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]

7 [Turn over 8 cm h cm 6 cm 10 cm 13. (a) The diagram below shows a parallelogram. Find the value of h. Answer (a) h = ……………………………… [2] (b) The area of the trapezium shown below is 240 cm2. Given that AE = 12 cm and AB = 14 cm, find the length of CD. Answer (b) CD = …………………………… cm [2] B A D C E 12 cm 14 cm

8 14. (a) It is given that     26 3 4a a p p a    . Without using the calculator and showing your working clearly, find the value of p when 2a . Answer (a) p = …….……………………………[2] (b) In the diagram below, ABCD is a rhombus. It is given that 116ABC   . Find ACD . Answer (b) ACD = ………………………° [2] B A D C 116°

9 [Turn over 15. (a) The interior angle of a regular n-gon is 144 . Find the value of n. Answer (a) n = …….……………………………[2] (b) A polygon has four interior angles each of size 152 , six exterior angles each of size 23 and the remaining exterior angles are each of size 22 . Find the number of sides of the polygon. Answer (b) ……………………… [3]

10 Section B (40 marks) Answer all the questions in this section. 16. The table below shows part of the income tax rates in Singapore for the year 2017. Chargeable Income Income Tax Rate (%) Gross Tax Payable ($) First $20,000 Next $10,000 0 2 0 200 First $30,000 Next $10,000 - 3.50 200 350 First $40,000 Next $40,000 - 7 550 2,800 First $80,000 Next $40,000 - 11.5 3,350 4,600 First $120,000 Next $40,000 - 15 7,950 6,000 In 2017, Mr Tan earned a gross annual income of $110 400. He was eligible for the following relief: personal relief of $3500, a wife relief of $2000, a child relief of $4200 for each child, CPF contributions of $23 000 and donation of $1500 to charitable organisations. Based on the income tax above, find his income tax payable for the year 2017 if he is married with 2 children. [2]