Math - Sec2 - SA2 - 2023 - Juying Sec

NAME: __________ ( MARKS :. ___ /50 CLASS:2 __ _ Friday MATHEMATICS PAPER 1 29 September 2023 1 hour 15 minutes JUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCH JUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCH JUYJNGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCH JUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCHOOLJUYINGSECONDARYSCH JUYING SECONDARY SCHOOL END OF YEAR EXAMINATION SECONDARY TWO G3 READ THESE INSTRUCTIONS FIRST Write your name, register number, class and date in the space provided. 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 rr, use either your calculator value or 3.142, unless the question requires the answer in terms of rr. 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 50. 195 BP-191

BP-192 Answer all questions. I . . f GMm 1. t 1s given that == -,-. r· (a) Find f when G = 10, M = 15, m = 3 and r === -3. Answer f = ... . . ..... ..... .. ...... [1] (b) Express r i n terms off , G, Mand m. Answer r = . . . . . . . . . .. . . . . . . . . . . . . [2] 2. (a) Solve the inequality 15 > 1 - 2x . Answer . ... . . . . .. . . . . .. . .. . . .. . . .. [2] (b) 'x = -7 fulfils the inequality 15 > 1- 2x.' Determine if this statement is true or false. Ans,ver This statement is .... .......... because ........ ..... .... .......... .. .... .......... .. ... .. ...... . [l] 196

3. (a) Factorise 16 - 9x 2 . Annver . . . . . . ... . .. .. . . . . . . .. . . . . . [1] (b) Hence, express - 1 - - x 2 as a sinele fraction in its simplest fom1. 3x+4 (16-9x ) ~ Annver . . . . . . . . . . . . . . . . . . . . . . . . . . . [2] 197

4. Expand and simplify the follow ing. (a) 9xy - (x + 3y) 2 (b) (4x - 1)(x 2 - 2x + 3) 5. Factorise completely. (a) 4x 2 + 10xy - 14y 2 (b) 4 - 4x 2 + y + xy 198 Answer . . .. . . . . . . . . . . ... . . . . . . . . . . [2] Annver . .. . . . ... . . . . . . . . .. . . . . . . . . [2] Answer ............. ...... ... .. ... (2] Answer ................. .. ... .. .. . [3]

6. The land area of Singapore is 25 km2. 199 This area is represented on a map as 1 cm2 (a) Find the actual area of a park that is represented by 0.7 cm2 on the map. Answer [l] (b) The running path within the park measures at 8400 m. Find the distance, in centimetres, of the running path on the map. Answer ..... ....... .. .......... cm [2] (c) A new scale of 1: 400000 is used. Find the distance, in centimetres, of the running path on the map using this new scale. Answer .... ...... .. .. .. ........ cm [2] BP-195

7. Andrew works at an insurance company. He needs to call clients quite often . The following table records the talk time, in minutes , he has used on his mobile phone for the past 15 days . 49 8 51 37 45 23 15 5 36 40 17 20 34 10 (a) Complete the stem and leaf diagram to illustra te the information above. Answer Stem 0 3 4 5 Leaf Key: 015 represents 5 minutes (b) Find the percentage of his usage that is more than 14 minute s and less than 41 minutes . [2] Answer ..................... .. % [2] 200 BP~19fi

BP-197 8. The diagram shows a circle with centre O and radius 11 cm. C, H, ~ and G are points 01_1 the circumfe_rence of the circle. T . • The hne AD touches the circle at C and IS parallel to EC. 1 J l ti On Bis a point on AD such that angle ABO = 140° and angle OCD = 9~ vv· E D -·· A Calculate the length of BH. Answer ........................... [4] 201

9. The table shows the lifespans, x hours, of 12 light bulbs. 202 13 , 27 3 17 15 24 23 21 14 6 17 13 (a) Complete the group frequ ency table for the lifespan of the light bulbs. Lifespan, x hours Frequency O<x:s;S 5 < X :s; 10 10 < X :s; 15 15 < X :s; 20 20 < X :s; 25 25 < X :s; 30 (b) Using the frequency table in (a), calculate an estimate for the mean lifespans of the light bulbs . [2] Answer .. . .... ...... ...... . hours [2] BP~ 198

10. The diagram below shows triangle XYZ in which LXYZ = 90°, XY = (a + 1) cm, YZ = ( 2a + 1) cm and XZ = (2a + 3) cm. a+l X .....-------~ y "fuition 2a + 3 2a + 1. \Vlt z (a) Fom1 an equation in a and show that it reduces to a" -6a - 7 = 0. Ansvver (b) Hence, calculate the length ofXZ. [2] Answer x = ........................ [3] 203

11. The figure shows a parallelogra m with its sides as indicated. 204 (2x+ y+ 2) cm 1 Tuitior1 ( x+St. WI (3x-y+l9) cm (a) By forming two equations in terms of x and y, solve them simultaneously to find the values of x and ofv. Answer x = .. ..... ............... . y =....... ... . .. . . ... .... . . [4) (b) Hence, find the perimeter of the parallelogram. Ansv,:er ................ .. ...... cm [2] BP~200