Ib Pase Paper, Maths Hl

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M10/5/MATHL/HP2/ENG/TZ1/XX

22107204

mathematics higher level PaPer 2 Thursday 6 May 2010 (morning) 2 hours iNsTrucTioNs To cANdidATEs  Write your session number in the boxes above.  not open this examination paper until instructed to do so. do  graphic display calculator is required for this paper. A  section A: answer all of section A in the spaces provided.  section B: answer all of section B on the answer sheets provided. Write your session number on each answer sheet, and attach them to this examination paper and your cover sheet using the tag provided.  At the end of the examination, indicate the number of sheets used in the appropriate box on your cover sheet.  unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. 0 0 candidate session number

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14 pages © international Baccalaureate organization 2010

0114

–2–

M10/5/MATHL/HP2/ENG/TZ1/XX

Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. 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 given for a correct method, provided this is shown by written working. You are therefore advised to show all working. Section a Answer all the questions in the spaces provided. Working may be continued below the lines, if necessary. 1. [Maximum mark: 4] The graph below shows y = a cos (bx) + c . y

4 2 x

–2

0 –2 –4

2

4

6

Find the value of a , the value of b and the value of c . .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... 2210-7204

0214

–3– 2. [Maximum mark: 5] The system of equations 2 x − y + 3z = 2 3 x + y + 2 z = −2 − x + 2 y + az = b

M10/5/MATHL/HP2/ENG/TZ1/XX

is known to have more than one solution. Find the value of a and the value of b . .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... .................................................................... ....................................................................

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0314

–4– 3. [Maximum mark: 6]

M10/5/MATHL/HP2/ENG/TZ1/XX

In the right circular cone below, O is the centre of the base which has radius 6 cm. The points B and C are on the circumference of the base of the cone. The height AO  of the cone is 8 cm and the angle BOC is 60 . A

diagram not to scale

O B
 Calculate the size of the angle BAC .

C...
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