2018 XMS EOY 1E

XMS 2018 EOY 1E Section A (40 marks) Answer all the questions in this section. 1. Evaluate     4 3 32 71.9 406 23.5   and correct your answer to 4 significant figures. Answer ..…………………………[1] 2. (a) Solve the inequality 1 32 x  . Answer (a) …..…………..……………………………[1] (b) Hence, state the largest value of x, given that x is a perfect square. Answer (b) x = ………..……………………………[1]

2 3. Write down, from the following list, 37, 1.4, 4, 1, 27 (a) the prime number(s), Answer (a) ……………………..……………………………[1] (b) the rational number(s). Answer (b) ……………………..……………………………[1] 4. Consider the sequence –20, –13, –6, 1, 8, …. (a) Write down, in terms of n, a formula for the nth term of the sequence. Answer (a) ……………….……………………………[1] (b) Hence explain why 100 is not a term in the sequence. Show your working clearly. Answer …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… ………………………………………………………………………………………………… [1]

3 [Turn over 5. It is given that 522 5 7a   and 322 5 7b   . (a) Find the highest common factor of a and b. Answer (a) ……………………………[1] (b) Find the smallest positive integer m such that am is a perfect cube. Answer (b) m = …………………………[1] 6. (a) Find the gradient of the line L1. Answer (a) ..….……………………………[1] (b) Hence state the equation of L1. Answer (b) ….……………………………….[1] – 8 y x 4 O L1

4 7. A cyclist starts cycling at a speed of 120 m/min at 9.15 am. (a) Convert 120 m/min into km/h. Answer (a) ………………………… km/h [1] (b) If the cyclist increases his speed by 0.8 km/h, he would be able to complete his journey at 10.45 am. Find the distance covered by the cyclist. Answer (b) ………………………… km [1] 8. Given that 23ab and : 4 : 5bc  , find a : c. Answer a : c = ……………… : ……………… [2]

5 [Turn over 9. The width of a rectangle is x cm and the length is 2x cm. If the length is increased by 10% and the width is decreased by 20%, determine if there is a percentage increase or decrease in the area of the rectangle and find this percentage. Answer There is a percentage ………………………… of ………………………….%. [3] 10. Solve 2 5 2 74 xx x   . Answer x = …………………………… [3]

6 11. Three alarms sound at regular intervals of 12 seconds, 45 seconds and 60 seconds respectively. If all three sound together at 8.30 am, find the total number of times they will sound together by 9.45 am. Answer ……………………………[3] 12. (a) Factorise 2 3 236a mn a m n completely. Answer (a) …….……………………………[1] (b) Expand and simplify  1 12 3 2 53 xx   . Answer (b) ………………………………[2]

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