2017 XMS EOY 1E

2017 XMS EOY 1E Section A (40 marks) Answer all the questions in this section. 1. Evaluate 2 2 3 3 930.25 5 10.5 3   and correct your answer to 1 significant figure. Answer ..…………………………[1] 2. Arrange 3.103 , 10331000 , 3, 3.1 in ascending order. Answer ….………, …………, …………, ………… [1] 3. (a) Solve the inequality 65 y  . Answer (a) …..…………..……………………………[1] (b) Hence if y is a perfect cube, state the smallest value of y. Answer (b) y = ………..……………………………[1]

2 4. In June 2011, James placed a sum of money in an investment fund that pays simple interest at a rate of 2.8% per annum. By the end of June 2015, James had earned a total interest of $5376. Find the amount of money James put in the investment fund in June 2011. Answer $ ..………………… [2] 5. It is given that 42 3 5p   and 32 5 11q   . (a) Find the smallest positive integer m for which pm is a multiple of q. Answer (a) m = …………………………[1] (b) Find the smallest positive integer n for which pn is a whole number. Answer (b) n = …………………………[1]

3 [Turn over 6. Consider the sequence 24, 17, 10, 3, 4, …. (a) Write down an expression, in terms of n, for the nth term of the sequence. Answer (a) …….……………………………[1] (b) Hence explain why 700 is not part of the sequence. Show your working clearly. Answer …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… ………………………………………………………………………………………………… [1] 7. Given that 10 6 2 9 8 5 xy xy   , find the ratio of x : 2y. Answer x : 2y = ……………… : ………………[3]

4 8. A rectangular tray of brownie measures 48 cm by 20 cm by 8 cm. It is to be cut into small cubes of identical size such that there is no leftover. (a) Find the largest possible length of each cube. Answer (a) ………………………… cm [2] (b) Hence, find the total number of cubes obtained. . Answer (b) …………………………[1]

5 [Turn over 9. Solve  5 7 3 642 x x   . Answer x = …….……………………………[3] 10. Using a computer software, Sam drew a triangle that had a base thrice that of its height, h cm. He then enlarged his original triangle such that the area of the triangle increased by 20%. Given that the area of his enlarged triangle was 115.2 cm2, calculate the value of h. Answer h = …………………………… [3]

6 11. (a) Factorise    2 2 4 2a b b   completely. Answer (a) …….……………………………[1] (b) Expand and simplify  13 4 5 2 42xx   . Answer (b) ……………………………[3] 12. The radius of a wheel of a unicycle is 0.2 m. A clown cycles at an average speed of 9 km/h during a performance. (a) Convert 9 km/h into m/min. Answer (a) ………………………… m/min [1] (b) Find the number of revolutions made by the wheel in 40 minutes, giving your answer correct to the nearest whole number. Answer (b) …………………………[3]

7 [Turn over 13. In the diagram below, ABCF is a trapezium and CDEF is a parallelogram. AB = 5 cm, AG = 4 cm and AFE is a straight line. The ratio of the height of the parallelogram to the height of the trapezium is 3 : 2. The area of the trapezium is half the area of the parallelogram. (a) Find the height of the parallelogram. Answer (a) …….……………………… cm [1] (b) Find DE. Answer (b) …………………………… cm [3] A B C G F D E 5 cm 4 cm

8 14. (a) If    4 2 1 3 2ax a x    , find the value of a when 3x . Answer (a) a = …….……………………………[3] (b) A piece of wire is 2 m long. Alvin cut it into three pieces. One piece is 34 21 y m and the other is  2 4 5 7 y m long. Express the length of the remaining piece, in terms of y, and as a single fraction. Answer (b) …………………………… m [3]

9 [Turn over Section B (40 marks) Answer all the questions in this section. 15. 120 students were surveyed to find out which of the three modes of transport the students prefer to use to travel to school. Their choices are presented in the pie chart shown below. (a) Find the value of x. [2] (b) Find the number of the students who go to school by car. [1] 66° Walk Bus (2x + 14)° Car 84°

10 16. In the diagram below, PQR is a straight line and TQ is the angle bisector of PQS . 72PTQ   ,  2 16PQT b    ,  33TQS a    ,  4 20QRS c    , PT // QS and QT // RS. Find, stating the reasons clearly, the values of a, b and c. [3] (2b16)° Q P T R 72° (3a+3)° (4c20)° S