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 students studies. Language Frequency French 20 Japanese 42 Thai 18 Complete the pie chart to show this information. [2]

5 7 Use a ruler and compasses only for this question. You must show all your construction arcs. Line L is the perpendicular bisector of .FG Construct a circle that passes through the points F , G and .H [2]

6 8 (a) By using prime factorization, explain why 2420 is not a perfect cube. Answer …………………………………………………………………………………………... …………………………………………………………………………………………………… …………………………………………………………………………………………………… [2] (b) When written as a product of its prime factors, the lowest common multiple of two numbers is 2420 and the highest common factor of these two numbers is 110. Given that neither of these two numbers is 2420, find the value of these two numbers. Answer ……..…….… and ……….……… [2] 9 (a) Simplify 1 15 3 12 27 8 x y −   . Answer …………………………………… [2] (b) (i) Factorize 42 8xy y x−+− completely. Answer …………………………………… [2] (ii) Hence solve the equation 42 871xy y x−+− = . Answer x=….….....…. , y=….…....…… [1]

7 10 Susan draws the diagram below to show her annual expenditure on flight tickets and hotel stays. The vertical bars represent the amounts spent on hotel stays. The line graph represents the amount spent on flight tickets. (a) State one aspect of the graph that may be misleading and how this may lead to a misinterpretation of the annual amount spent on hotel stays. Answer …………………………………………………………………………………………... …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… [2] (b) Susan claims that, the years when she spends more on flight tickets corresponds to when she spends more on hotel stays. Does the chart support her claim? Justify your answer with reference to the chart. Answer The chart support / does not support her claim because ……………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… [1]

8 11 (a) The following shows two sets. {4 , 8 , 12 , 16, 20, 24}A= {8 ,16, 24}B= Use the following set notations to complete this statement. φ⊂ ⊄ ∈∉ ∪ ∩ (i) B …………….. A (ii) 22 …………….. A [1] [1] (b) Shade the given set on the Venn diagram below. [1] (c) There are 120 students in a group. The Venn diagram below shows the number of students who study History (H), Geography (G) and Economics (E). (i) Find the value of x and state what this value represents. Answer x=………………………………… and it represents ……………………………….. …………………………………………………………………………………………………… [1] ξ ξ 21 25 32 9 17 7 x 4 5

9 (ii) Two of the students who study Economics are chosen at random. Find, as a fraction in its simplest form, the probability that one of these students also studies Geography but not History and the other student also studies History but not Geography. Answer …………………………………… [2]

10 12 Find five positive integers that satisfy all four of the following conditions. (1) Mode = 5 (2) Median = 5 (3) Mean = 6 (4) Range = 7 Answer ………. , ………. , ………. , ………., ………. [1] 13 The following shows a list of ingredients for a recipe for making shortbread biscuits. Ingredients to make 25 biscuits • 250 grams of flour • 100 grams of sugar • 175 grams of butter (a) Write down the ratio of flour, sugar and butter in its simplest form. Answer ………..….…. : ……..…..…... : ……….…..…. [1] (b) Raju is making shortbread biscuits for a party using this recipe. She wants to make as many biscuits as possible. She has 1.5 kg of flour, 0.5 kg of sugar and 1 kg of butter. Calculate the maximum number of biscuits Raju can make. Answer ……….