2024 TPSS EMATH P1 PRELIM QP

This document consists of 20 printed pages TAMPINES SECONDARY SCHOOL Secondary Four Express / Five Normal Academic Preliminary Examination 2024 NAME CLASS REGISTER NUMBER MATHEMATICS 4052/01 Paper 1 22 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST For Examiner’s Use Write your name, class and register number 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. 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. For π, 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 number of marks for this paper is 90. [Turn over O

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = h r2 3 1π Volume of a sphere = 3 3 4 rπ Area of a triangle ABC = C absin2 1 Arc length = rθ , where θ is in radians Sector area = 21 2 r θ , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = f fx Σ Σ Standard deviation = 22       Σ Σ−Σ Σ f fx f fx

3 Answer all the questions. 1 Find the largest prime number that satisfies the inequality 38 282 x− < . Answer ....………………………….…….. [2] 2 Expand and simplify 3( 5 )a ab−− . Answer ...….……………………….…….. [1] 3 Factorise 624 100xy− completely. Answer …………………………………… [2] 4 (a) Sketch the graph of ( )23 x y= , indicating the points of intersection between the axes, if any. [1] (b) State a possible equation for the graph shown below. Answer …………………………………… [1] x y O -4 -2

4 5 At the end of 2023 there were 27000 rhinos living in the wild. The number of rhinos is expected to increase exponentially by 3% each year. Calculate the number of rhinos expected to be living in the wild at the end of 2027. Give your answer correct to the nearest ten thousand. Answer …………………………………… [2] 6 The table below shows the favourite language that each of 80 stude