YIJC_9758_2024_Promo

This document consists of 5 printed pages and 1 blank page. [Turn Over YISHUN INNOVA JUNIOR COLLEGE JC 1 PROMOTIONAL EXAMINATION Higher 2 CANDIDATE NAME CG MATHEMATICS Paper 1 Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) 9758/01 30 September 2024 3 hours READ THESE INSTRUCTIONS FIRST Write your CG, index number and name on the work you hand in. Answer all 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. The total number of marks for this paper is 100.

2 ©YIJC 9758/01/JC1PE/24 1 A concert sells tickets under three different age categories: ‘Senior Citizen’, ‘Adult’ and ‘Child’. Three groups of people A, B and C went to the concert on 3 different days. For Group A, all tickets were purchased at the original price s. For Group B, ‘Senior Citizen’ tickets were purchased at a 20% discount, while tickets under the other two categories were purchased at the original prices. For Group C, ‘Child’ tickets were purchased at half the ‘Adult’ original price, while ‘Senior Citizen’ and ‘Adult’ tickets were purchased at the original prices. The numbers in each age category for each group and the total price of the tickets for each group, are given in the following table. Group Senior Citizen Adult Child Total Price A 5 12 6 $2440 B 15 10 5 $2660 C 8 10 12 $2560 (a) Express this information as 3 linear equations and hence find the original price of a ticket in each of the age categories. [3] (b) The Lee family, consisting of 2 senior citizens, 2 adults a nd 3 children , went to the concert. Assuming their tickets were purchased at the original prices, find the total price they paid. [1] 2 Given that ( )23 1 2 14 n r nrn = =+ , find an eppression in terss of n for ( ) 2 1 34 n rn rn =+ + . eeave oour answer in fullo factorised fors. [4] 3 (a) By first expressing 2 23xx−+ in completed square form, show that 2 23xx−+ is positive for all real values of x . [2] (b) Without the use of a calculator, solve the inequality ( )( )2 2 2 3 1 0 2 x x x xx − + −  −− . [3] (c) Hence solve the inequality ( )( )2 3 1 0 2 x x x xx − + −  −−