NJC_9758_2025_Prelim_P1

* © NJC 2025 NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 PRELIMINARY EXAMINATION Higher 2 NAME SUBJECT CLASS 2ma2 REGISTRATION NUMBER MATHEMATICS 9758/01 Paper 1 15 September 2025 3 hours Candidates answer on the Printed Answer Booklet. Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) READ THESE INSTRUCTIONS FIRST Write your name, class and registration number on the work you hand in. Write in dark blue or black pen. Answer all the questions. Write your answers on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. 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 must present the mathematical steps using mathematical notations and not calculator commands. You must show all necessary working clearly. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 5 printed pages.

2 © NJC 2025 1 Paul is helping his friends to convert their foreign currencies back to Singapore Dollars. The amounts of foreign currencies converted, and the total amount received in Singapore Dollars are shown in the following table. Alex Nicholas Palmer Maybelline US Dollar (USD) 150 250 425 a Japanese Yen (JPY) 5500 9500 1000 0 Chinese Yuan (CNY) 1000 2200 2000 1200 Total amount: Singapore Dollars (SGD) 419.30 797.20 913.10 568.40 However, he has forgotten the amount of US Dollar that Maybelline has passed to him. Assuming that, for each foreign currency, the exchange rate quoted for each of the friends is the same, calculate the value of a. [4] 2 Do not use a calculator in answering this question. (i) Find the values of z and w that satisfy the equations ( )1 i 2 2 4izw+ + =− + and 3 4 2izw− = + , expressing your answers in the form icd+ , where ,cd R . [4] (ii) Points W and Z represent w and z found in part (i). Find w z in the form i,pq+ where ,pq R . Hence, state the transformation that maps line segment OZ onto line segment OW. [2] 3 (i) On the same axes, sketch the graphs of =− − by xa and =−y x a , where a and b are positive constants and 1.ab State, in terms of a and b, the coordinates of the points where the curves cross the x- and y- axes. [3] (ii) Hence or otherwise, solve the inequality −  −− b xaxa . [4] 4 A curve has equation ( )fyx= , where ( ) 22f1 x q x= − − for 1q . State th