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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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turn over

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...