BWSS 2023 Sec 4N Math Prelim Paper 2

I believe, therefore I am MATHEMATICS SYLLABUS A Secondary 4 Normal Academic/ 4 Normal Technical (OOS) 3 August 2023 2 hours Candidates answer on the Question Paper. Additional Materials: Writing papers upon request READ THESE INSTRUCTIONS FIRST 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. Section A Answer all the questions. Section B Answer one question. 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 of the marks for this paper is 70. 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. DO NOT OPEN THIS PAPER UNTIL YOU ARE TOLD TO DO SO This document consists of 18 printed pages, including this cover page. Class Full Name Index Number Preliminary Examination 2023 For Examiner’s Use 70 N Calculator Model No.: 4045/02

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3 Section A (62 marks) Answer all the questions in this section. 1 (a) Evaluate 5.48 × √983 (0.15)2 . (i) Write down your answer correct to 2 significant figures. Answer ……....................................... [1] (ii) Write down your answer as a whole number. Answer ……....................................... [1] (b) The population of Asia is approximately 4 758 460 732. (i) Write the value correct to the nearest million. Answer ……........................... millions [1] (ii) The land area of Asia is estimated to be 4.46 × 107 square kilometres. Calculate the number of people per square kilometre in Asia. Answer ……....................................... [2] 2 (a) Simplify 8(𝑦 1 2𝑧)3 ÷ √4𝑦3 . Answer ........................................ [2] (b) Given 3m × 34 = 9, find m. Answer m = ........................................ [2]

4 3 Two lines intersects at point R. Find the coordinates of point R. Answer R = ........................................... [3] 4 A reservoir has an area of 1250 m2. It is represented on the map by an area of 50 cm2. Find the scale of the map in the form of 1 : n. Answer ...................... : .................... [2] y x 4x – y + 15 = 0 3x + 5y – 6 = 0 R

5 5 The number of hours spent on online activities by students in a particular week are recorded. The results are shown in the table below. Number of hours 0 < x ≤ 2 2 < x ≤ 4 4 < x ≤ 6 6 < x ≤ 8 8 < x ≤ 10 Frequency p 9 10 25 16 (a) The modal online hours spent by students in a week is 6 < x ≤ 8. Find the largest possible value of p. Answer p = ……....................................... [1] (b) The estimated mean online hours spent by students in a week is 6.25. Find the value of p. Answer p = …....................................... [3]

6 6 (a) ABCDE is a pentagon. AB is parallel to DC, angle ABC = 75° and angle BAE = 105°. Find the value of angle x°, stating all reasons clearly. Answer x° = …....................................... [3] (b) ABCDEF is a regular hexagon. The length of each side is 10cm. Calculate the area of the hexagon. Answer ….........................................cm2 [3] A B C D E F

7 7 ABCE is a parallelogram. AED is a straight line. Given that EC = 5cm, AD = 11cm and perimeter of parallelogram = 26cm. (a) Show that AE = 8cm. Answer [1] (b) If CD = 4cm, explain how you know that angle CDE is a right angle. Show any calculations you make. Answer ………………………............................................................................................... ……………...………..………………..……………………..………………………………… ………….…………………………………………………………………..…….………. [2] (c) Find angle CED. Answer ........................................ [2] A B C D E 5cm 11cm

8 8 (a) Alan, Benny and Charles ran for the President of the student council. Alan won 42%, Ben won 38% and Charles won 52 votes. Find the total number of votes cast. Answer ................................ votes [2] (b) The usual price of a calculator is $38. It was sold at a promotion price of $32. Find the percentage decrease. Answer .................................... % [2] (a) The total participants registered for a marathon run was 224. The ratio of male runners to female runners was 3:4. On the actual day of the marathon run, a few more female runners who did not register joined in and the ratio of male runners to female runners became 8:11. Find the total number of female runners for the marathon run on the actual day. Answer ........................................ [2]

9 9 (a) Benny travelled 2 5 of his journey by train, 1 4 by bus, 1 3 by car and the remaining 3km on foot. Find the total length of the journey. Answer ........................................km [2] (b) A train travelled 240km at speed x km/h. When the engine was replaced by an improved model, the speed of the train increased by 20 km/h and the travel time was reduced by an hour. Form an equation and show that it reduces to x2 + 20x – 4800 = 0. Hence, find the value of x. Answer x = …..................................... km/h [4]

10 10 (a) Triangles PQR and TRS are congruent. PQ = 3cm, QR = 4cm, TS = 5cm and angle QPR = x°. . (i) Express angle TSR in terms of x°. Answer …......................................... [1] (ii) Find the length of PT. Answer …......................................cm [1] (b) The two triangles in the diagram are similar. AE = 6cm, AB = 3.5cm and BC = 10cm. (i) Write down the pair of similar triangles. Answer Triangle …….……….. is similar to triangle ……….…….. [1] (ii) Find the length of DE Answer …................................... cm [2] T P Q R S 3cm 4cm 5cm x° E 6cm A B C D 3.5cm 10cm