CHIJ SJC 4048_01 AS

Updated as at 11 Aug 2021 4048 4EXP/5NA EM Prelim 2021 CHIJ St Joseph’s Convent Solutions for 4 EXP Elementary Math Preliminary Exam Paper 1 2021 Qn Marking Point 1 6− 2 3 4 12 24 2 3 16 15 3 125 3 xx x x and x x x  −  − −     3, 4, 5 3(i) (2 5)( 2)xx+− 3(ii) [2(2 3) 5][(2 3) 2] (4 1)(2 5) yy yy − + − − = − − 4(a) 332 3 5 4(b) 2 3 2 a b c = = = 4(c) 36 5(i) (2a + 2b)2 = [2(a + b)]2 = 4(a + b)2 = 4(a2 + b2 + 2ab) = 4[(a – b)2 + 2ab + 2ab] = 4[(a – b)2 + 4ab] = 4(196) = 784 5(ii) (2a)2 – (2b)2 = 4a2 – 4b2 = 4(a2 – b2) = 4(a + b)(a – b) Since a > 0 and b > 0, a + b > 0. From (i), (a + b)2 = 196  a + b = 196 = 14  (2a)2 – (2b)2 = 4(a + b)(a – b) = 4(14)(–6) = –336

Updated as at 11 Aug 2021 4048 4EXP/5NA EM Prelim 2021 Qn Marking Point 6 Original area of triangle = ( )( )ACAB2 1 New area of triangle = ( ) )100+1(902 1 ACxAB.  ( ) ( )( ) ( )( ) ( )( )ACAB ACABACABx. 2 1 2 1 - )100+1( 902 1 = 100 125 ( )( ) ( )( )ACAB x.ACAB 2 1 ]1 - )100+1(90[2 1 = 4 5 0.9 + 1000 9x − 1 = 4 5 1000 9x = 4 5 + 0.1 1000 9x = 20 27  x = 9 1000×20 27 = 150 7(i) 14 7(ii) 35 7 12 25 12 37 t t t =− =− = 8(a)(i) 1426 115 15 $186 8(a)(ii) 1426 100115  or 186 10015  $1240 8(b) 1240 1007.50 100%1240 18.75% −  = 9(a)(i) 1 9(a)(ii) 2

Updated as at 11 Aug 2021 4048 4EXP/5NA EM Prelim 2021 Qn Marking Point 9(b) 2 2 2 54 9 1 ()9 1 (54)9 6 k r kF r kF r F F = = = = = 10(a) 'AB 10(b) (i)  (ii)  (iii)  11(a) 168.3 cm 11(b) The key here is that the response should refer to the “change” of the gradient of the graph for female. This can be done explicitly or implicitly. Explicitly mentioning about the steepness of the curve of the graph: • It does no longer go straight up, it straightens out. • The curve levels off. • It is more flat after 12. • The line of the girls starts to even out and the boys line just gets bigger. • It straightens out and the boys graph keeps rising. • You can see the gradient is less. • The rate of change of the graph decreases from 12 years on. • [The student computed the angles of the curve with respect to the x-axis before and after 12 years.] Implicit comparison using the actual amount of growth before 12 years and after 12 years of age: • From 10 to 12 the growth is about 15 cm, but from 12 to 20 the growth is only about 17 cm. • The average growth rate from 10 to 12 is about 7.5 cm per year, but about 2 cm per year from 12 to 20 years. 12(a