Nan-Hua-High-School-E-Math-Prelim-2023

BP - 209 Name ( ) &++& NAN HUA HIGH SCHOOL PRELIMINARY EXAMINATION 2023 *.+++ Subject Paper Level Date Duration Mathematics 4052t01 Secondary Four Express 17 August 2023 2 hours 15 min REAO THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [] at the end of each question or part question. lf working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. lf the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Gives answers in degrees to one decimal place. For n, use either your calculator value or 3.142. For Examine/s Use U P A This paper consists of286 printed pages and 2 blank pages PartnerlnLeaming 207 Class Page I of 28

BP-211 Nan Hua High School Preliminary Examination 2023 Mathematics 405201 Answer all questions. 1 3' - 3tt +3" +3" Find the value of x. Answer x=.... tl] 2 Charles invested with a bank that pays interest of 3.5% per annum compounded half- yearly. He received 53500 as interest at the end of 3 years. Find the original amount that Charles invested. Give your answer to the nearest dollar. Answer S Izt PartnerlnLeaming 209 Page 3 of28

BP -?12 Nan Hua High School P rel im i n ary Exam i natio n 2023 Mathematics 4052f01 3 Ken draws this graph to show his annual electricity cost for his S-room flat for year 2020, 2021 and2022. I\\1-..\I ELE CTRICITY BILL 4800 Cost of electricity ($) 2020 2021 2422 Year State one aspect ofthe graph that may be misleading and explain how this may lead to a misinterpretation of the graph, t2l PartnerlnLeaming 210 Page 4 of28

BP-213 Nan Hua High School Preliminary Examination 2023 Mathematics 4052J01 4 The marked price ofa 65-inch lIltra HD 4K TV is $6000. Mr Lim buys the TV on hire purchase scheme with down payment of 20% on the marked price. He then pays monthly instalments over 4 years at a simple interest rate of 1.37% per annum. Calculate the total amount that Ivft Lim pays for the television. Awwer $ 5 The table shows the time, to the nearest hours, taken by 12 students to complete a project. Time I (hours) Frequency 30<r<35 I 35<t <40 2 40<t<45 5 45<t<50 4 (a) Calculate an estimate for the mean time taken Answer t2) (b) Calculate an estimate for the standard deviation ofthe time taken. Answer hows [] hours [1] PartnerlnLeaming 211 Page 5 of 28

BP-214 Nan Hua High School Preli m in ary Exam ination 2023 Mathematics 405201 6 The average mass ofhaemoglobin in a red blood cell is about 3l picograms. (a) Express 3l picograms in grams, giving your answer in standard form. I picogram = l0-''z grams] Answer (b) There are 5 x 106 red blood cells in I cubic millimetre ofblood. Calculate the mass, in grams, of haemoglobin in 1 cubic millimetre of blood. Give your answer in standard form. Answer c tll c tll PartnerlnLeaming 212 Page 6 of28

BP-215 Nan Hua High School Preliminary Exam ination 2023 Mathematics 405201 7 In the diagram, C is the point (0, -5) and I is a point on the y-axis. The line l-B meets the horizontal line through C at point B. The equation of line lB is y =2x +9. v A y:2x +9 I c(0.-5) (a) State the equation of the line parallel to line lB, passing through (0,7), Answer (b) Find the coordinates of point I and point B. Answer A ( B( B tll ) t2l PartnerlnLeaming 2.13 Page 7 of 28 , '..'...'...'...'. )

BP-216 Nan Hua High School Preliminary Examination 2023 Mathematics 405201 8 The ratio ofthe number of employees in company P to that in company Q was 3: 4 8 employees left company Q to join company P. The number of employees in company P now is 4 more than company p. Find the original number of employees in company P. Answer t3l PartnerlnLeaming 214 Page 8 of28

BP -217 Nan Hua High School Preliminary Examination 2023 Mathematics 4052J01 9 E B t) Straight lines lC, AD, BE, BD, CE intersect to form the figure in the diagram. Find the value of .r. Answer r = C .4 PartnerlnLeaming 215 Page 9 of28 t2l /\ I"

BP" 21 8 Nan Hua High School Preliminary Examin ation 2023 Mathematics 405201 l0 (a) Factorise completely 3fg+l-g-3f . (b) Factorise completely 44-11k2. Answer Answer t2) t2l t3l I I Make .x the subject of the formula w = 22 . 3x-y Answer PartnerlnLeaming 216 Page 10 of28

BP- 21 I Nan Hua High School P reli m i n ary Exam in ation 2023 Mathematics 4052J01 t2 (' ti I L) In the diagram,lBC is a tangent to the circle. The line lD cuts the circle at E. Aagle BAD = 4l'and angle ,4 BD = 113" . Explain why ED is not a diameter of the circle. Give reasons for each step ofyour working. Page I I of28 t3l PartnerlnLeaming 217 I \