1 霹雳怡保培南独立中学 SM POI LAM (SUWA) IPOH MID-YEAR EXAMINATION 2022 MATHEMATICS PAPER 2 DATE: 09 MAY 2022 (MONDAY) TIME: 1405-1535 (1 hour 30 minutes) NAME：______________________ REG NO: _________________ CLASS： J3HE, J3REN, J3PIN Additional materials: Answer Paper INSTRUCTIONS Write your name, register number and class on all the work you hand in. Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. Do not use an erasable pen or correction fluid. Answer all questions. You should use a calculator where appropriate. You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. At the end of the examination, fasten all your work securely together. The number of marks for each question or part question is shown in brackets [ ]. The total mark for this paper is 50. This paper consists of 4 pages, including this cover page. Prepared by ： ………..…………….. (Ms Leow Sook Wan) Checked by： ……………………….. (Mr Ong Eik Hooi) Do Not Turn This Page Until You Are Told To Do So
2 1. (a) (i) Express 2−4 4 2−9 + 4 2−3 as a single fraction in its simplest form. [3] (ii) Hence, solve the equation 2−4 4 2−9 + 4 2−3 = 0. [2] (b) Solve ( − 3) 2 − 16 = 0 [2] 2. (a) Simplify the expressions and leave your answers in positive index notation. (i) (7 2) 0 ÷ (4 3 ) −1 [2] (ii) ( 27 3 ) 2 3 × ( 4 3 ) −1 [3] (b) Given that 27×3 9 −2 = 1 3 , find the value of n. [2] (c) Light travels at a speed of 300 000 000 m/s. (i) Express this speed, in km/h, leaving your answer in standard form. [2] (ii) Taking the distance between the Earth and the Moon to be 4.06 × 105km, find the number of seconds that light takes to travel this distance. [2] 3. (a) James scored 15 more marks for his Geography test than his Mathematics test. 1 4 of his Geography score was less than 1 3 of his Mathematics score. Moreover, the sum of both scores was not more than 178. Given that all test scores are integers, (i) write down the two inequalities to represent the above information, [2] (ii) find the greatest possible score for his Geography test, [1] (iii) find the least possible score for his Mathematics test. [1] (b) Given the inequality −2(+1) 3 < + 3 ≤ 25 − 4, find the range of that satisfy the inequality and represent the solution on a number line. [3]
3 4. A bus commutes passenger to and from Singapore and Kuala Lumpur. (a) On a certain trip, the bus leaves Singapore at 2000 h and arrives at Kuala Lumpur at 0420 h the next morning. Find the time taken, in hours and minutes, for the journey. [1] (b) The fare of an adult ticket from Kuala Lumpur to Singapore is RM23.50 and the child’s fare is RM15.90. Mr Ku boarded this bus with his wife and three children. Given that the exchange rate is S$100 = RM259, calculate the total amount in S$ that Mr Ku has to pay for the family. Give your answer correct to 2 decimal places. [2] (c) The distance between Kuala Lumpur and Singapore is 650 km. (i) If the bus travel from Singapore to Kuala Lumpur at an average speed of x km/h, write down an expression for the time taken, in hours, for the journey. [1] (ii) On the return trip from Kuala Lumpur, the bus increases its speed by 5 km/h. Write down an expression for the time taken, in hours, for the return journey. [1] (iii) If the difference in time between the two journey is 2 hours 45 minutes, form an equation in x and show that it can be reduced to 11 2 + 55 − 13000 = 0 [3] (iv) Solve the equation 11 2 + 55 − 13000 = 0, giving yours answers correct to 2 decimal places. [3] (v) Hence, find the time taken, in hours and minutes, for the return journey. [2]
4 5. Answer the whole of this question on a sheet of graph paper. The following table gives the corresponding values of x and y which are connected by the equation = 19 − 4 − 3 2 x −4 −3 −2 −1 0 1 2 3 4 y −13 4 15 19 12 −1 −45 (a) Calculate the value of and of . [2] (b) Using a scale of 2 cm to represent 1 unit on the x-axis for −4 ≤ ≤ 4 and 2 cm to represent 10 units on the y-axis for −45 ≤ ≤ 25, draw the graph of = 19 − 4 − 3 2 . [3] (c) From the graph, find the maximum value of = 19 − 4 − 3 2 . [1] (d) Use your graph to (i) find y when = −2.5, [1] (ii) find x for which 19 − 4 − 3 2 = 0. [2] (e) (i) On the same axis, draw the line = −3 + 1 for −4 ≤ ≤ 4. [1] (ii) Hence write down the points if intersection of the curve = 19 − 4 − 3 2 and the line = −3 + 1. [2] -End of paper-
