MI_9758_2024_Promo_PU1

© Millennia Institute 9758/01/PU1/EOY/24 [Turn over 2024 End-of-Year Examination Pre-University 1 MATHEMATICS 9758/01 Paper 1 14 October 2024 QUESTION PAPER 2 hours 15 minutes 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 are required to 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 75. This document consists of 6 printed pages. H CANDIDATE NAME CLASS ADMISSION NUMBER

2 © Millennia Institute 9758/01/PU1/EOY/24 1 The sum, nS , of the first n terms of the sequence 1 2 3, , , ...u u u is given by 2 nS n kn=+ , where k is a non-zero constant. (i) Find nu in terms of n and k. [2] (ii) Hence determine if the sequence is an arithmetic progression. [2] 2 (i) Without using a calculator, solve the inequality 2 32 24 xx x −+ + . [4] (ii) Hence solve the inequality 2 32 24 xx x ++ − . [2] 3 (i) A curve C has equation 32y ax bx cx d= + + + , where a, b, c and d are constants. The curve C intersects the y-axis at the point (0, 7) and passes through the points ( 2, 11)−− , (1, 1) and (3, 19) . Find the values of a, b, c and d. [4] (ii) C first undergoes a reflection about the y-axis and subsequently a translation of 1 unit in the positive y-direction. Find the equation of the resulting curve. [2] 4 Referred to the origin O, the points A, B and C have position vectors a, b and c. C lies on AB such that : 1:3AC AB = . (i) Find c in terms of a and b. [2] (ii) Show that the area of triangle OAC is given by k ab , where k is a constant to be determined. [2] It is now given that a and b are unit vectors. (iii) Using the result in part (i), find the value of ( )2 −a b c . [3]

3 © Millennia Institute 9758/01/PU1/EOY/24 [Turn over 5 (a) Describe a sequence of 2 transformations that transforms the curve C with equation 2 2 19 x y+= onto the curve D with equation ( ) 2 221xy− + = . [2] (b) The diagram shows the curve with equation f ( )yx= . The curve passes through the