SGSS 4N Prelim 2023 P2 MS

2023 E Math 4NA PRELIM Paper 2 Marking Scheme Solutions 1a 2 321 733 −  + = 4.19 (3sf) 1b 3 47.53 3.25 2.712 4.3 − −+ = -1.4327 = -1.43 2a Mean = fx/ f = (1)(5) + (2)(3) + ……. / 25 = 3.4 2b 6 36025 86.4o  = 3 2160 =24 × 33 × 5 3bi 2160 =24 × 33 × 5 2520 =23 × 32 × 5 × 7 Hcf = 23 × 33 × 5 = 360 3bii 2520 = 23 × 32 × 5 × 7 2520 k = 23 × 32 × 5 × 7 × 2 × 5 × 7 k = 2 × 5 × 7 = 70 4a 3 2 1 45 (5)(3 ) 4(2 1) 20 15 8 4 20 74 20 xx xx xx x +− −+= −−= −= 4b 63 6 3 3 7 49 2 10 7 10×2 49 5 7 xx x x x  = = {keep, change, flip}

Solutions 5a (H,1) (H,2) (H,3) (H,4) (H,5) (H,6) (T,1) (T,2) (T,3) (T,4) (T,5) (T,6) 5bi bii 4/12 = 1/3 3/12 = 1/4 6a a : b 8 : 6 b: c 9 : 3 a : b : c × 3 24 : 18 × 2 18 : 6 a : b : c 24 : 18 : 6 4 :3 :1 6bi ii 5 26 26 / 5 5.2 x x x    x = 5 7ai ii 203000 = 2.03 × 105 0.0001894 = 1.894 × 10-4 7b (5.3×10a) × (2.5×10b) = k × 10n, where 1≤ k <10. = 13.25 × 10a+b = 1.325 × 10 × 10a+b = 1.325× 10a+b+1 n = a+b+1 8a a2 = b2 +c2 - 2bc cos A FH2 = 62 + 72 -2(6)(7) cos 55o FH2 = 36.819 FH = 6.0679 FH = 6.07 (3sf)

Solutions 8b sin sin100º 8.1 12.2 8.1sin100ºsin 12.2 sin 0.6538 40.8º or 180-40.8º= 139.3º(reject) hence angle 40.8º PQR PQR PQR PQR PQR = = = = = 9 100% + 3.5% = 103.5% 103.5% $12 420 1 % $120 100% $12 000 9b 100 (1000)( )(2)50 100 50 20 50 / 20 2.5 PRTI R R R = = = == 9c 5 Total amount = 1 100 3.725000 1 100 29980.149 29980.149 25000 4980.149 4980.15 {2 $. ) n rP I A P decimal place for c  + =+  = =− =− = = 10a B P= (-1)2+(-1)+4 = 4

Solutions 10 ci ii Min point =(-0.5, 3.8) y =7.75 [7.6 to7.8] 10d Draw a line at x = -1 to the curve Gradient = 3 [2.8 to 3.2] 11a c2 = a2 +b2 (Pythagoras thm) XY2 = XN2 +NY2 XN2 = XY2 - NY2 = 82 - 32 = 55 XN = 7.4162 = 7.42 (3 sf) (shown) 11b tan 40º 7.4161tan 40º 7.4161 tan 40º 8.8382 8.84 (3 ) XN NZ NZ NZ sf = = = = = 11c Area =½ ×base× height [for rt-angled triangle] Base YZ = 3 + 8.8382 = 11.838 {don’t use round off values} Area= ½ × 11.838 × 7.4161 = 43.895 = 43.9 cm2 (3 sf) 11d Volume of prism = area ×length = 43.895 × 15

Solutions = 658.45 = 658 cm3 (3 sf) 12a Area pf regular pizza with radius = 22.5/2 = 11.25 cm 𝐴 = 𝜋𝑟2 = 3.142 ( 11.25)2 = 397.659 = 398 cm2 12b Compare Size (area) Area of large pizza = 𝜋𝑟2 = 3.142 ( 15)2 =706.95 Area of personal pizza =3.142 ( 7.5)2 = 176.737 Area of regular piz