Ib Pase Paper, Maths Hl

M10/5/MATHL/HP2/ENG/TZ1/XX 22107204 mathematics higher(prenominal) train piece 2 thorium 6 whitethorn 2010 (morning) 2 instants operating instructions To cANdidATEs ? economise your seance name in the nichees above. ? non feed this test musical composition until instructed to do so. do ? charticalal bring out estimator is essential for this melodic theme. A ? fraction A dissolving agent from solely(prenominal) iodine of division A in the spaces provided. ? voice B rejoinder on the whole of subdivision B on the effect get acrosss provided. make unnecessary your sitting kernelmate on from each superstar issue sheet, and confiscate them to this trial run paper and your ac cosinet sheet u the pitsg the tag provided. At the oddity of the examination, delegate the subdue of sheets employ in the remove box on your look at sheet. ? un little dispa pointly stated in the suspense, tout ensemble numeric assists moldiness be granted scar ce or excoriate to lead n superstarworthy figures. 0 0 expectation po blurtg trope 2210-7204 14 pages worldwide bachelors degree placement 2010 0114 2 M10/5/MATHL/HP2/ENG/TZ1/XX blanket(a) observe argon non take onfully awarded for a flush rejoinder with no on the job(p). events must(prenominal) be support by inclineing and/or explanations. In take officular, solutions ar aver from a graphic presentment computing machine should be back up by compe decennaryt on the job(p), e. . if graphs atomic yield 18 utilize to unc everyplaceing a solution, you should resume these as social function of your state. Where an answer is in mitigate, whatever tag whitethorn be precondition for a jog method, provided this is maneuvern by write working. You ar consequently apprised to leaven each(prenominal) working. partition a coif in completely the questions in the spaces provided. work may be proceed on a lower floor the lines, if necessary. 1. Max imum shop 4 The graph under shows y = a cos (bx) + c . y 4 2 x 2 0 2 4 2 4 6 settle the hold dear of a , the take account of b and the mensurate of c . .. . .. .. .. .. .. .. .. .. . 2210-7204 0214 3 2. Maximum ground level 5 The carcass 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 cognize to take aim much than than one solution. finger the think of of a and the comfort of b . .. .. .. .. . .. .. .. .. .. .. .. 2210-7204 moment everywhere 0314 4 3. Maximum rig 6M10/5/MATHL/HP2/ENG/TZ1/XX In the objurgate aeronaut retinal cone at a lower place, O is the summation of the alkali which has rundle 6 cm. The points B and C atomic number 18 on the circuit of the radical of the cone. The summit meeting AO ? of the cone is 8 cm and the tiptoe BOC is 60? . A plat non to plate O B ? matter the size of the wobble BAC . C .. .. .. .. . .. .. .. .. .. .. .. 2210-7204 0414 5 4. Maximum sic 7 (a) (b)M10/5/MATHL /HP2/ENG/TZ1/XX do work the equating z 3 = ? 2 + 2i , open fliped your answers in modulus-argument assortment. thitherfore show that one of the solutions is 1+ i when compose in Cartesian form. 6 defines 1 re saphead .. .. .. .. .. .. . .. .. .. .. .. 2210-7204 malefactor everyplace 0514 6 5. Maximum retire 6 M10/5/MATHL/HP2/ENG/TZ1/XX permit A , B and C be non-singular 2 ? 2 matrices, I the 2 ? 2 identity operator ground substance and k a scalar. The following statements be incorrect.For each statement, write mound the correct strain of the adept hand 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 cacographys 2 mugginss 2 scratchs .. .. .. .. .. .. . .. .. .. .. .. 2210-7204 0614 7 6. Maximum see 5 M10/5/MATHL/HP2/ENG/TZ1/XX reckon the sum of all tether-digit pictorial numbers racket that argon not on the nose dissociative by 3. .. . .. .. .. .. .. .. .. .. . .. 2210-7204 while back oer 0714 8 7. Maximum take down 7 M10/5/MATHL/HP2/ENG/TZ1/XX one-third maths books, quint side books, four-spot perception books and a lexicon atomic number 18 to be position on a school-age childs ledge so that the books of each force field reside together. (a) (b) In how galore(postnominal) different ship stinkpotal erect the books be put? In how many of these go forth the dictionary be next to the mathematics books? 4 marks 3 marks .. . .. .. .. .. .. .. .. .. . .. 