ANDSS 4E2024EM Prelim P1 QP

This document consists of 27 printed pages. Setter: Mr Azmi O ANDERSON SECONDARY SCHOOL Preliminary Examination 2024 Secondary Four Express and Five Normal CANDIDATE NAME: CLASS: / INDEX NUMBER: MATHEMATICS Paper 1 4052/01 14 Aug 2024 2 hours 15 min 0800 – 1015 h Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid/tape. Answer all the questions. If working is needed for any question it must be neatly and clearly shown in the space below the question. 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . At the end of the examination, fasten all your work securely together. 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 90.

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where  is in radians Sector area = , where  is in radians Trigonometry Statistics Mean = Standard deviation = n rP ÷ ø öç è æ + 1001 rlp 24 rp hr 2 3 1 p 3 3 4 rp Cab sin2 1 r 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+= f fx   22        −  f fx f fx

3 Prelim 4E/5N MATH 2024 4052/1 1 Expand and simplify ( )( )5 2 5 2a a b a b−+ . Answer …..…………..…………… [2] 2 Given that 23 3 90xx ++= , find x . Answer x= …..…………..…………… [2]

4 Prelim 4E/5N MATH 2024 4052/1 3 Simplify 2 22 2 4 3 6 26 x xy x y x xy y + − − +− . Answer …..…………..…………… [3]

5 Prelim 4E/5N MATH 2024 4052/1 4 Two integers, A and B, can be written as products of prime factors. 237mA += 37mBq=   The lowest common multiple (LCM) of A and B is 33 5 7 . (a) Write down the value of m and q. Answer m= …..…………..…………… [1] q= …..…………..…………… [1] (b) Find the highest common factor of A and B. Answer …..…………..…………… [1]

6 Prelim 4E/5N MATH 2024 4052/1 5 Below is a graph from the Annual Climate Singapore 2023, which shows the top 10 warmest years in Singapore since 1929. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. …………………………………………...……………………………………………………… ….……………………………………………………………………………………………….. ……….………………………………………………………………………………………….. …………….………………………………………………………………………………….[2]

7 Prelim 4E/5N MATH 2024 4052/1 6 (a) Simplify 2 9 3 627 y x − −   , leaving your answer in positive index. Answer …..…………..…………… [2] (b) Given 2 25 5 125 y x− = , express x in terms of y. Answer …..…………..…………… [2]

8 Prelim 4E/5N MATH 2024 4052/1 7 (a) Factorise 229 24 16x xy y++ completely. Answer …..…………..…………… [1] (b) Hence factorise ( ) 8 8 4 2144 9 24 16a a a y y− + + completely. Answer …..…………..…………… [2]

9 Prelim 4E/5N MATH 2024 4052/1 8 The intensity of a sound detected by a receiver is inversely proportional to the square of the distance of the receiver from the source of the sound. When the distance is r metres, the intensity of the sound detected is q decibels. When the distance is reduced by 40%, (a) find the intensity of the sound detected, in terms of q. Answer …..…………..…………… decibels [2] (b) calculate the percentage difference in the intensity of the sound detected. Answer …..…………..…………… % [1]

10 Prelim 4E/5N MATH 2024 4052/1 9 Sketch the graph of 3 xy −= on the axes below. Indicate clearly the coordinates of the points where the graph crosses the axes. [1] 10 ABCD is a rhombus and RD CS= . SCB, DCR and AQR are straight lines. Prove that triangles SCD and RDA are congruent. .…………………………………………...……………………………………………………... …………………………………………………………………………………………………... …………………………………………………………………………………………………... ………………………………………………………………………………………………..[3] y x A B C D R S Q