NYGH 2020-S4EOY-Adv Math with ans

Class Register Number Name 南洋女子中学校 NANYANG GIRLS' HIGH SCHOOL End-Of-Year Examination 2020 Secondary 4 ADVANCED MATHEMATICS 1 hour Tuesday 6 October 2020 1215 - 1315 READ THESE INSTRUCTIONS FIRST 1. Write your name, register number and class on all the work you hand in. 2. Answer all questions. 3. Write your answers and working on the separate writing paper provided, unless otherwise stated. 4. Write in dark blue or black ink on both sides of the paper. 5. You may use an HB pencil for any diagrams or graphs. 6. Do not use staples, paper clips, glue or correction tape/fluid. 7. Omission of essential working will result in loss of marks. 8. The use of an electronic calculator is expected, where appropriate. 9. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 10. At the end of the examination, fasten all your work securely together. 11. The number of marks is given in brackets [ ] at the end of each question or part question. 12. The total number of marks for this paper is 40. Setter: L. Lioe This document consists of 3 printed pages, including this cover page. NANYANG GIRLS' HIGH SCHOOL [ Turn over

2 1 Expand 4+2x()−12 as a series of descending powers of x up to and including the term in x−72 and state the range of values of x for which the expansion is valid. [4] 2 There are 5 male and 4 female job applicants waiting for their turn in a job interview. Two particular males are Andy and Ben, and one particular female is Mandy. They sit in a row of 9 seats in the waiting room. Find the number of ways of arranging them in each of the following cases: (i) there is no restriction, [1] (ii) Mandy occupies the centre seat with Andy on her left and Ben on her right (need not be adjacent), [2] (iii) the female and male applicants alternate. [2] 3 (a) The sum of the first three terms of an arithmetic progression is 45 and the 40th term of the progression is 91. Find (i) the first term of the series and the common difference, [3] (ii) the sum of the terms from the 15th to the 100th terms. [2] (b) In a geometric progression, the first term is 8 and the sixth term is −14. Find (i) the sum Sn of the first n terms of the progression, [2] (ii) the sum to infinity S of the progression, [1] (iii) the smallest prime number n such that Sn−S<0.01. [2] 4 Find the equation of the normal to the curve at the point . [6] 5 (a) Find x3∫lnx dx. [4] (b) Evaluate . [4] xy+y2=2x(1,−2)3x1+4x2dx03∫

3 6 Find the volume generated when the area bounded by the curve and the lines and is rotated through one revolution about the y-axis. Give your answer in exact form. [3] 7 An insurance agent spends a period of successive days selling a particular insurance policy to his clients. If he manages to sell the policy on any given day, the probability that he successfully sells the policy on the following day is 0.8. If he fails to sell the policy on any given day, the probability of success on the next day is 0.3. If he successfully sells a policy on Tuesday, calculate the probability that (i) he successfully sells a policy on Thursday, [2] (ii) he successfully sells a policy on Friday, given that he did not manage to sell it on Wednesday. [2] END OF PAPER y=lnxy=1x=1

4 Answer Key 1 12x−12−12x−32+322x−52−522x−72+... The expansion is valid for |x| >2. 2i 9! =362880 2ii 1×4×4×6!=11520 2iii 5!×4!=2880 3ai So the first term is a=13 and the difference is d = 2. 3aii Sum of terms=10836 3bi Sn=1631−−12⎛⎝⎜⎞⎠⎟n⎛⎝⎜⎜⎞⎠⎟⎟ 3bii S=163 3biii The smallest prime value of n is 11. 4 y=34x−114 5a 34x43lnx−916x43+c, c is arbitrary constant 5b 143732−1⎡⎣⎢⎤⎦⎥ 6 π(e2−3)2 cubic units 7i 0.7 7ii 0.45