Montfort Secondary School 2025 Prelim Elementary Mathematics P1

Name: ______________________________ ( ) Class: ___________ Secondary 4 Express/ 5 Normal (Academic)MATHEMATICS 4052/01Paper 1 26 August 2025 (Tue)Candidates answer on the Question Paper.2 hours 15 minutesREAD THESE INSTRUCTIONS FIRSTWrite your name, class and register number on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fluid.Answer all questions.The number of marks is given in brackets [ ] at the end of each question or part question. 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 total number of marks for this paper is 90.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.This document consists of 22 printed pages.Mathematical Formulae MONTFORT SECONDARY SCHOOL PRELIMINARY EXAMINATION

2 2025 Preliminary Examination Compound interestTotal amount = 1100nrPMensurationCurved surface area of a cone = πrlSurface area of a sphere = 2π4rVolume of a cone = hr2 π31Volume of a sphere = 3 π34rArea of triangle ABC = Cabsin 21Arc length = r, where is in radiansSector area = 2 21r, where is in radiansTrigonometryCcBbAasinsinsin2222cosabcbcAStatisticsMean = fxfStandard deviation = 22ffxffxAnswer all the questions.

3 2025 Preliminary Examination 1The number of people in a theatre is given as 2500, correct to the nearest hundred.Write down the minimum number of people that could be in the theatre at this time.Answer ………………………….[1]2Solve 7825x. Answer x………………………….[1]3Simplify 9523abab.Answer ………………………….[1]4(a)Calculate 3226.184.520.4.Write down the first six digits of your answer.Answer ………………………….[1](b)Write your answer to part (a) correct to 2 significant figures. Answer ………………………….[1][Turn over

4 2025 Preliminary Examination 5The sum of the first n terms of a linear sequence is 171.2nn(a)Find the first 3 terms of the sequence. Answer ……………… , ……………… , ………………[2](b)Find in terms of n, an expression for the nth term of the sequence.Answer ………………………….[1] 6The bar graph below shows the results of a survey conducted on the quality of food

5 2025 Preliminary Examination (e.g. ingredients, portion and taste, etc.) in a school canteen. Quality of food in a school canteen Number of respondents StronglyUnsatisfiedUnsatisfiedSatisfiedStronglySatisfiedSomewhatSatisfiedResponses(a)Calculate the number of respondents who answered Satisfied as a percentage of the respondents who answered Unsatisfied.Answer ………………………….%[1](b)Suggest the use of another statistical diagram to represent the results of the survey conducted that shows the relative size of a part in relation to the whole.Answer ………………………….[1][Turn over

6 2025 Preliminary Examination 7 sin20.8xFind two possible values of x in the range π02x radians. Answer x………………. or x………………. [2]8Yue makes 40 medium fruit pies.The number of small, medium and large pies he makes made each day are in the ratio 5 : 2 : 8 respectively. (a)How many large fruit pies does he make?Answer ………………………….[1](b)How many fruit pies does he make altogether?Answer ………………………….[1]9Express as a single fraction in its simplest form 21343xx.Answer ………………………….[2]10The stem-and-leaf diagram shows the heights of 10 students.

7 2025 Preliminary Examination Stem Leaf1501481612217123 Key: 15 | 0 represents 150 cm (a)Find the mean height.Answer ………………..…… cm[1](b)Find the standard deviation of the heights.Answer ………………..…… cm[1](c)It was discovered that all the heights had been recorded wrongly.The correct height of each student was 2 cm taller.Without any calculations, explain how the mean and standard deviation will change after the height adjustment. …...………………………………………………………………………………………………………………………………………………………………………………………...…...…………………………………………………………………………………………[2] [Turn over11(a)Express 450 as the product of its prime factors.

8 2025 Preliminary Examination Answer ………………………….[1](b)Find two numbers, both smaller than 100, that have a lowest common multiple of 450 and a highest common factor of 15.Answer ……………… and ………………[2]12Andrew invests $15000into an account.The balance, $A, of the account after t years is given by the formula 150001.032tA. (a)Calculate A when 3t.Answer $ …………………………[1](b)Find the percentage increase in the balance after the 3 years.Answer ………………………….%[2]13The drawing in the answer space below shows the positions of the towers A, B and C.

9 2025 Preliminary Examination CAB(a)Construct the perpendicular bisector of BC.[1](b)Construct the bisector of angle ABC.[1](c)A mall is to be built equidistant from AB and BC, and is nearer to C than to B.Mark clearly a possible position of this mall and label it, M.[1] [Turn over14Given that 22uvut, express u in terms of v and t.

10 2025 Preliminary Examination Answer …………………………..[3]15Factorise completely.(a)832xxyAnswer …………………………..[1](b)6496axaybxbyAnswer …………………………..[2]16The graph of 2(1)yxq is given below.