2024 JC2 H2 Math prelim - EJC

Error! Reference source not found. EUNOIA JUNIOR COLLEGE JC2 Preliminary Examination 2024 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CIVICS GROUP INDEX NO. MATHEMATICS Paper 1 9758/01 09 September 2024 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civics group and index number 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. DO NOT WRITE ON ANY BARCODES. Answer all questions. Write your answers in the spaces provided in the Question Paper. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. 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. This document consists of 22 printed pages and 2 blank page(s). Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total

1 The sum of the digits of a certain three-digit number is 15. The sum of the digit in the tens placing and twice the digit in the hundreds placing is equal to the digit in the units placing. If the digits are reversed, the new number is 21 more than 5 times the old number. What is the number? [4] 2 Do not use a calculator in answering this question. Find the complex numbers z and w which satisfy the following simultaneous equations 2 5i,zw−= 3i * 5.zw− =− Give your answers in the form iab+ , where a and b are real numbers. [5] 3 The curve with equation 1yp xq=− + , where p and q are constants, is transformed by a reflection in the x-axis, followed by a translation of 3 units in the negative y-direction, followed by a stretch of scale factor 4 parallel to the x-axis. A point on the curve 1yp xq=− + has coordinates 3 ,34 −− . (a) Find the resulting coordinates of this point after it undergoes the same sequence of transformations. [1] The resulting curve has asymptotes 1x=− and 2y= . (b) Find the values of p and q. [5] 4 A curve C has equation 2 25 114 1 xxy x ++= + . (a) Sketch C, indicating on the diagram the equations of any asymptotes, and the coordinates of any turning points and any axial intercepts. [4] A curve D has parametric equations 23sin 2 1x =− , 23 23cos2y =+ for 22  −   . (b) Find the cartesian equation of curve D. [2] (c) Hence, on the same diagram as in part (a), sketc