2017 SNGS Sec 4 EM Prelim P1

3 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn Over Answer all the questions. 1 Solve 5123 x . Answer……………………….. [1] 2 Factorise completely babxax 2323 22  . Answer ………………………….[ 3] 3 Solve the inequalities 3297  x . Answer ................................... [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 how much the farmer has to pay for the fertiliser. [1 litre = 1000 ml] Answer $..................................[2]

4 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 5 (a) Given that 1168  a , find a. Answer (a) 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. Answer (b) k =.…………………….[1] 6 Express as a single fraction in its simplest form )24( 3 )2( 2 2 tt   . . 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. Answer (a) ……… … …….. N[1] (b) …..…… … …… N[1] 8 The initial population of some biological organisms is 600. The population, P organisms, 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. Answer (i) P = …………………… [1] (ii) Find the percentage increase in the population over the first 3 days. Answer (ii) ………………… % [2]

6 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 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? Answer ..… .................................[3] R S 

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 minute. Answer …. ...................................[3] 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. Answer x = …. ..............................[1] (b) What is the special name of the quadrilateral? Justify your answer. Answer ..................................... [2]

8 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 13 The diagram shows a heptagon and a triangle. (a) Find the sum of the interior angles of the heptagon. Answer (a) ................................. [1] (b) Calculate the sum of the angles a, b, c, d, e, f, g, h, i and j in this diagram. Answer (b) ................................. [2] c b a d e f g h i j

9 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn Over 14 (a) Express 4536 as the product of its prime factors. Answer (a) ................................. [1] (b) Given that 34536 pk  , where k and p are integers and p is as large as possible. Find the value of k . Answer (b) ................................. [1] (c) The lowest common multiple of two numbers is 4536. The highest common factor of these two numbers is 189. Given that both numbers are between 189 and 4536, find the two numbers. Answer (c) ……...... .. , ............... [2]

10 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 15 A group of solid cones have equal heights. The mass, M grams, of each cone is directly proportional to the square of its radius, r centimetres. (a) When the radius of the cone is R cm, the mass of the cone is 384 grams. Find the mass when the radius is R4 1 cm. Answer (a) .......................grams [2] (b) One of the cones, A, has a radius 25% more than cone B. Write down the ratio of the mass of cone A to the mass of cone B. Answer (b) ................ : ............. [2]

11 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 [Turn Over 16 In triangles WXZ and XYZ, angle XWZ = 90o, angle WXZ = angle XZY. WX = 5 cm and XZ = 23 cm. (a) Calculate angle WXZ. Answer (a) .........................................[2] (b) Find the shortest distance from X to ZY produced. Answer (b) ................................ cm [2] X Y W 5 cm 23 cm Z

12 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/01 17 The diagram shows a two dimensional frame. It consists of three quarters of a circle of radius 20 cm and centre O. OA, OB, OC, OD and the arc ABCD are made of wire. (a) Calculate the total length of the wire used for the frame. Answer (a) ...............................cm [2] The frame is now bent into a cone by folding the arc ABCD into a circle and joining the radii OA and OD. The cone is used as a framework for a lampshade. (b) Calculate the area of fabric needed to cover the curved surface of the lampshade. Answer (b) ...............................cm2 [2] 20 cm A B O D C B C A D O