Jeju North London Collegiate School

KOR 123

Answer all questions in the answer booklet provided. Please start each question on a new page. Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Solutions found from a graphic display calculator should be supported by suitable working. For example, 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. 1. [Maximum marks: 31] This question considers how to calculate volumes of revolution using related rates of change. ai) Given that x=( 4 θ+9) 1 2 and y=6 e 1 2 x+1 find expression for dx dθ and dy dx [4] ii) Hence find dy dθ when θ=4 correct to 3 significant figures. [3] The graph shows the curve C with parametric equations x=tanθ and y=sinθ for 0≤θ≤ π 2 . Point P lies on the curve C with coordinates (√3 , √3 2 ). bi) Find the exact value of θ at P. [2] The line l is normal to the curve C at the point P, and cuts the x-axis at Q. ii) Show that the equation of l is y=−8 x+ 17 √3 2 [5] 4 iii) Hence find the exact c