NHHS 2023 Prelim Math P1 (QP with Ans Key)

Page 1 of 30 Name ( ) Class PRELIMINARY EXAMINATION 2023 Subject : Mathematics Paper : 4052/01 Level : Secondary Four Express Date : 17 August 2023 Duration : 2 hours 15 min READ 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. If 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. 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. Gives answers in degrees to one decimal place. For π, use either your calculator value or 3.142. This paper consists of 26 printed pages and 2 blank pages. U P A NAN HUA HIGH SCHOOL For Examiner’s Use

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 2 of 30 Compound interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1  Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin  2 2 2 2 cosa b c bc A   Statistics Mean = f fx   Standard deviation = 22          f fx f fx

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 3 of 30 Answer all questions. 1 11 11 113 3 3 3x    Find the value of .x Answer x ………………………………….. [1] 2 Charles invested with a bank that pays interest of 3.5% per annum compounded half-yearly. He received $3500 as interest at the end of 3 years. Find the original amount that Charles invested. Give your answer to the nearest dollar. Answer $ …………………………………...... ... [2]

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 4 of 30 3 Ken draws this graph to show his annual electricity cost for his 5-room flat for year 2020, 2021 and 2022. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. …………………………… ……... … …………………………………………….......................... …………………………… ……... … …………………………………………….......................... …………………………… ……... … …………………………………………….......................... ……………………………………………………………………………………………… [2] 2022 Year Cost of electricity ($) 2021 2020 4800 ANNUAL ELECTRICITY BILL

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 5 of 30 4 The marked price of a 65-inch Ultra 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 Mr Lim pays for the television. Answer $ ………………………………...... [2] 5 The table shows the time, to the nearest hours, taken by 12 students to complete a project. Time t (hours) Frequency 30 35t  1 35 40t  2 40 45t  5 45 50t  4 (a) Calculate an estimate for the mean time taken. Answer …………………………… ……. hours [1] (b) Calculate an estimate for the standard deviation of the time taken. Answer …………………………… ……. hours [1]

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 6 of 30 6 The average mass of haemoglobin in a red blood cell is about 31 picograms. (a) Express 31 picograms in grams, giving your answer in standard form. [1 picogram = 1210 grams] Answer …………………………… …….. g [1] (b) There are 65 10 red blood cells in 1 cubic millimetre of blood. Calculate the mass, in grams, of haemoglobin in 1 cubic millimetre of blood. Give your answer in standard form. Answer …………………………… …….. g [1]

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 7 of 30 7 In the diagram, C is the point (0, 5) and A is a point on the y-axis. The line AB meets the horizontal line through C at point B. The equation of line AB is 2 9.y x  (a) State the equation of the line parallel to line AB, passing through (0, 7). Answer …………………………… …….. [1] (b) Find the coordinates of point A and point B. Answer A (……………… , ………… ….. ) B (……………… , ………… ….. ) [2] ( 0 , 5 ) O O

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 8 of 30 8 The ratio of the 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 Q. Find the original number of employees in company P. Answer …..…………………………… …… [3]

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 9 of 30 9 Straight lines AC, AD, BE, BD, CE intersect to form the figure in the diagram. Find the value of x. Answer x = …………..…………………… [2]

Nan Hua High School Preliminary Examination 2023 Mathematics 4052/01 Page 10 of 30 10 (a) Factorise completely 3 1 3 .fg g f   Answer …………………………… ……...... [2] (b) Factorise completely 244 11 .k Answer …………………………… ……...... [2] 11 Make x the subject of the formula 2 .3 x yw x y   Answer …………………………… ……...... [3]