Broadrick EM 2024 Maths Sec Prelim - P1

[Turn Over NameClassIndex Number BROADRICK SECONDARY SCHOOLSECONDARY 4 EXPRESS /SECONDARY 5 NORMAL ACADEMICPRELIMINARY EXAMINATION 2024MATHEMATICSPaper 1Candidates answer on the Question Paper4052/01Aug 2024 2 hours 15 minutes READ THESE INSTRUCTIONS FIRSTWrite your name, class and index 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 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of .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.For Examiner’s UseError InQuestion NumberMarks DeductedRounding-offReasoningPresentationFor Examiner’s Use90This document consists of 21 printed pages.Setter(s) :

2 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1 Mathematical FormulaeCompound interestTotal amount = nrP1001MensurationCurved Surface area of a cone = rlSurface area of a sphere = 24rVolume of a cone = hr231Volume of a sphere = 334rArea of triangle ABC = ab21sin CArc length = rθ, where θ is in radiansSector area = 221r, where θ is in radiansTrigonometryCcBbAasinsinsinAbccbacos2222StatisticsffxMeanStandard deviation = 22ffxffx

3 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1[Turn Over Answer all the questions.1Evaluate 23(3.85)100.9(6)3.114 , giving your answer to 4 significant figures.Answer….........……………..…….. [1]2The frequency table shows the reaction time, t seconds, for a chemical to change the colour of the litmus paper in 100 laboratory sessions.Time (t sec)0 < t ≤ 11 < t ≤ 22 < t ≤ 33 < t ≤ 44 < t ≤ 5Frequency828441822Calculate an estimate for the (a)mean reaction time,Answer….........……………..….. s [1](b)standard deviation of the reaction times.Answer….........……………..….. s [1]3Given that 2352525xmnxx, express m and n in terms of x.Answerm = ..............………..…….. n = [2]

4 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1 ...........…………..…….. 4The highest common factor of two numbers is 18.The lowest common multiple of the two numbers is 324.Both numbers are greater than 20.Find the two numbers.Answer….........…… and …..…….. [2]5A map has a scale of 1 : 50 000.(a)The distance between two towns on the map is 7.5 cm. Calculate the actual distance between the two towns in kilometres.Answer….........………..…..….. km [1](b)A lake covers an actual area of 2.25 square kilometres. Find the area of the lake on the map in square centimetres.

5 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1[Turn Over Answer….........……………..... cm2 [2]6A wooden block has a mass of 115 grams, correct to the nearest gram. The volume of the block is 6 cm3, correct to the nearest cm3.Find the largest possible density of the block in g/cm3.MassDensityVolume Answer….....……………..… g/cm3 [2]7 yIn the following graph, write down a possible value of n and the corresponding value of b for the equation. (1,1)nyxbxAnswern = ..............………..…….. b = ...........…………..…….. [2]

6 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1 8 A BC14.67.631°In triangle ABC, AB = 14.6 cm, BC = 7.6 cm and angle BAC = 31°.Find (a)obtuse angle ACB, Answer….........…………...……. ° [2](b)area of triangle ABC.Answer….........…………...….. cm2 [2]9Keila travels from Singapore to Japan. She wants to change 850 Singapore dollars ($) into Yen (¥).The exchange rate in Singapore is $100 = ¥11600 and the exchange rate in Japan is ¥1 = $0.0086.She claims that she will receive more if she changes the money in Singapore.Justify if her claim is true.Show your working.Answer......................................................................................................................................................................................................................................................................

7 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1[Turn Over ...................................................................................................................................[3]908070605010The graphs below show the average test scores of Class A and Class B over three consecutive years.70656055502022 2023 2024Class A2022 2023 2024Class B(a)What feature of the graph misleads readers to think that the scores of Class A in 2022 had increased to 6 times that in 2024?……………......................................................................................................…………….................................................................................................................................................................................................................................[1](b)Hailey claims that the scores of Class A and Class B shows the same improvement from 2022 to 2024.Do you agree?Explain your answer.……………......................................................................................................……………......................................................................................................……………......................................................................................................…………….................................................................................................................................................................................................................................[1]

8 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1 11The number 5252pq is a perfect cube where p and q are greater than 1.Find the smallest possible integer values of p and of q.Answerp = ...........…………..…….. q = ...........…………..…….. [2]12(a)Simplify 33216y. Answer….........……………..…….. [1](b)3512555kUse laws of indices to find the value of k.Show your working.

9 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1[Turn Over Answerk = .…...……...…………... [3]13Given that  = {integers x : 20px}A = {factors of 24}B = {prime numbers}C = {perfect squares}(a)List the elements of A if p = 2.Answer….........……………..…….. [1](b)For 0p, list the elements of ' BCsuch that n' = 4BC.Answer….........……………..…….. [1](c)Find the smallest p such that = AC.Answerp = ...........…………..…….. [1]14A company divided a bonus among its employees A, B, and C in the ratio 2 : 3 : 7. C’s bonus was X % more than the combined bonus of A and B.Find X.

10 Broadrick Secondary School, Preliminary Examination 2024, Sec Four Express/ Five Normal (Academic), Mathematics Paper 1 AnswerX = ......………………..….. [2]15In the diagram, two circles with centres O and P respectively intersects at A.The two circles have the same radius and AB // OP.Show that AB = OP. OPAB Answer [3]