EJC_9758_2024_Promo

Error! Reference source not found. EUNOIA JUNIOR COLLEGE JC1 Promotional Examination 2024 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CIVICS GROUP INDEX NO. MATHEMATICS Paper 1 9758/01 07 October 2024 3 hours Additional Materials: Printed Answer Booklet List of Formulae (MF27) READ THESE INSTRUCTIONS FIRST 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. This document consists of 7 printed pages and 1 blank page.

Error! Reference source not found. 1 A small furniture factory produces standardised stools, chairs and tables using both metal and plastic as raw materials. The table below shows the amount of each raw material required to make one unit of each type of furniture. Furniture Item Amount of raw material needed (in kg) Metal Plastic Stool 1 2 Chair 4 2 Table 10 4 Given 68 kg of metal and 32 kg of plastic, determine the number of each type of furniture that could be produced such that all three types of furniture are made, and all the raw materials are fully utilised. [4] 2 Solve the inequality 2 531 2 xx +− −  . [3] 3 The graph of ( )fyx= is given below. It has one vertical asymptote 1x=− and one oblique asymptote 4yx=− . It cuts the x-axis at 0x= and 3x= . It has turning points at ( )3, 9−− and ( )1, 1− . On separate diagrams, s ketch the graph s of the following, stating the equations of any asymptotes, and indicating any axial intercepts and turning points. (a) 1 f ( )y x= , [3] (b) f ( )yx = . [3] x y O 3

Error! Reference source not found. 4 In a triangle ABC, 5 cmAB= and 4 cmAC= . If angle BAC is decreasing at a constant rate of 0.2 radians per second, find the rate of change of the length BC at the instant where π 3BAC= radians, giving your answer in centimetres per second to 3 significant figures. [5] 5 a and b are vectors such that 2=a and 6=b . The angle between a and b is 5π 6 . (a) Find the exact length of projection of a onto b. [2] (b) By considering ( ) ( )3 2 3 2++a b . a b , find the exact value of 32+ab . [4] 6 (a) Write down the derivative of sin n with respect to  , where n is a constant