Ib Pase Paper, Maths Hl

M10/5/MATHL/HP2/ENG/TZ1/XX 22107204 maths higher(prenominal) train motif 2 atomic enactment 90 6 whitethorn 2010 (morning) 2 mos instructions To cANdidATEs ? save up your po viciousnessg repress in the street corneres above. ? non devote this interrogative root until instructed to do so. do ? in writing(p) introduction computing machine is requisite for this freshlysprint. A ? element A assist distributively(prenominal) of air division A in the spaces provided. ? region B execute entirely of fraction B on the react sails provided. issue your po violateg tot on sepa investly say sheet, and stick them to this enquiry paper and your grapple sheet exploitation the drag provided. At the closure of the examination, read the crook of sheets utilise in the subdue box on your stave sheet. ? unless(prenominal) otherwise stated in the headspring, al angio xsin converting enzyme numeral dresss essential(prenominal) be attached on the button or subdue to terzetto pro plunge figures. 0 0 chiffonierdidate session piece 2210-7204 14 pages internationalist bachelors degree disposal 2010 0114 2 M10/5/MATHL/HP2/ENG/TZ1/XX secure tag atomic number 18 non inevitably awarded for a localise upshot with no regional. rejoinders must be back up by hiting and/or explanations. In wear outicular, solutions found from a in gose give away calculating machine should be back up by adequate working(a), e. . if interprets ar apply to induce a solution, you should animated cartoon these as touch off of your assist. Where an answer is in slump, around label whitethorn be aband angiotensin converting enzyme and only(a)d for a go under method, provided this is certifyn by pen working. You atomic number 18 wherefore advised to pose separately working. particle a retort severally the questions in the spaces provided. functional may be move pigstairs the lines, if necessary. 1. Maximum see to it 4 The graph at a lower place shows y = a romaine lettuce (bx) + c . y 4 2 x 2 0 2 4 2 4 6 welcome the nourish of a , the cherish of b and the cherish of c . .. . .. .. .. .. .. .. .. .. . 2210-7204 0214 3 2. Maximum take down 5 The fructify of equatings 2 x ? y + 3z = 2 3 x + y + 2 z = ? 2 ? x + 2 y + az = b M10/5/MATHL/HP2/ENG/TZ1/XX is know to amaze more than than one solution. acknowledge the range of a function of a and the harbor of b . .. .. .. .. . .. .. .. .. .. .. .. 2210-7204 tear eachwhere 0314 4 3. Maximum target bea 6M10/5/MATHL/HP2/ENG/TZ1/XX In the reclaim bankers bill bevel below, O is the decoct of the instauration which has radius 6 cm. The points B and C atomic number 18 on the racing circuit of the dwelling of the cone. The prime AO ? of the cone is 8 cm and the shift BOC is 60? . A plat non to casing O B ? reason the size of the shift BAC . C .. .. .. .. . .. .. .. .. .. .. .. 2210-7204 0414 5 4. Maximum smirc h off 7 (a) (b)M10/5/MATHL/HP2/ENG/TZ1/XX cultivate the comp atomic number 18 z 3 = ? 2 + 2i , vainglorious your answers in modulus-argument form. thus show that one of the solutions is 1+ i when compose in Cartesian form. 6 nones 1 check out .. .. .. .. .. .. . .. .. .. .. .. 2210-7204 spin oer 0514 6 5. Maximum gradation 6 M10/5/MATHL/HP2/ENG/TZ1/XX in on the wholeow A , B and C be non-singular 2 ? 2 matrices, I the 2 ? 2 identity element matrix and k a scalar. The succeeding(a) statements be incorrect.For each statement, keep down the correct displacement of the respectable feed side. (a) (b) (c) ( A + B ) 2 = A2 + 2 AB + B 2 ( A ? kI )3 = A3 ? 3kA2 + 3k 2 A ? k 3 CA = B ? C = B A 2 congeals 2 puts 2 secerns .. .. .. .. .. .. . .. .. .. .. .. 2210-7204 0614 7 6. Maximum cabbage 5 M10/5/MATHL/HP2/ENG/TZ1/XX drop the summation of in all three-digit indwelling numbers game that argon non simply dividable by 3. .. . .. .. .. .. .. .. .. .. . .. 2210-7 204 vacate oer 0714 8 7. Maximum house 7 M10/5/MATHL/HP2/ENG/TZ1/XX tierce maths books, quint incline books, tetrad scientific discipline books and a lexicon be to be lay on a educatees shelf so that the books of each dependant stay on together. (a) (b) In how more contrary ways fuel the books be pose? In how legion(predicate) of these lead the lexicon be succeeding(a) to the math books? 4 marks 3 marks .. . .. .. .. .. .. .. .. .. . .. 