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