PHS 4NA Math 4045 P1 2022

Name:Index No.:Class:PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/01PAPER ONE25 July 2022 Monday 2 hours PRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLPRESBYTERIAN HIGH SCHOOLSECONDARY FOUR NORMAL (ACADEMIC)PRELIMINARY EXAMINATIONSDO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.READ THESE INSTRUCTIONS FIRSTWrite your name, index number and class on all the spaces provided above.Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, 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 80.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 . Note that all the diagrams in this paper are not drawn to scale.For Examiner’s UseCategoryAccuracySymbolsOthersMarks DeductedQuestion No. Setter: Mrs Joyce YeoVetter: Ms Cynthia ChuaThis question paper consists of 19 printed pages (including this cover page) and 1 blank page. Mathematical FormulaeCompound Interest Total Marks

2 Presbyterian High School4045/01/4NA Prelim/2022 Total amount = nrP1001MensurationCurved surface area of a cone = lrSurface area of a sphere = 24rVolume of a cone = hr231Volume of a sphere = 334rArea of triangle ABC = Cabsin21Arc length = r, where  is in radiansSector area = 221r, where  is in radiansTrigonometryCcBbAasinsinsinAbccbacos2222StatisticsMean = ffxStandard deviation = 22ffxffx

3 Presbyterian High School4045/01/4NA Prelim/2022 [Turn over Answer all the questions.1(a)2 11.751.313Write these numbers in order of size, starting with the smallest.Answer,, , [1](b)Express 73.4% as a fraction.Answer[1]2 AdultChild (Ages 4 – 12)One-Day Admission Ticket$68$58Universal Express Pass$50$50(Source: www.rwsentosa.com)The table shows the cost for one-day admission ticket to Universal Studios.The Universal Express Pass can be purchased to skip the queue at participating rides and shows.Mr and Mrs Teo bought one-day admission tickets for themselves and their son (12 years old) and daughter (13 years old). They also bought Universal Express Passes for each of their two children.Calculate the total cost of the tickets.Answer$ [2]3Solve 4352x.

4 Presbyterian High School4045/01/4NA Prelim/2022 Answerx =[2]4 ABCDEFGHThe diagram shows a regular octagon ABCDEFGH.Calculate y. yo Answery =[2]5p is inversely proportional to q2.When p = 3 when q = 2.Find the value of p when q = 10.Answerp =[2]6(a)Given that 6305555v, find v.Answerv =[1](b)Given that 1464w, find w.

5 Presbyterian High School4045/01/4NA Prelim/2022 [Turn over Answerw =[1]7(a)0yxThe diagram shows the sketch of 2yxk.State a possible value of k.Answerk =[1](b)–21 yx–3 7State the equation of the line of symmetry of this graph of a quadratic function.Answer[1]

6 Presbyterian High School4045/01/4NA Prelim/2022 8In the diagram, AB is parallel to CD and EF. Angle 40ABC and angle 135CEF.40o135oABCDEFCalculate angle BCE. Answero[2]9(a)sin0.6m Given that m is an obtuse angle, find m.Answerm =[1](b)cos133cosn Given that n is an acute angle, find n.Answern =[1]

7 Presbyterian High School4045/01/4NA Prelim/2022 [Turn over 10On the grid below, draw a reduction of figure P using a scale factor of 13.P [2]11A car is travelling at a constant speed of 90 km/h.(a)How many minutes does the car take to travel 105 km?Answerminutes[2](b)Convert 90 km/h to m/s.

8 Presbyterian High School4045/01/4NA Prelim/2022 Answerm/s[1]12In 2021, Jane’s annual salary was $22 140.This was an increase of 2.5% on her annual salary in 2020.(a)Calculate her annual salary in 2020.Answer$ [2](b)The income tax rates for 2021 were: Chargeable IncomeIncome Tax Rate (%)Gross Tax Payable ($)First $20 00000Next $10 0002200(Source: www.iras.gov.sg)Calculate the amount of income tax she paid in 2021.Answer$ [1]13Express 25139xx as a single fraction, in its simplest form.

9 Presbyterian High School4045/01/4NA Prelim/2022 [Turn over Answer[3]14ABCD is a quadrilateral and E is a point on AD. BC = CD and BE is parallel to CD. Angle 124ABC, angle 110BCD and angleangle 85CDA. ABCED124o110o85o(a)Find angle BAD. Answero[1](b)Find angle BDE. Answero[2]15(a)Jerry deposits $60 500 in a bank at 1.2% per annum interest for 3 years. Calculate the simple interest earned for 3 years.Answer$ [1](b)Tom invests $12 000 for 4 years.He receives compound interest at 1.15% per year.How much is the investment worth at the end of the four years?Give your answer to the nearest cent.

10 Presbyterian High School4045/01/4NA Prelim/2022 Answer$ [2]16A cone has a vertical height of 11.5 cm, radius r cm and volume 434 cm3.r11.5 Calculate r. Answerr =[3]