June 2007 Question Paper

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6. (a) Express 3 sin x + 2 cos x in the form R sin (x + α) where R > 0 and 0 < α < 2π .(4)(b) Hence find the greatest value of (3 sin x + 2 cos x) 4 .(2)(c) Solve, for 0 < x < 2π, the equation3 sin x + 2 cos x = 1,giving your answers to 3 decimal places.(5)7. (a) Prove thatsinθ+cosθcosθ= 2 cosec 2θ, θ ≠ 90n°.sinθ(4)(b) Sketch the graph of y = 2 cosec 2θ for 0° < θ < 360°.(2)(c) Solve, for 0° < θ < 360°, the equationsinθ+cosθcosθ= 3sinθgiving your answers to 1 decimal place.(6)N26109A 4
8. The amount of a certain type of drug in the bloodstream t hours after it has been taken is given bythe formulax =- tD 81where x is the amount of the drug in the bloodstream in milligrams and D is the dose given inmilligrams.A dose of 10 mg of the drug is given.e ,(a) Find the amount of the drug in the bloodstream 5 hours after the dose is given.Give your answer in mg to 3 decimal places.A second dose of 10 mg is given after 5 hours.(2)(b) Show that the amount of the drug in the bloodstream 1 hour after the second dose is13.549 mg to 3 decimal places.(2)No more doses of the drug are given. At time T hours after the second dose is given, the amountof the drug in the bloodstream is 3 mg.(c) Find the value of T.(3)ENDTOTAL FOR PAPER: 75 MARKSN26109A 5
Page 1 and 2: Paper Reference(s)6665/01Edexcel GC
Page 3: 4. f(x) = - x 3 + 3x 2 - 1.(a) Show

June 2007 Question Paper

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