CJC Promos 2025 Question Paper

9758/01/J1PROMO/2025 [Turn Over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC1 Promotional Examination CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 9758/01 Paper 1 8 Oct 2025 3 hours Additional Materials: Printed Answer Booklet List of Formulae (MF27) READ THESE INSTRUCTIONS FIRST 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. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 7 printed pages and 1 blank page.

2 9758/01/J1PROMO/2025 1 A sequence nT is given by ( ) 2ln a nT n bn c= + + for n + . The first three terms of the sequence are 9, 17.306 and 31.901. (a) Find the values of a, b and c, correct to the nearest integers. [3] (b) Using the integer values found in part (a), find the sum of the first hundred terms of nT . [1] 2 Differentiate 1 2 tan 1 x x −   − with respect to x. You should simplify your answer as a single fraction in its simplest form. [4] 3 Without using a calculator, solve the inequality ( )( ) 3 2 5 2 2 x x x x− + − . [3] Hence, solve the following inequalities. (a) ( )( ) e3 e2 5e 2 2 e x x xx− +− [2] (b) ( )( ) 12 4 5 4 4 x x x x − + − [2] 4 Aenicillin, a type of bacteria, is grown in a petri dish . Its population doubles every six hours. Denoting the amount of Aenicillin at the beginning of the first day as 0x , (a) write down a recurrence relation for nx , n ≥ 1, the amount of Aenicillin in the petri dish at the end of nth day, [1] (b) find nx , expressing your answer in the form of f ( ), 1nx n n= . [1] The growth rate of another bacteria, Benicillin, is known to follow the recurrence relation 1 ,1nnu u n n−= +  where nu is the amount of Benicillin at the end of nth day. The amount of Benicillin in the petri dish at the beginning of the first day, 0,u is 1 unit. (c) Write down 10uu− , 21uu− and 32uu− . Hence find a quadratic expression for ( ) ( ) ( ) ( )1 0 2 1 1 2 1 ... n n n nu u u u u u u u − − −− + − + + − + − in terms of n. [3] (d) Show that ( )10 1 n r r n r u u u u− = − = − . Using your results in part (c), find nu expressing your answer in the form of f ( ), 1nu n n=