CCHM 4048_01 AS

[Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2022 SECONDARY 4 MATHEMATICS 4048/01 Paper 1 Wednesday 14 September 2022 Candidates answer on the Question Paper. 2 hours This document consists of 17 printed pages and 1 blank page. _________________________ Parent’s Signature Solutions

2 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = nrP      + 1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin == Acbcba cos 2 222 −+=   f xf 22      −     f xf f xf

3 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 [Turn over Answer all the questions. 1 Evaluate 3 9.45 36.03 26.9  − , correct to 3 significant figures. 3 9.45 36.03 18.931... 26.9 18.9 (3sf)  =− − =− Answer ................................... [1] 2 Simplify 22 16 12 32 18 ab ab − − . 2 2 2 2 16 12 4(4 3 ) 32 18 2(16 9 ) a b a b a b a b −− =−− 4(4 3 ) 2(4 3 )(4 3 ) ab a b a b −= +− 2 43ab= + Answer ................................... [2] 3 Ken drives at an average speed of 85 km/h on the expressway for the first stage of his journey. After exiting the expressway, he continues to drive at an average speed of 60 km/h on the city roads for the second stage of his journey. If the average speed of his entire journey is 75 km/h , find the ratio of the time taken for the first stage of his journey to the time taken for the second stage of his journey. Let time taken for first and second part of journey be x and y hours respectively. total distance travelled = (85 60 ) km, to tal time = ( ) hoursx y x y++ 85 60 75xy xy + =+ 85 60 75( )x y x y+ = + 85 60 75 75x y x y+ = + 10 15xy= 3 2 x y = Ratio = 3: 2 Answer ................................... [2] 4 Factorise completely 22 3 12 8x x y xy+ − − . 22 3 12 8x x y xy+ − − (2 3) 4 (3 2 )x x y x= + − +