2024 4NA Prelim Peirce Secondary school P2

ClassRegister No. Candidate Name PEIRCE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 NORMAL ACADEMIC MATHEMATICS 4045/02 Paper 2 2 August 2024 2 hours Additional Materials: Plain Paper (for rough work) INSTRUCTIONS TO CANDIDATES Candidates answer on the Question Paper. Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions from Section A and only one question from Section B. 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 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. Give answers in degrees to one decimal place. Forπ, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. For Examiner’s Use PARENT’S SIGNATURE Total This paper consists of 23 printed pages and 1 blank page. Setter: Mr Goh [TURN OVER Mathematical Formulae Compound interest

Total amount = (1)100nrP+ Mensuration Curved Surface area of a cone = prl Surface area of a sphere = 24rπV olume of a cone = 213rhπV olume of a sphere = 343rπArea of triangle ABC = 1sin2abCArc length = rθ, where θ is in radians Sector area = 212rθ, where θ is in radians Trigonometry sinsinsinabcABC== 2222cosabcbcA=+− Statistics Mean = fxf∑∑Standard deviation = 22fxfxff⎛⎞∑∑−⎜⎟∑∑⎝⎠ Section A (62 marks) Answer all the questions in this section. 1 Factorise the following completely. (a) 2253rr+− Answer …………………………………… [2] (b) 5102axaybxby+−−

Answer ……………………………………………………… [2] (c) 23649y− Answer ……………………………………………………… [ 1] 2 Mdm Lee wants to invest $150 000 with an investment company over a duration of 15 years. There are 2 options, A and B. Option A Mdm Lee will immediately receive a one-time payout of $40000. Subsequently, for the next 15 years, Mdm Lee will receive a yearly payout of $12000. Option B The investment company will invest $150 000 based on 3.8% per annum compounded yearly. Mdm Lee will receive the total investment after 15 years. Which option should Mdm Lee choose ? Show all workings clearly. Answer [ 3] 3 (a) Johnny took the 1400 hrs train from Alpha city to Oasis. Johnny arrived in Oasis at 1840 hrs and the average speed of the train is 200 km/h. Calculate the distance of the train ride.

Answer ……………………………………………………… km [2] (b) Janelle cycled for 40 km for 6 hours. She rested for 30 minutes before continuing her journey at an average speed of 50 km/h