Seng Kang Sec Sch P1 2020

- SENG KANG SECONDARY SCHOOL PRELIMINARY EXAMINATION 2020 MATHEMATICS 4 NORMAL ACADEMIC 4045/01 12 AUGUST 2020 READ THESE INSTRUCTIONS FIRST Candidates answer on lhe Question Paper. Write your class, index number and name 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. Arlswer all questions . If woru,g is needed for any question It must be shown with the answer. Omission of essential working wll result In loss of marks. 2 hours The use of an approved scientific calculator is expected, where appropriate. If lhe degree of accuracy is not specified In the question, and If the answer Is not exact, give the answer lo three significant figures . Give answers In degrees to one decimal place . For", use either your calculalor value or 3.142 , untess the question requires the answer In terms of" . At the and of the examination, fasten all your work securely together. The number of marks Is given in brackets [ J at the end of each question or part question. The total of the marks for this paper Is 80. 80 Parent'• / Guardian'• Slgnatura: ............... ..... . , ...... • • • • • • •·· This document consists of 16 printed pages and O blank page. [Tum Over 2 MolMllflllicoJ Fo,,,,11/u Compo11nd In/era/ Total amount= JI+...!:_) • • \ IOO Geometry and Me0311remenl Trigonometry Statistics Curved surface area of a cone= nrl Surface area ofa sphere= 4111·' Volume ofa cone= !,.,.,h 3 Volume ofa sphen:= i,.,., 3 Area of triangle ABC= .!.ab sin C 2 Arc length= rO , where (J is in radians Sectorarea=.!., 20 , where fJ is in radians 2 a' =b' +c' -2bccosA Lfx Mean=~ ~I Lfx' (Lfx)' Standard deviation = Lf - Lf

3 (a) Express i as a decimal. Answer all 01e questions. Answ,,r , , , ................................................. (I) (b) Write 1720.9394 in 3 significant figures Answ,,r ..... ............................................... (I) (c) In 2018. the men's marathon world record was 2 hours 2 minutes and 50 seconds. In 2019. a new world record was set and it was 3 rnins 17 seconds raster than the previous record. Write down the timing or the new world record set in 2019. Answer ..................... hours ............ ........ minutes .................... seconds (2) 2 y is pmportjnnal 'to~ cube of .r. Given thaty = 3 when .r = 2. find y when .r = 5. Answer y= .. .. ........ , .. , .. ..... .. [2] [Tum Over 3 Ct,oco/a1, Brownt, fkcipe 280g ofnour 140g of butter 4 eggs I OOg or cocoa powder 50g of chocolate chips 260g of brown sugar 4 The above recipe makes exactly 24 brownies (a) Find the ratio of the mass of brown sugar to mass of butter in the recipe. A111wter ... ......................... ....................... [I] (b) Mrs Brown wants to make 100 brownies to sell. How many kilograms of nour will she need? A,uw,,r ................................................ kg [2] 4 Factorise (a) 8.r' - 6xy3. (b) 2m1 - 18. A,uw,,r .... .. .. ...... ...... ... ...... ...... . .. (I] A,uw,,r [2]

5 5 The distance from Ali ' s house to his school is 2.2 /c111. (a) A map has a scale of I : 50 000. Calculate the distance of Ali ' s house to the school on the map. Answer .... .... .. ........ .. .. ... ......... cm (I] (b) Ali 's school covered an actual area o f 8 1cm'. Calculate the area . in square centimetres , covered by the school on the map. Answer .. cm' 121 6 (a) An expression for the nth tenn of a sequence is 5 + 3n. Find the 7'" tenn of the sequence . Answer (I] (b) Johnny said that 38 is a tenn in the sequence . Show clearly with working if Johnny is right or wrong . Answer Johnny is ...... . . .. . because .......... .. ... .. .... .. ....... .. .. ... .. .. .. ........ ... .. (2) ................................................................. ........................... ,., ..... [Tum Over 7 6 (a) II is given that x and y arc integers such that - 4 5 x 5 2 and 3 Sy 5 6 . (b) Find the smallest value of x + 2y. Answer (I) Solve I < 2x - 3 5 9. Answer (II) Represent the solution on the number line below . Answer Ill .. .... .. 12] :x [21 8 The diagram shows an incomplete regular polygon with n sidcs ,~le and I square . Find the value of n. Answer ...... ..... ... ... .............. ......... (4]

