ．－32B ．－32C ．12D ．327.如图，第一个图形有3条线段，第二个图形有6条线段，第三个图形有10条线段，那么第10个图形有线段的条数是〔 〕A ．66B ． 55C ．54D ． 488.数列{a n }满足a 1=0，a 2=2，且a n+2=a n+1-a n ，那么a 2021=〔 〕A ．0B ．2C ．—2D ．—40269.在等差数列{a n }中，其前n 项和为S n ，且S 2021=-2021，a 1007=3，那么S 2021=〔 〕 A ．-2021 B ．1006 C ．-1006 D ．20212210．数列{a n }中，a 3＝2，a 7＝1，假设{1a n ＋1}为等差数列，那么a 11＝( ) A ．0 B.12 C.23D ．2二、填空题：〔每一小题5分，一共25分〕11．设向量a ＝(1，2m )，b ＝(m ＋1，1)，c ＝(2，m )，假设(a ＋c )⊥b ，那么m ＝ ．12.如图，山顶上有一座铁塔，在地面上一点A 处测得塔顶B 处的仰角α=60°，在山顶C 处测得A 点的俯角β=45°，塔高BC 为50m ，那么山高CD 等于 m. 13.有一列数1234251017--，，，，…，那么第7个数是 ． 14.某校生物老师李老师在生物实验室做试验时，将水稻种子分组进展发芽试验；第1组取3粒，第2组取5粒，第3组取7粒。