SOTA 2023 Prelim MAA HL Paper 3

Yr6/5/MATAA/HP3/Aug2023 4 pages © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher Level Paper 3 Preliminary Examinations Monday 28 August 2023 1 hour Instructions to candidates • Do not open this examination paper until instructed to do so. • A graphic display calculator is required for this paper. • Answer all questions on the answer sheets provided. Write your name and class on each answer sheet, and attach them to this examination paper. • Unless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures. • A clean copy of the mathematics: analysis and approaches formula booklet is required for this paper. • The maximum mark for this examination paper is [55 marks]. Question Marks 1 2 Name: ____________________________________ Class: ____________________________________ Index: ____________________________________ 55

Yr6/5/MATAA/HP3/Aug2023 - 2 - Answer all questions on the answer sheets 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 mark: 27] This question asks you to work with parametric equations. These are types of equations that employs an independent variable called a parameter (here denoted by ) and in which dependent variables,and, are defined as continuous functions of the parameter and are not dependent on another existing variable. Figure 1 shows the section ABCD of a mound at a skateboard park. Figure 1 The section from B to C is part of the curve OBCE with parametric equations. , for and where is a constant. (a) Find in terms of, (i) the length of the straight-line OE. (ii) the maximum height of the mound. [4] (b) (i) Find and . (ii) Hence find in terms of . [4] The straight-line sections AB and CD are inclined at 30° to the horizontal, and are tangents to the curve at B and C respectively. BC is parallel to the axis. BF is parallel to the axis. (c) (i) Show that at the point B the parameter satisfies the equation (ii) Find the value of that is a solution of this equation in degrees. (iii) Show that . (iv) Hence, find OF in terms of . [5] (This question continues on the following page) qxy ( )sinxa qq=- ( )1c o sya q=- 02qp££0a>aad d x q d d y q d d y x qx-y-( )1sin 1 cos 3 qq=- q1.5BF a=a Diagram not to scale.

Yr6/5/MATAA/HP3/Aug2023 Turn over - 3 - (Question 1 continued) (d) Find BC and AF in terms o