7 9 (a) Rearrange a = :. , to make x the subject. (b) Solve these simultaneous equation s. 2x + y = J - 2y + 3x = 8 Answer x = . . . .... ...................................... (2] An.,,wr x e •••••••••••••••••••••••••••u,, .. ,.,..., .. ,,, y • .......................................... IJJ [Tum<>wr 8 10 A bag contains 6 green counters, 9 white counten and I yellow counter . (a) A counter is taken from this bag at random . (I) Find the probability that this counter is green . Answer .. (II) Find the probability that this counter is green or white . . . . . . . . .... . . . . . ... . .. . . .. .. I I I Answer (b) (I) Two counters are taken from the bag. one after another . without replacement. Complete the tree diagram to show all the possible outcomes . Answer ( ) ( J 1• Counter 2 .. Counter Green Yellow White~::: ~cllow ( 6 ) 9 Green Yellow White Yellow (II) l' lnd tho IX\lblblllty that the two coontcn arc of the aamc colour . . ..... .. .... [I) 121 Answer .............. , ... ...... ... . ..... ... .. (21

II / 9 I I I I Jay 111 \11 1 I I Peter i i I I I I I I I Siti \\l \JJ 11111 IJ IV I I I I I I Srya ll~IJI\UW Key: I Li Ming 111 I represents 4 cups A survey is conducted to find out the number of cups of bubble tea each student drink in the month of December . The pictogram above shows the survey resu lts of S studenta . (a) How many cups of bubble tea did they drink in total? An.rwer ... ...... .. .. .. ... .... .... . .............. (I) (b) Find the difference in the number of cups of bubble tea drank by Srya and Li Ming. Amwer . ... ... .... ..... . ..... ... ......... (I) (c) The survey results is presented using a pie chart instead. The size o f the sector rcpn:, cn1ing 1he number of cups of bubble tea drank by Jay is 72°. Calculate the size of the sector representing the number of cups of bubble 1ea drank loy Srya . A,u wer • 121 [Tum Over 10 12 Figure ABCD and PQRS arc drawn on the grid below . A,uwer (a) 8 C I ~ I ~In A Q R I \ I \ \. DI \ s (a) Draw an enlargement of ABCD using the scale factor of 0.5. Label the figure WXYZ. (21 (b) Is ABCD similu to PQRS ? Justi fy your answ er. Ans14>er .... . ...... ... , ., . . •..•.... . , ... . . , . . .. ... , .. .. ... ... . ... .... . ... ... ... , ... •... .. .. _ •... .. 121

13 11 2 I 2 6 3 2 2 2 5 4 4 7 8 Key 5 2 4 7 8 2 11 means 2 1 cm The stem and leaf diagram below represents the height of 17 plants that Sammy measured in his fann recently. (a) Write down the modal height of the plants. Answer .... ..... .... ..... .... c1n (b) Find the interquartile range of the heights of the plants. [I] Answer ..... ....................................... cm 121 (t) Peter also planted 17 plants where the median height of the plants is 46cm. Sammy said that his plants arc ~enerally taller than Peter's plants. Do you agree with Sammy's statement? Explain with reason. Answer with Sammy's statement because ...... ..................................................... . ... .................................................................................................................................... .... .................. [I] [Tum Over 14 IS 12 A solid cone has a radius of6cm and a total surface area of30l.6cm ' . Find the slant height of the cone. Answer ............................................. cm 13] The cash price ofa computer is $2199. A customer can buy the computer on hire purchase with a down-payment ofS200 and monthly instalments over 5 years and at an interest rate of 3.