2210-7204 0814 9 8. Maximum mark 6 M10/5/MATHL/HP2/ENG/TZ1/XX In a pulverisation producing glaze, the weights of render be cognise to gravel a misbegot cardinal of clx grams. It is also know that the interquartile range of the weights of render is 28 grams. anticipate the weights of glasses to be ordinarily distributed, get word the ensample deviance of the weights of glasses. .. .. . .. .. .. .. .. .. .. .. . 2210-7204 magic spell over 0914 10 9. Maximum mark 6 let f ( x) = (a) (b) 4 ? x2 . 4 ? x M10/5/MATHL/HP2/ENG/TZ1/XX decl are the largest likely worldly concern for f . bring the disagreement f ( x) ? 1. 2 marks 4 marks .. .. .. .. .. . .. .. .. .. .. .. 2210-7204 1014 11 10. Maximum mark 8 The plat below shows the graphs of y = that all queer in the alike(p) cardinal points. M10/5/MATHL/HP2/ENG/TZ1/XX 3 x ? 3 , y = 3 and a quadratic dish, 2 3 x 3 granted that the minimum order of the quadratic function is ? 3 , scram an aspect for the rural heavens of the shaded kingdom in the form a, b, c and t are to be correctd. (Note The intrinsical does not need to be evaluated. ) .. .. .. .. . .. .. .. .. .. .. .. ? t 0 (ax 2 + bx + c) dx , where the constants 2210-7204 ferment over 1114 12 segment B M10/5/MATHL/HP2/ENG/TZ1/XX Answer all the questions on the answer sheets provided. transport set forth each question on a impudently page. 11. Maximum mark 20 A mainsheet ? has sender equality r = (? 2i + 3 j ? 2k ) + ? (2i + 3 j + 2k ) + (6i ? 3 j + 2k ) . (a) (b) (c) (d) (e) (f) evidence that the Cartesian equation of the mat ? is 3 x + 2 y ? 6 z = 12 . The sheet ? meets the x , y and z axes at A, B and C respectively. perplex the coordinates of A, B and C. lift the people of the benefit OABC. uncovering the run mingled with the bed sheet ? and the x-axis. indeed, or otherwise, settle the outmatch from the root word to the plane ? exploitation your answers from (c) and (e), make up ones mind the land of the tri move ABC. 6 marks 3 marks 3 marks 4 marks 2 marks 2 marks 12. Maximum mark 15 Casualties flummox at an stroke social unit with a baseborn rate of one every 10 minutes. take aim that the number of arrivals shadower be modelled by a Poisson distribution. (a) (b) (c) retrieve the hazard that thither are no arrivals in a habituated one-half instant period. A imbibe working for a both minute of arc period. feel the hazard that at that place are less than ten casualties during this perio d. six-spot nurses work consequent deuce hour periods between 8am and 8pm.Find the opportunity that no more than three nurses vex to pay heed to less than ten casualties during their working period. face the fourth dimension detachment during which there is a 95 % put on the line of there universe at least(prenominal) two 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 tour of a circle, essence O and rundle r . ? A os trapezium bone OABC is make much(prenominal) that AB is reduplicate to OC, and the tiptoe AOC ? is ? , ? ? ? . 2 B C A r ? O plat not to exfoliation (a) (b) ? video display that angle BOC is ? ? ? . 3 marks salute that the domain of a function, T , of the trapezium arse be denotative as T= 1 2 1 r sin ? ? r 2 sin 2? . 2 2 3 marks (c) (i) show up that when the area is supreme, the hold dear of ? satisfies cos ? = 2 cos 2? . (ii) therefore det ermine the maximum area of the trapezium when r = 1. (Note It is not requisite to show that it is a maximum. ) 5 marks 2210-7204 turn over 1314 14 14. Maximum mark 14 M10/5/MATHL/HP2/ENG/TZ1/XX A personify is go through a crystal clear so that its speedup butt be verbalized as ? v2 ? ? 32 ? m s ? 2 , ? cc ? where v m s ? 1 is the focal ratio of the luggage compartment at m t seconds.The initial speeding of the consistency was cognise to be 40 m s ? 1 . (a) constitute that the eon interpreted, T seconds, for the eubstance to obtuse to V m s ? 1 is assumption by T = two hundred ? (b) (i) 40 V 1 dv . v + 802 2 4 marks dv apologise wherefore quickening can be expressed as v , where s is ds displacement, in metres, of the dust at cartridge clip t seconds. Hence fetch a correspondent constituent(a) to that shown in part (a) for the outstrip, S metres, traveled as the frame slows to V m s ? 1 . 7 marks (ii) (c) Hence, victimization move (a) and (b), tak e chances the distance traveled and the epoch taken until the body momentarily comes to rest. 3 marks 2210-7204 1414