PHS 4NA Math 4045 P2 2022

Name:Index No.:Class:PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/02PAPER TWO26 July 2022 Tuesday 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 work you hand in.Write in dark blue or black ink.Show your working in the space provided below each question.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.Section AAnswer all questions.Section BAnswer one question.The number of marks is given in brackets [ ] at the end of each question or parts of 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 total number of marks for this paper is 60.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.For Examiner’s UseCategoryAccuracySymbolsOthersMarks DeductedQuestion No. Setter: Mrs Joyce YeoVetter: Ms Cynthia ChuaThis question paper consists of 16 printed pages (including this cover page) and 0 blank page. Mathematical FormulaeCompound Interest Total Marks

2 Presbyterian High School4045/02/4NA 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 School4045/02/4NA Prelim/2022 [Turn over Section A (52 marks)Answer all the questions in this section.1The stem-and-leaf diagram shows the weight, in kilogram, of 20 students.401579950111459960366712 Key: 4 | 0 means 40Find (a)the number of students with weight more than 59,Answerstudents[1](b)the median weight.Answerkg[1]2The amounts of flour, butter and sugar required to bake a cookie are in the ratio 3 : 2 : 1.The total weight of all three ingredients is 450 grams.Find the amount of each ingredient used.Answerflour: gbutter:gsugar: g[3]

4 Presbyterian High School4045/02/4NA Prelim/2022 3(a)Calculate (i)the exact value of 9.34.625.72.1,Answer[1](ii)23152.57.Give your answer correct to 1 decimal place.Answer[1](b)The table shows the number of coronavirus cases of four countries in Europe.CountryNumber of cases (millions)France30.51Germany27.77Russia18.41Italy18.18(Source: https://www.worldometers.info/coronavirus/)Calculate the total number of coronavirus cases of the four countries.Give your answer in standard form.Answer[2]4(a)Expand and simplify 413xx. Answer[2](b)(i)Solve the inequality 374x.Answer[1](ii)Write down the largest integer value for x.

5 Presbyterian High School4045/02/4NA Prelim/2022 [Turn over Answer[1]5(a)Write 1008 as a product of its prime factors. Answer[2](b)What is the largest perfect square that is a factor of 1008?Answer[1](c)2337802357 Write down the lowest common multiple of (LCM) of 1008 and 3780.Give your answer as a product of its prime factors.Answer [1]

6 Presbyterian High School4045/02/4NA Prelim/2022 6The diagram shows a quadrilateral ABDE. ACD and BCE are straight lines and AB is parallel to ED.BAEDC8126.5(a)Complete the sentence.The mathematical name of quadrilateral ABDE is.[1](b)Given that triangle ABC is similar to triangle DEC, identify all pairs of angles in triangle ABC and triangle DEC that are equal.Answer[2](c)AB = 8 cm, BC = 6.5 cm and DE = 12 cm.(i)Find the scale factor of enlargement of triangle ABC to triangle DEC.Answer [1](ii)Calculate EC. Answer cm[2]

7 Presbyterian High School4045/02/4NA Prelim/2022 [Turn over 7(a)Factorise completely 3624axayxy. Answer[2](b)Rearrange this equation xbybx to make b the subject. Answerb =[3]

8 Presbyterian High School4045/02/4NA Prelim/2022 8This table of values is for 32368yxxx.x– 3 – 2– 1012345yp01080– 8q028(a)Calculate the value of p and the value of q.Answerp =q =[2](b)On the grid provided, plot the graph of 32368yxxx for 35x.Answer on next page[3](c)Find the value of x when y = 20.Answerx =[1](d)By drawing a tangent, find the gradient of the curve 32368yxxx when x = 4.Answer [2]

9 Presbyterian High School4045/02/4NA Prelim/2022 [Turn over Answer: 8(b) 12345x–3–2–10302010y –30–20–10

10 Presbyterian High School4045/02/4NA Prelim/2022 9PRS is a right-angled triangle and PQR is a straight line.PS = 10 cm, SR = 6 cm, angle90QRSand angle 32QSR.S PRQ61032o(a)Find sinSPR. Give your answer as a fraction in its lowest terms.Answer[1](b)Calculate the length of QS.Answercm[2](c)Show that the angle PSQ is 21.1.Answer[2](d)Calculate the area of triangle QPS.Answer cm2[2]