DHS P1

© DHS 2019 This question paper consists of 26 printed pages and 2 blank pages. Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 MATHEMATICS (Higher 2) 9758/01 Paper 1 September 2019 3h o u r s Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, index number and class on the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figur es, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. For teachers’ use: Qn Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total Score Max Score 4 5 6 7 7 7 8 9 1 0 1 3 1 2 1 2 1 0 0 www.KiasuExamPaper.com 165

2 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 1 A confectionary bakes 20 banana cakes, 50 chocolate cakes and 3 0 durian cakes every day. The total price of 1 banana cake, 1 chocolate cake and 1 durian cake is $29.50. On a particular day, at 7 pm, the confectionary has collected $730 from the sales of the cakes, and there were half the banana cakes, one-tenth of the chocolate cakes and one third of the durian cakes left. In order to sell as many cakes as possible, all cakes were discounted by 40 % from their respective selling price from 7 pm onwards. By closing time, all the cakes were so ld and the total revenue for the entire day was $880. Determine the selling price of each type of cake before discount. [4] www.KiasuExamPaper.com 166

3 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over 2( a ) Without using a calculator, solve 2 2.30 1 9 1x x d [3] (b) Solve 32(3) e 0 , ax bxab x where a and b are positive constants. [2] www.KiasuExamPaper.com 167

4 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 3 The points A and B have position vectors a and b with respect to origin O, where a and b are non-zero and non-parallel. (i) Given that B lies on the line segment AC such that 5BC P o ba , find the value of .P Hence find OC o in terms of a and .b [2] (ii) The point N is the midpoint of OC. The line segment AN meets OB at point E. Find the position vector of E.[ 4 ] www.KiasuExamPaper.com 168

5 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over www.KiasuExamPaper.com 169

6 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 4 The function f is defined as follows: 1f( ) ,xx a x b xa d where a is a positive constant. (i) Given that 1f exist, show that 1.bad [2] www.KiasuExamPaper.com 170

7 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over (ii) Given that 1a and 2b , find 1f( )x and the domain of 1f. [5] www.KiasuExamPaper.com 171

8 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 5( a ) Describe a sequence of two transformations that maps the graph of 2 ln 1 xy x §· ¨¸ ©¹ onto the graph of 2 21ln . 4 xy x §· ¨¸©¹ [2] (b) The diagram below shows the graph of f( ) .yx It has a maximum point at (1 ,1 )A and a minimum point at 1 4(1, ).B The graph has asymptotes 1 2 ,y 0x and 2.x y x O www.KiasuExamPaper.com 172

9 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over Sketch, on separate diagrams, the graphs of (i) ,f( 2 )yx [2] (ii) 1 ,f( )y x [3] stating clearly the equations of any asymptotes, coordinates of any points of intersection with both axes and the points corresponding to A and B. www.KiasuExamPaper.com 173

10 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 1 6 The sequence of complex numbers ^` nw are defined as follows >@ >@

2 1( 1 ) 1( 1 ) for . 1 ii i n nnwn n

 ] (i) Show that >@ > @ > @arg( ) arg(1 ( 1) a ,i) irg(1 arg(1 ( i ))1nwp n q nr n where p, q and r are constants to be determined. [1] Consider a related sequence ^`nz where 12 ,nnzw ww } the product of the first n terms of the above sequence. (ii) Use the method of differences to show that 1 4 .a ʌD U J L D U J > @r) ig n nzn [4] www.KiasuExamPaper.com 174