Exam (elaborations) Mathematics International Advanced Subsidiary/Adva

• Use black ink or ball-point pen. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). • Fill in the boxes at the top of this page with your name, centre number and candidate number. • Answer all questions and ensure that your answers to parts of questions are clearly labelled. • Answer the questions in the spaces provided – there may be more space than you need. • You should show sufficient working to make your methods clear. Answers without working may not gain full credit. • Inexact answers should be given to three significant figures unless otherwise stated. Information • A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. • There are 9 questions in this question paper. The total mark for this paper is 75. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice • Read each question carefully before you start to answer it. • Try to answer every question. • Check your answers if you have time at the end. • If you change your mind about an answer, cross it out and put your new answer and any working underneath. 2 *P66387A0232* Leave blank 1. A curve has equation y x x x = − 2 5 − + x 3 2 7 0 3 2 (a) Find, in simplest form, d d y x (3) The point P lies on the curve and has x coordinate 1 2 (b) Find an equation of the normal to the curve at P, writing your answer in the form ax + by + c = 0, where a, b and c are integers to be found. (5) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 3 *P66387A0332* Turn over Leave blank Question 1 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q1 (Total 8 marks) 4 *P66387A0432* Leave blank 2. A tree was planted. Exactly 3 years after it was planted, the height of the tree was 2m. Exactly 5 years after it was planted, the height of the tree was 2.4m. Given that the height, H metres, of the tree, t years after it was planted, can be modelled by the equation H3 = pt 2 + q where p and q are constants, (a) find, to 3 significant figures where necessary, the value of p and the value of q. (4) Exactly T years after the tree was planted, its height was 5m. (b) Find the value of T according to the model, giving your answer to one decimal place