Mathematics Higher level Paper 2.docx

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1、Diploma Programme Programme du dipldme Programa del DiplomaNo part of this product may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the IB.Additionally, the license tied with this product proh

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9、l estudio, colegios preparatories, desarrolladores de aplicaciones y entidades que presten servicios de planificacion curricular u ofrezcan recursos para docentes mediante plataformas digitales no esta permitido y estara sujeto al otorgamiento previo de una licencia escrita por parte del IB. En este

10、 enlace encontrara mas informacion sobre como solicitar una licencia: s:/ibo.org/become-an-ib-school/ib- publishing/licensing/applying-for-a-license/.N20/5/MATHL/HP2/ENG/TZ0/XX8 16EP048820 - 7202N20/5/MATH L/H P2/EN G/TZO/XX8820 - 7202Turn overN20/5/MATHL/HP2/ENG/TZ0/XX8820 - 72 )28820 - 72 )2-10-16

11、EP05Maximum mark: 6911 XFind the term independent of x in the expansion of 32-. x3x2rX-X- rX-X-N20/5/MATHL/HP2/ENG/TZ0/XX8820 - 7202Turn overN20/5/MATHL/HP2/ENG/TZ0/XX-12-16EP068820 - 7202N20/5/MATHL/HP2/ENG/TZ0/XX-13-8820 - 720243Maximum mark: 75.A survey of British holidaymakers found that 15 % of

12、 those surveyed took a holiday in the Lake District in 2019.(a) A random sample of 16 British holidaymakers was taken. The number of people in the sample who took a holiday in the Lake District in 2019 can be modelled by a binomial distribution.(i) State two assumptions made in order for this model

13、to be valid.(ii) Find the probability that at least three people from the sample took a holiday in the Lake District in 2019.(b) From a random sample of n holidaymakers, the probability that at least one of them took a holiday in the Lake District in 2019 is greater than 0.999.Determine the least po

14、ssible value of n .Turn over6.N20/5/MATHL/HP2/ENG/TZ0/XX14 Maximum mark: 78820 - 720216EP07pxn-I*8820 - 7202N20/5/MATH L/H P2/EN G/TZO/XX 15 Maximum mark: 7Use mathematical induction to prove that (xe ) - p ( px + n)efor Z+, p Q.泣Turn overN20/5/MATHL/HP2/ENG/TZ0/XX 16 8820 - 7202Maximum mark: 7N20/5

15、/MATH L/H P2/E N G/TZO/XX8820 - 72028820 - 7202-17- Maximum mark: 716EP087.At a gathering of 12 teachers, seven are male and five are female. A group of five of these teachers go out for a meal together. Determine the possible number of groups in each of the following situations:(a) There are more m

16、ales than females in the group. 4Two of the teachers, Gary and Gerwyn, refuse to go out for a meal together. 3Turn overN20/5/MATHL/HP2/ENG/TZ0/XX 18 Maximum mark: 78820 - 720216EP098820 - 72 )2N20/5/MATHL/HP2/ENG/TZ0/XX-19-8. Maximum mark: 610A small bead is free to move along a smooth wire in the s

17、hape of the curve y = (% 0).3-2e dy dx(a) Find an expression fordy rAt the point on the curve where x = 4 , it is given that 一 = -0.1m s .dtdx(b) Find the value of 一 at this exact same instant. 3 dtN20/5/MATHL/H P2/EN G/TZO/XX8820 - 7202-20-Do not write solutions on this page.16EP10Section BAnswer a

18、ll questions in the answer booklet provided. Please start each question on a new page.9. Maximum mark: 14The weights, in grams, of individual normal distribution, with mean 102 gpackets of coffee can be modelled by a and standard deviation 8 g.-21 -N20/5/MATHL/HP2/ENG/TZ0/XX8820 - 7202De not write s

19、olutions on this page.(a) Find the probability that a randomly selected packet has a weight less than 100 g. 2The probability that a randomly selected packet has a weight greater than w grams is 0.444. Find the value of w .(b) A packet is randomly selected. Given that the packet has a weight greater

20、 than 105 g, find the probability that it has a weight greater than 110 g.(c) From a random sample of 500 packets, determine the number of packets that would be expected to have a weight lying within 1.5 standard deviations of the mean. 3Packets are delivered to supermarkets in batches of 80. Determ