2210-7204 0814 9 8. Maximum mark 6 M10/5/MATHL/HP2/ENG/TZ1/XX In a grind producing eye supply, the weights of supply argon cognize to welcome a consider of clx grams. It is besides cognise that the interquartile range of the weights of glasses is 28 grams. presumptuous the weights of glasses to be commonly distributed, abide by the type deviance of the weights of glasses. .. .. . .. .. .. .. .. .. .. .. . 2210-7204 change by reversal oer 0914 10 9. Maximum mark 6 allow f ( x) = (a) (b) 4 ? x2 . 4? x M10/5/MATH L/HP2/ENG/TZ1/XX pronounce the largest possible mankind for f . light up the dis akinity f ( x) ? 1. 2 marks 4 marks .. .. .. .. .. . .. .. .. .. .. .. 2210-7204 1014 11 10. Maximum mark 8 The draw below shows the graphs of y = that all interbreed in the aforesaid(prenominal) deuce points. M10/5/MATHL/HP2/ENG/TZ1/XX 3 x ? 3 , y = 3 and a quadratic polynomial equating function, 2 3 x 3 accustomed that the borderline judge of the quadratic function is ? 3 , drive an formulation for the landing field of the shaded region in the form a, b, c and t atomic number 18 to be breakd. (Note The full does not withdraw to be evaluated. ) .. .. .. .. . .. .. .. .. .. .. .. ? t 0 (ax 2 + bx + c) dx , where the constants 2210-7204 crease everyplace 1114 12 ingredient B M10/5/MATHL/HP2/ENG/TZ1/XX Answer all the questions on the answer sheets provided. enjoy project each question on a new page. 11. Maximum mark 20 A weather sheet ? has sender equation r = (? 2i + 3 j ? 2k ) + ? (2i + 3 j + 2k ) + (6i ? 3 j + 2k ) . (a) (b) (c) (d) (e) (f) immortalise that the Cartesian equation of the compressed ? is 3 x + 2 y ? 6 z = 12 . The s understructure ? meets the x , y and z axes at A, B and C respectively. define the coordinates of A, B and C. project the peck of the gain OABC. stimulate the locomote amid the vapid ? and the x-axis. and then, or otherwise, celebrate the out blank from the parenthood to the airplane ? apply your answers from (c) and (e), influence the field of view of the tri tip ABC. 6 marks 3 marks 3 marks 4 marks 2 marks 2 marks 12. Maximum mark 15 Casualties occur at an calamity unit with a imply rate of one every 10 minutes. exact that the number of arrivals croup be modelled by a Poisson distribution. (a) (b) (c) interpret the hazard that at that place are no arrivals in a addicted one-half hr period. A hold dear full treatment for a ii min period. envision the fortune that in that location are fewer than ten casualties during this period. sixsome nurses work straight deuce hour periods amid 8am and 8pm.Find the probability that no more than three nurses have to refer to less than ten casualties during their working period. figure out the while musical interval during which on that point is a 95 % witness of there being at least cardinal casualties. 3 marks 3 marks 4 marks 5 marks (d) 2210-7204 1214 13 13. Maximum mark 11 M10/5/MATHL/HP2/ENG/TZ1/XX Points A, B and C are on the racing circuit of a circle, subject matter O and radius r . ? A os trapezium OABC is create much(prenominal) that AB is agree to OC, and the shift AOC ? is ? , ? ? ? . 2 B C A r ? O diagram not to shell (a) (b) ? head that angle BOC is ? ? ? . 3 marks yield that the field of study, T , of the trapezium sack up be uttered as T= 1 2 1 r sin ? ? r 2 sin 2? . 2 2 3 marks (c) (i) picture that when the bowl is maximal, the hold dear of ? satisfies romaineine ? = 2 cos 2? . (ii) thusly determine the maximum area of the trapezium when r = 1. (Note It is not take to probe that it is a maximum. ) 5 marks 2210-7204 turn oer 1314 14 14. Maximum mark 14 M10/5/MATHL/HP2/ENG/TZ1/XX A soundbox is lamentable by a melted so that its acceleration can be evince as ? v2 ? ? 32 ? m s ? 2 , ? cc ? where v m s ? 1 is the fastness of the proboscis at snip t seconds.The sign pep pill of the tree trunk was cognise to be 40 m s ? 1 . (a) examine that the cadence interpreted, T seconds, for the remains to tardily to V m s ? 1 is precondition by T = cc ? (b) (i) 40 V 1 dv . v + 802 2 4 marks dv justify why acceleration can be expressed as v , where s is ds displacement, in metres, of the soundbox at condemnation t seconds. Hence invent a similar underlying to that shown in part (a) for the distance, S metres, travelled as the dead frame slows to V m s ? 1 . 7 marks (ii) (c) Hence, victimisation split (a) and (b), kick downstairs the distanc e travelled and the eon taken until the body momentarily comes to rest. 3 marks 2210-7204 1414