9758 H2 Mathematics EJC Practice Paper

9758 H2 Mathematics ~~ JCT Revision Package 2021 ~I~ Practice Papers ~Ur'7 Instructions : After completing your topical revi sion, complete Practice Papers A to E under time constraint of 2.5 hours each . Practice Paper A (2.5 hours, 80 marks) 1 A musical was held in a conf crcncc hall ~t has a maximum capacity of 800 scats. Three categories of tickets Cat A, Cat Band Cat C were sold at $60, $45 and SIS respectively . It was known that 720 tickets were sold and a total of $19200 was collected from the ticket sales . Furthermore, the combined number of Cat A and Cat B tickets sold was half of the number of Cat C tickets sold. For each category of tickets, find the amount of money collected from their sales . [4] 2 Jason is considering to invest $50,000 in a fund at the end of 2018 . The fund will credit an amount of $300 at the end of 2019 . At the end of each subsequent year, the amount credited increases by $150 as compared to the amount credited in the previous year . (l) Find the amount of money that will be credited in the fund at the end of 2022. [2] (iJ) Given that the money in Jason's account first exceeds $70,000 at the end of year N, find the value of N. [4] 3 ex2 - l2ex - 30 . · The cwve Chas equation y = - ---- , where c 1s the exponcnttal constant. x-5 (i) Sketch C, indicating clearly the equations of the asymptotes and the coordinates of any points of intersection with the axes. [ 4] (ii) State the exact coordinates of the point of intersection of the asymptotes . [ 1] (iii) Deduce the exact range of values of m such that the equation ex2 -12ex-30 2e - - - ---,-- =m--- (x- 5)2 x - 5 has no real root. (21 4 The sum of the f arst n terms of a series is given by 20 - S ( t, } (i) Show that the series is a geometric series. (ii) Explain why this series converges and find its sum to infinity . [3] [2] A new geometric series is formed by using the even-numbered terms (i.e. u2 , u, ,u6 , ... ) of the above seri es. Find the sum of the first 20 terms of thi s new series . [3] ] 7

I I euno1a JUNIOlt COLLIGI (a) Engraving is the process of incisin a des. serial numbers arc commonly en J ~gn or text onto a surface. For instance, identify them individually. Today grav onto nems such as machine parts, in order to the job required a mechanical linkage kn computers arc used for engraving, but in the past own as a pantograph. A A pollllcr that conlrOls tbr cngravw,g bit mova Oliff lhe SIC!Kil. The diagram shows a simple pantograph, in the x-y plane, consisting of two pairs of parallel rigid rods, joined together at four joints. The rods are free to rotate at these joints. One end of the pantograph is fixed at the origin O represented by the point (0, 0). Points ( x, y) are defined relative to the fixed point 0. A pointer is attached to A, while the engraving bit is attached to B. The engraver controls the pantograph by moving the pointer over a stencil, which then causes the engraving bit to trace out a copy o