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1 JUNYUAN SECONDARY SCHOOL MID YEAR EXAMINATION 2014 SECONDARY ONE EXPRESS CANDIDATE NAME CLASS 1 E INDEX NUMBER MATHEMATICS 15 MAY 2014 2 hours READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all the questions in this paper. Show all your working on the same page as the rest of the answer. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. 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 . At the end of the examination, fasten all your work securely together. 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. For Examiner’s use [Turn over For Examiner’s Use For Examiner’s Use 2 Answer all questions. 3 Represent the numbers , 2.7, -3 and 0.5 on a number line. 2 1 Answer: 3.15, Given the numbers -3.15, 2 22 , 3.2, 7 (a) .......as shown in answer space.................. [2] 2 2 , 1 3 , 7, (a) write down the irrational number(s), (b) arrange them in descending order. Answer: (a).................................................................. [1] (b).................................................................. [2] 3 (a) Take to be 22 7 17 2 3 7 9 , evaluate giving your answer in decimal 3 17.95 1.292 correct to 5 significant figures. (b) A number is approximated to 3 significant figures and its value is given as 91400. What is the largest integer it could have been? Answer: (a).................................................................. [2] (b).................................................................. [1] [Turn over For Examiner’s Use For Examiner’s Use 3 4 On a certain morning, the temperature in London was – 12 OC, the temperature in Hong Kong was 8 OC and the temperature in Singapore was 26 OC. (a) Find the difference in temperature between London and Singapore. (b) The temperature in Beijing was mid-way between the temperatures of London and Hong Kong. What was the temperature of Beijing that morning? Answer: (a).................................................................. [1] (b).................................................................. [2] 5 (a) Compute 45 3871 3871 35 without using a calculator. Show your working clearly. (b) Factorise the following completely, (i) 2 x 2 y 3 z 8xy 2 z 3 , (ii) 3 x( y 2) 4(2 y ) . Answer: (a) .................................................................. [1] (b)(i).................................................................. [1] (ii).................................................................. [1] [Turn over For Examiner’s Use For Examiner’s Use 4 6 Showing your working clearly, evaluate (a) 5 (4)2 (3)3 2 (9) , (b) 1 3 1 1 5 1 2 4 2 . 1 1 4 2 Answer: (a).................................................................. [2] (b).................................................................. [3] 7 An advertisement signboard has 3 different coloured neon lights that flash at different intervals. The blue neon light flashes every 20 seconds, the orange neon light flashes every 36 seconds and the green neon light flashes every 55 seconds. If all 3 neon lights flash together at 15 45, find the next time that they will flash together again. Answer: ........................................................................ [3] [Turn over For Examiner’s Use For Examiner’s Use 5 8 Furby is 11 years older than her brother. If her brother is x years old, how old was Furby 6 years ago? Answer: 9 (a) .................................................................. [2] Using a calculator, evaluate (i) 3 599 7.84 2.465 , correct to 4 significant figures. 3 3 (ii) 3 (b) 5 0.39 9 , correct to 3 decimal places. 1 5 0.591 3 Elsa buys 3 files at 49 cents each and 5 pens at $1.99 each at the school bookshop. The shopkeeper asks for $12.42. Show using estimation that the shopkeeper has made a mistake. Answer: (a)(i)............................................................... [1] (ii)................................................................ [2] (b)................................................................ [2] [Turn over For Examiner’s Use For Examiner’s Use 6 10 Express 2( x 1) 1 2 x as a single fraction in its simplest form. 3 6 ….................................................................. [3] Answer: 11 In the diagram below, AB is parallel to CD. PAC and PBD are straight lines. Calculate the values of (a) x, (b) y. P y A B x 46o 24o 52 C Answer: D (a) x = ........................................................ [2] (b) y = ......................................................... [3] [Turn over For Examiner’s Use For Examiner’s Use 7 12 (a) (b) Given that a 3 , b 2 , and c 1 , find the value of a b 2 c 3 . Given that x 2 , y 8 and z 4 , find the value of Answer: 6 x 3z . y (a).................................................................. [2] (b).................................................................. [2] 13 (a) Express 126 as the product of its prime factors, giving your answer in index form. (b) Find the smallest positive integer value of n for which 126n is a multiple of 35. (c) The lowest common multiple of 6, 14 and x is 126. Find the 2 possible values of x which are odd numbers. Answer: (a) ................................................................. [2] (b) ................................................................. [2] (c) ................................................................. [2] [Turn over For Examiner’s Use For Examiner’s Use 8 14 Solve the following equations. (a) 3(5m 2) 6 2(4 5m) , (b) 3 4 k 2 3k Answer: (a).................................................................. [2] (b).................................................................. [2] 15 (a) Subtract the sum of (2 x 2 7 x 4) and (5 x 7) from the product of 4 and ( x 2 3 x) . (b) Solve the equation x 1 x 2 x . 3 4 2 Answer: (a).................................................................. [4] (b).................................................................. [3] [Turn over For Examiner’s Use For Examiner’s Use 9 16 The lines AB and CDE are parallel. CDB = 125 and DBE = 102. Giving your reasons, find the values of x A B y 125 C (a) x, (b) y, (c) z. D Answer: 102 z E (a) x =............................................................... [1] (b) y = .............................................................. [1] (c) z = .............................................................. [2] 17 Simplify (a) 2a 3b a 8a 2b , (b) (3 p 2q) (q 3 p) . Answer: (a)................................................................... [1] (b)................................................................... [2] [Turn over For Examiner’s Use For Examiner’s Use 10 18 (a) The sum of three consecutive odd numbers is 237. By forming an algebraic equation, find the largest odd number. (b) Given that 343000 2 x 5 y 7 z , (i) find the values of x, y and z. (ii) Hence, determine the cube root of 343 000. Answer: (a) .................................................................... [3] (b)(i) ................................................................... [2] (ii) ...................................................................[1] 19 3 ropes of different lengths, 240 cm, 318 cm and 426 cm are to be cut into equal lengths with no remainder. (a) What is the greatest possible length of each piece of rope? (b) Hence, find the total number of pieces of ropes that can be obtained. Answer: (a).................................................................... [2] (b).................................................................... [1] [Turn over For Examiner’s Use For Examiner’s Use 11 20 The figure shows a rectangle ABCD where AB is 2 y 8 cm. X is a point on the length DC such that DX is y 7 cm and the perimeter of rectangle is 60 cm. (a) (b) Expressing in term of y, find the length of (i) AD, (ii) XC. Hence, find the area of ABCD if y 3.8 cm. 2 y 8 cm A D y 7cm Answer: B C X (a)(i) AD = ....................................................cm [2] (ii) XC = ....................................................cm [2] (b) ....................................................cm [2] End of Paper [Turn over 12 BLANK PAGE [Turn over