2017 SNGS Sec 4 EM Prelim P1 Solutions

3 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over Answer all the questions. 1 Solve 5123 x . 73 x 7 3x Answer.. 7 3x ………………… [1] 2 Factorise completely babxax 2323 22  . )23()23(2 babax  )1)(23( 2  xba )1)(1)(23(  xxba Answer…… )1)(1)(23(  xxba …… [3] 3 Solve the inequality 3297  x . x297  and 329  x 162 x 62  x 8x 3x 83  x Answer (a).... 83  x ............................... [2] 4 A farmer has 1500 tomato plants. He wants to apply 220 ml of liquid fertilizer to each plant. The fertilizer is sold in containers each holding 50 litres and costing $ 235. Calculate the total cost of the fertilizer that the farmer bought. [1 litre = 1000 ml] 0003302201500  ml l330 No of containers = 6.650 330  Total cost = 1645$2357  Answer $1645…………………… [2]

4 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over 5 (a) Given that 1168  a , find the value of a. 043 222   a 043  a 4 3a Answer (a) 4 3a …………… [2] (b) Mercury is the fastest planet with an orbital speed of .km/h1072.1 5 Neptune is the slowest planet with an orbital speed of .km/h1095.1 4 Given that the orbital speed of Mercury is k times of the orbital speed of Neptune, find the value of k. Give your answer to a sensible degree of accuracy. 82.8 1095.1 1072.1 4 5    or 8.8 or 9 Answer (b) ……… 8.82 or 8.8 or 9……………… [1] 6 Express as a single fraction in its simplest form )24( 3 )2( 2 2 tt   )24( 3 )2( 2 2 tt   )2(2 3 )2( 2 2    tt 2)2(2 )2(34   t t 2)2(2 23   t t 2)2(2 23   t t Answer...……………………… [3]

5 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over 7 The mean weight of five rocks on Earth was 3.462 N. The standard deviation of the weights of the five rocks was 0.0683 N. The five rocks were then weighed on the Moon. The weights of the five rocks on the moon were 16.5% of their weights on Earth. For the weights of the five rocks on the Moon, find (a) the mean, (b) the standard deviation of the weights. (a) Mean weight = 3.462 × ଵ଺.ହ ଵ଴଴ = 0.571 (3sf) (b) Standard Deviation = 0.0683 × ଵ଺.ହ ଵ଴଴ = 0.0113 (3sf) Answer (a) …… 0.571………………… N[1] (b) … 0.0113…………………… N[1] 8 The initial population of biological organisms is 600. The population after t days is given by the formula P = 600  t21.3 . (i) Calculate P when t = 3. Give your answer correct to the nearest whole number. P = 600  321.3 =19845.6 Nearest whole number = 19846 Answer (i) ……… 19846……………… [1] (ii) Find the percentage increase in the population over the first 3 days. %100600 6006.19845  or %100600 60019846  = 3207.6% = 3210% (3sf) = 3207.6% = 3210% (3sf) Answer (ii) ………… 3210…………… % [2]

6 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over 9  = {all triangles} R = {right-angled triangles} S = {isosceles triangles} A is a triangle with angles 45 , 45 and 90 . B is a triangle with sides 6 cm, 6 cm and 3 cm. C is a triangle with sides 3 cm, 4 cm and 5 cm. On the Venn Diagram below, write A, B and C in the appropriate subsets. [3] 10 Ahmed , Baz and Colin share a bag of Jelly sweets. Ahmed takes 8 3 of the Jelly sweets. Baz takes 70% of the remaining Jelly sweets and Colin takes the other 12 Jelly sweets. How many Jelly sweets are in the bag altogether? Let x be the jelly sweets. Ahmed has x8 3 of sweets. Baz has xx 16 7 8 5 10 7      Colin has xxx 16 3 16 7 8 31  1216 3 x 64x Answer ............. 64x ..................[3] R S  C B A

7 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over 11 Roger can assemble 7 toy cars in 5 hours. Paul can assemble 8 toy cars in 6 hours. Roger and Paul work together to assemble a total of 20 toy cars. If they continue to assemble at the same rate, how long will it take them to assemble the 20 toy cars? Give your answer in hours and minutes, to the nearest minutes. In 1 h Roger will assemble 5 7 toys In 1 h Paul will assemble 6 8 toys Time taken for both to assemble 20 toys = 41 137 6 8 5 7 20        h = 7h 19 mins Answer ...7h 19 mins .................[3]

8 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn over 12 Sally is drawing a quadrilateral ABCD such that AB is parallel to DC. The angles, in degrees, of the quadrilateral are angle DAB = 10x + 70, angle ABC = 61  3x, angle BCD = 56 + 12x and angle ADC = 6x  2. (a) Calculate the value of x. (a) 180267010  xx (int. s, AB parallel DC) 7x Answer(a) x = ..........7....................[1] (b) What is the special name of the quadrilateral? Justify your answer. The quadrilateral is a parallelogram (opposite angles are equal)  DAB =  BCD = 140 ADC =  ABC = 40 Or DAB +  ABC = 180 ( sum of interior angles in parallel line) AD // BC Answer ................................. [2]