BSS 2023 Maths Sec 4E Prelim MS - P2

Broadrick Secondary School Prelims P2 2023 Elementary Mathematics - Secondary Four Express Mark Scheme Qn Mark Scheme 1(a) = 23 (2 8 4)x x x− − + − = 23 2 8 4x x x− + − + = 22 7 7xx− + + 1(b) = 1 2 3 2 (2 3)( 2) x x x x −++ − + = 11 22xx +++ = 2 2x+ 1(ci) = 22( 4) 4 25x− − + = 2( 4) 9x−+ 1(cii) 2( 4)x− is a square number, which makes it always 0 . Hence adding 9 will always make the expression positive for any value of x. 2(a) 90GAO =  (tan ⊥ radius) reflex 126 2AOC =  (  at centre = 2  s at circum.) = 252º 252 180AOE = − = 72º 180 72 2OAE −= (base  s of isos.  ) = 54º 90 54EAG = − = 36º 2(b) EAF = DCF (  s in same seg.) AFE = CFD (vert. opp.  s) FEA = FDC (  s in same seg.)  Triangle EAF and triangle DCF are similar. (AA) 3(ai) DB = 3a – b 3(aii) EC = – 3 4 (3a – b) + 3a = – 9 4 a + 3 4 b + 3a = 3 4 a + 3 4 b

3(b) AD = 4a – (3a – b) = 4a – 3a + b = a + b EC = 3 4 (a + b) = 3 4 AD Since EC = 3 4 AD , they are parallel vectors. Hence EC is parallel to AD. 3(ci) 1 3 3(cii) 3 7 4(a) 100 x 4(b) 100 0.64x+ 4(c) 100 100 4.60.64xx−= + 100( 0.64) 100 4.6( 0.64) xx xx +− =+ 64 4.6 ( 0.64)xx=+ 24.6 2.944 64 0xx+ − = 24600 2944 64000 0xx+−= 28(575 368 8000) 0xx+ − = 2575 368 8000 0xx+ − = (Shown) 4(d) 2575 368 8000 0xx+ − = 2368 368 4(575)( 8000) 2(575)x −  − −= 368 18535424 1150x −= 3.4237x= or 4.0637x=− (rej.) Cost to buy 20 litres of petrol in Jun 2022 = (3.4237 0.64) 20+ = $81.27 (to nearest cents) Jason is incorrect as it will cost $81.27, which is more than $80, to buy 20 litres of petrol in June 2022. 5(a, c, di, dii) Refer to answer behind 5(b) 054º ( )1 5(e) 44 metres ( )1

5(f) 9tan 44 = 1 9tan 44 − =  11.6 = (to 1 d.p.) 6(a) 180 60AED = − (adj.  s on a st. line, equilateral  ) = 120º 180 120 35ADE = − − (  sum of  ) = 25º 9 sin 25 sin 35 AE = 9sin 25 sin 35AE =  = 6.63131 = 6.63 cm (to 3SF) 6(b) AC = 6.63131 + 9 + 5 = 20.631 cm 2 2 217.5 7 20.631cos 2(17.5)(7)ABC +−= 2 2 2 1 17.5 7 20.631cos 2(17.5)(7)ABC −  +−=  = 106.696º = 106.7º (to 1 d.p.) 6(c) Area of triangle ABC = 1 17.5 7 sin106.6962    = 58.7 cm² (to 3SF) 7(a) 231 3 2(5 ) (5 )3 4 3 h = 11 (5)32h= 1 (5)(3)2h= 15 2h= = 7.5 cm (Shown) 7(b) 1 42 5 7.5 EF = 1 20 2 7.5EF = 8 3= cm Volume of empty space = 2 18 (4)33 