VJC_9758_2024_Promo_Qns

2024/VJC/Math Dept VICTORIA JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION H2 MATHEMATICS 9758 QUESTION PAPER 3 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (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. The total number of marks for this paper is 100. This document consists of 5 printed pages and 3 blank pages.

2024/VJC/Math Dept 1 A small garment shop produces dresses, blouses and skirts. The production process includes cutting, sewing and packaging. The table below shows the time in mi nutes required to produce each piece of garment. The total time spent on cutting, sewing and packaging are 3150, 4300 and 480 minutes per week respectively. Garment Time required (min) Cutting Sewing Packaging Dress 45 70 8 Blouse 50 60 6 Skirt 20 25 3 Write down and solve equations to find the number of pieces of each garment the shop produces each week. [4] 2 (a) Without using a calculator, solve the inequality 2 2 23 1 0 2xx xx   . [3] (b) Hence, find the set of values of x for which 2 2 2e 3e 10 2e+ e xx xx   . [2] 3 The diagram shows the curve f( )yx which cuts the axes at 0,Aa  and  ,0Bb , where a and b are positive constants. (a) State, if it is possible to do so, the coordinates of the points where the following curves cut the axes. (i) 1f( )yx  [1] (ii) f( 2 )yx [1] (iii) f( 3 )yx [1] (b) Sketch the curve 1 f( )y x , stating the equations of any asymptot es and the coordinates of the point where 1 f( )y x crosses the axes. [3] x y O

2024/VJC/Math Dept 4 (a) The sum, nS , of the first n terms of a sequence 123, , , . . .uuu is given by 1 2 375 5 n n nS   . Show that 1 3 5 n nuk    , where k is a constant to be determined. Find S . [4] (b) Another sequence of numbers 123, , , . . .vvv is such that 1 2 21 n i i nv n   . Find the exact value of 11 i i v    . [3] 5 A curve C has equation 223241xx y y . (a) Show that d3 .d4 yx y x yx   [2] (b) Find the acute angle between the t