CCHM 4048_02 AS

2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2022 SECONDARY 4 MATHEMATICS 4048/02 Paper 2 Wednesday 31 August 2022 Candidates answer on the Question Paper 2 hours 30 minutes This document consists of 23 printed pages and 1 blank page. Solutions

2 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 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 = f fx   Standard deviation = 22        −  f fx f fx 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 −+=

3 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over [Turn over for Question 1]

4 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 1 (a) Express as a single fraction in its simplest form ( )31 68 xx −− . Answer …………………………………….. [2] (b) Simplify 1 6 3 9 27b w −   . Answer …………………………………….. [2] (c) Simplify 2 2 5 12 4 25 20 4 pp pp −+ −+ . Answer …………………………………….. [3] ( ) ( ) 31 68 914 24 24 4 9 9 24 95 24 xx xx xx x −− −=− −+= −= ( )( ) ( )( ) 2 2 5 12 4 25 20 4 2 5 2 5 2 5 2 2 52 pp pp pp pp p p −+ −+ −−= −− −= − 1 3 1 6 3 9 1 9 3 6 3 2 3 2 27 27 27 3 b w w b w b w b −   = = = 95 24 x− 3 23 w b 2 52 p p − −

5 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 [Turn over (d) Solve the equation 31 122xx +=−− . Answer …………………………………….. [3] 31 122 31 122 2 12 22 4 xx xx x x x +=−− −=−− =− −= = ( ) ( )( ) ( )( ) 2 2 31 122 3 2 2 122 6 3 2 4 4 6 8 0 4 2 0 4 or 2 (rej. 2) xx xx xx x x x x xx xx x x x +=−− − + − =−− − + − =− + − − + = − − = = =  Alternative 4x=

6 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/02 2 A is the point (−5, −2) and B is the point (−1, 3). (a) Find the distance between point A and point B. Answer ……………………………….. units [2] (b) Line p passes through point A and point B. Show that the equation of line p is 4 5 17yx=+ . Answer [3] ( )( ) ( ) 2 2 distance 5 1 2 3 16 25 41 6.40 units (3 s.f.) AB= − − − + − − =+ = = ( ) ( ) 32gradient 15 5 4 −−= − − − = ( )( ) ( ) equation: 531 4 531 4 4 12 5 5 4 5 17 (shown) yx yx yx yx − = − − − = + − = + =+ Alternative equa