Math - Sec2 - SA2 - 2023 - Zhonghua Sec

275 ----- --- ---· ZHONGHUASECONDARYSCHOOL END-OF-YEAR EXAMINATION 2023 SECONDARY 2 EXPRESS CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052 29 September 2023 2 hours READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degree, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. 80

BP-272 l The diagram below shows a regular octagon and a regular decago n. Find the value of x. Answe r x = [2] 2 Expand and simplify 3 ( 8- Sq }2 . Answer [2] 276

--------------------· - BP-273 3 In the diagram, triangk A BC is sirnilar to triangle EBD. AB =5 cm , BC= 12 cm and BE=3 cm. ,..,.., 01• ti B 5cm ,1'- 10n 3cm E C Find the length of DC. Ans,ver cm [2] 4 A map is drawn to a scale of 1 : 20 000. (a) The distance between a pineapple plantation and a rnbber plantation on the map is 15 cm. Calculate the actual distance, in kilometres , between the two plantations. Answer km [1] 277

(b) The area of the pineapple plantation is 20 km' . Calculat e the area, in square centimetr es, of the pineapple lantation on the map. Answer cm2 [2] 5 A bag contains 7 red marbles , ~ green marbles and 4 blue marbles. (a) If a marble is drawn at random from the bag, find the probability that it is a green marble . Answer [l] (b) When x more blue marbles are adde:d to the bag, the probability of drawing a blue 1 marble be comes - . 3 Form an equation in x to find the value of x. Answe r [2] 278

6 (a) (b) 279 2x + 3 4- X Solve the inequality -- 2: --5 2 2x + 3 4- X Hence, write down the smallest prime number which satisfies --> --5 - 2 Answer (2] [1]

. . Jr P 7 It 1s given that -- = - . g +5 4 (a) Evaluate p when T = 392 and g = 3. (b) Express g in tem1s of T and p . 8 Solve the equation (2x- 3)( 3x+ 5) = 7 . 280 Answer p = Answer a= b Ans,ver x = or BP~276 [l ] [2] [3]

- ------- -- - -- 9 A ladder of length 4 m leans against a vertical wall and the bottom of the ladder is 1.5 m from the wall. The safe working angle for a ladder is between 74° and 76° to the horizontal. Is the ladder in a safe position to use? Show your working to justify your decision. 1----1 .-- Wall I---=.! U i ti O 11 l.5 m it ~ ! Ans1-ver The ladder is / is not* in a safe position to use because *Please circle accordingly 281 [3]

BP-278 10 The times taken , in minutes , by 20 students to complete an assignment are recorded. The results are shown in the st m-and-leaf diagram. Stem Leaf 2 ,., 5 5 6 7 7 9 ., 3 l l 4 7 4 2 2 5 8 8 5 l 6 7 8 ,., ., Key: 2 I 3 1m:ans 23 minutes (a) (i) Find the median time. Answer minutes [1] 282 ii) It was discov red that the times taken had been recorded incorrectly. The correct times taken \Vere all 3 minutes less than those recorded . State the correct median time taken. Answer minutes (b) Explain why the mean may not be an appropriat e average to use to summarise the times taken by these student s. [l] [1]

BP~279 11 The lengths of service of39 employees of an advertising agency are recorded in the table below. 283 Length of service (t years) 0< ts 5 5<tsl0 10<tsl5 20 <ts 25 (a) Write down the modal class. Number of em Ans11,·er (b) Calculate an estimated mean of the length of service of the 39 employees . Answer [l] years [2]

12 The number of hours, N, required to dig a trench, is inversely proportional to the square of the number of men available , X. It takes 6 men a total of 8 hours to dig a trench . (a) Find an equation connecting N and X. BP-280 A nstver [2] ---------- (b) When Xis increased by 100%, find the percentage reduction in the value of N. Answer % [2] ------------- 284