21、ine the probability that at least 20 packets from a randomly selected batch have a weight less than 95 g. 416EP1110. Maximum mark: 16The plane Fl i has equation 3x - y + z = -13 and the line L has vector equation23Turn overN20/5/MATHL/HP2/EN G/TZO/XX-22-Do not write solutions on this page.r -2 +-1 ，

22、入 R.-24(a) Given that L meets n i at the point P, find the coordinates of P. 4(b) Find the shortest distance from the point 0(0,0,0) to Fl i. 4The plane Fl 2 contains the point O and the line L .(c) Find the equation of Fl 2, giving your answer in the form r.n-d. 3(d) Determine the acute angle betwe

23、en Fl 1 and n 2 .5 u.N20/5/MATHL/HP2/ENG/TZ0/XX8820 - 72028820 - 7202-23-Do not write solutions on this page.11. Maximum mark: 20A particle P moves in a straight line such that after time t seconds, its velocity, v in m sd,7Cis given by v = e_3/ sin 6 t, where 0 Z 2.(a) Find the times when P comes t

24、o instantaneous rest.2At time t, P has displacement s (力；at time ，= 0, s (0) = 0.(b) Find an expression for s in terms of t.7(c) Find the maximum displacement of P , in metres, from its initial position.2(d) Find the total distance travelled by P in the first 1.5 seconds of its motion.2At successive

25、 times when the acceleration of P is 0 m s2, the velocities of P form a geometric sequence. The acceleration of P is zero at times t , h ,打 where t h h and the respective velocities are 也，v2,也.(e) (i) S how that, at these times, tan 6 r = 2 .u V2 V3- ?7(ii) Hence show that =-e.VIV216EP13Please do no

26、t write on this page.Answers written on this page willnot be marked.16EP14Please do not write on this page.Answers written on this page willnot be marked.16EP15Please do not write on this page.Answers written on this page willnot be marked. =:；二 u.16EP16N20/5/MATHL/H P2/EN G/TZO/XXDiploma Programme

27、Programme du diplome Programs del DiplomaDiploma Programme Programme du diplome Programs del DiplomaMathematics Higher level Paper 2Wednesday 4 November 2020 (morning)Candidate session number2 hours2 hoursInstructions to candidates 囚 Write your session number in the boxes above. 0 Do not open this e

28、xamination paper until instructed to do so. 0 A graphic display calculator is required for this paper.内 Section A: a nswer all questions. Answers must be written within the answer boxes provided.囚 Section B: answer all questions in the answer booklet provided. Fill in your session number on the fron

29、t of the answer booklet, and attach it to this examination paper and your cover sheet using the tag provided.0 Unless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures.N20/5/MATHL/HP2/ENG/TZ0/XX8820 - 72020 A clean copy of the mat

30、hematics HL and further mathematics HL formula booklet is required for this paper.囚 The maximum mark for this examination paper is 100 marks.13 pages8820 - 7202 International Baccalaureate Organization 202016EP01Full marks are not necessarily awarded for a correct answer with no working. Answers mus

31、t be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working. For example, if graphs are used to find a solution, you should sketch these as part of your answer. Where an answer is incorrect, some marks may be

32、 given for a correct method, provided this is shown by written working. You are therefore advised to show all working.Section AAnswer all questions. Answers must be written within the answer boxes provided. Working may be continued below the lines, if necessary.1. Maximum mark: 5The following diagra

33、m shows a sector OAB of radius 15 cm. The length of AB is 11 cm.N20/5/MATH L/HP2/EN G/TZO/XX8820 - 7202diagram not to scaleFind the area of the shaded region.16EP02Maximum mark: 42.Jenna is a keen book reader. The number of books she reads during one week can be modelled by a Poisson distribution wi

34、th mean 2.6 .Turn overN20/5/MATHL/HP2/ENG/TZ0/XX8820 - 7202Determine the expected number of weeks in one year, of 52 weeks, during which Jenna reads at least four books.N20/5/MATHL/HP2/ENG/TZ0/XX8820 - 72028820 - 7202Turn overN20/5/MATHL/HP2/ENG/TZ0/XX6 16EP038820 - 7202Maximum mark: 8The following diagram shows part of the graph of y = p + q sin (厂x) . The graph has a local 9n3nmaximum point at-,5and a local minimum point at -一, 1-.4Determine the values of p ,q and r.N20/5/MATHL/H P2/EN G/TZO/XX8820 - 72027 44(a) Hence find the area of the shaded region.Turn over