### Transcription

N13/5/MATME/SP2/ENG/TZ0/XX88137302candidate session numberMATHEMATICSSTANDARD LEVELPAPER 200Tuesday 12 November 2013 (morning)Examination code81 hour 30 minutes813–7302iNSTrucTioNS To cANdidATES Write your session number in the boxes above.do not open this examination paper until instructed to do so.A graphic display calculator is required for this paper.Section A: answer all questions in the boxes provided.Section B: answer all questions in the answer booklet provided. Fill in your session numberon the front of the answer booklet, and attach it to this examination paper andyour cover sheet using the tag provided. unless otherwise stated in the question, all numerical answers should be given exactly orcorrect to three significant figures. A clean copy of the Mathematics SL information booklet is required for this paper. The maximum mark for this examination paper is [90 marks].11 pages international Baccalaureate organization 201312EP01

–2–N13/5/MATME/SP2/ENG/TZ0/XXFull marks are not necessarily awarded for a correct answer with no working. Answers must be supportedby working and/or explanations. In particular, solutions found from a graphic display calculator should besupported by suitable working, for example, if graphs are used to find a solution, you should sketch theseas part of your answer. Where an answer is incorrect, some marks may be given for a correct method,provided this is shown by written working. You are therefore advised to show all working.Section aAnswer all questions in the boxes provided. Working may be continued below the lines if necessary.1.[Maximum mark: 5] 11 0 5 4 Let A 1 2 1 , and B 7 . 10 2 2 0 (a)Write down A 1 .[2](b)Hence or otherwise, solve the equation AX B .[3].12EP02

–3–2.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 6]Let f ( x) ( x 1)( x 4) .(a)Find the x-intercepts of the graph of f .[3](b)The region enclosed by the graph of f and the x-axis is rotated 360 about the x-axis.Find the volume of the solid formed.[3].turn over12EP03

–4–3.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 6]1Let f ( x) 3 x 4 .2(a)Find f ′ ( x) .(b)Find[2] f ( x)dx .[4].12EP04

–5–4.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 6]Two events A and B are such that P ( A) 0.2 and P ( A B ) 0.5 .(a)Given that A and B are mutually exclusive, find P ( B) .[2](b)Given that A and B are independent, find P ( B) .[4].turn over12EP05

–6–5.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 8]A particle moves along a straight line such that its velocity, v ms 1 , is given byv (t ) 10te 1.7 t , for t 0 .(a)On the grid below, sketch the graph of v , for 0 t 4 .[3]v321–101234 t–1(b)Find the distance travelled by the particle in the first three seconds.[2](c)Find the velocity of the particle when its acceleration is zero.[3].12EP06

–7–6.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 7]The time taken for a student to complete a task is normally distributed with a mean of20 minutes and a standard deviation of 1.25 minutes.(a)(b)A student is selected at random. Find the probability that the student completes the taskin less than 21.8 minutes.[2]The probability that a student takes between k and 21.8 minutes is 0.3. Find the valueof k .[5].turn over12EP07

–8–7.N13/5/MATME/SP2/ENG/TZ0/XX[Maximum mark: 7]Consider the graph of the semicircle given by f ( x) 6 x x 2 , for 0 x 6 .A rectangle PQRS is drawn with upper vertices R and S on the graph of f , and PQ onthe x-axis, as shown in the following diagram.ydiagram not to scaleSO(a)(b)RPQ6 xLet OP x .(i)Find PQ, giving your answer in terms of x .(ii)Hence, write down an expression for the area of the rectangle, giving your answerin terms of x .(i)Find the rate of change of area when x 2 .(ii)The area is decreasing for a x b . Find the value of a and of b .12EP08[3][4]

–9–N13/5/MATME/SP2/ENG/TZ0/XXDo NOT write solutions on this page.Section BAnswer all questions in the answer booklet provided. Please start each question on a new page.8.[Maximum mark: 14]Consider a circle with centre O and radius 7 cm. Triangle ABC is drawn such that its verticesare on the circumference of the circle.diagram not to scaleB710.412.2O1.058 CAˆ 1.058 radians .AB 12.2cm , BC 10.4cm and ACB(a)ˆ .Find BAC[3](b)Find AC .[5](c)Hence or otherwise, find the length of arc ABC .[6]turn over12EP09

– 10 –N13/5/MATME/SP2/ENG/TZ0/XXDo NOT write solutions on this page.9.[Maximum mark: 17] 11 4 1 2 Consider the lines L1 and L2 with equations L1 : r 8 s 3 and L2 : r 1 t 1 . 2 1 7 11 The lines intersect at point P.(a)Find the coordinates of P.[6](b)Show that the lines are perpendicular.[5](c)The point Q (7, 5, 3) lies on L1 . The point R is the reflection of Q in the line L2 .Find the coordinates of R.[6]12EP10

– 11 –N13/5/MATME/SP2/ENG/TZ0/XXDo NOT write solutions on this page.10.[Maximum mark: 14]Samantha goes to school five days a week. When it rains, the probability that she goes to schoolby bus is 0.5. When it does not rain, the probability that she goes to school by bus is 0.3. Theprobability that it rains on any given day is 0.2.(a)(b)(c)(d)On a randomly selected school day, find the probability that Samantha goes to school bybus.[4]Given that Samantha went to school by bus on Monday, find the probability that it wasraining.[3]In a randomly chosen school week, find the probability that Samantha goes to school bybus on exactly three days.[2]After n school days, the probability that Samantha goes to school by bus at least once isgreater than 0.95. Find the smallest value of n .[5]12EP11

Please do not write on this page.Answers written on this pagewill not be marked.12EP12