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
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