BSS 2023 Maths Sec 4E Prelim MS - P1

Broadrick Secondary School Prelims P1 2023 Elementary Mathematics - Secondary Four Express Mark Scheme Qn Mark Scheme 1(a) 31.764 1(b) 32 2(a) 681p 2(b) 7 3(a) A 3(b) D 4 The vertical axis of the bar chart does not start from zero. From the bar chart, it seems like the exchange rate for MYR is more than double for every 1 Singapore dollar in 2022 as compared to 2018. However, by calculation, the increase is only about 7%. 5 1st equation: 8 y ax=− + 23 56 xy+ = 2 3 30xy+= 3 2 30yx=− + 2nd equation: 2 103yx=− + By comparison, 2 3a= . 6 7(a) 223 = 12 7(b) 2 2 22 3 5m=   = 900 8(a) 31 x−  + and 51 2 xx −+ 31 x− −  2 2 5xx+  − 4x− 33x 1x Solution: 41 x−   8(b) Depth (cm) Time (s) – 4 – 3 – 2 – 1 0 1

9 (3 1) 2(1 )p q q− = + 3 2 2pq p q− = + 3 2 2pq q p− = + (3 2) 2q p p− = + 2 32 pq p += − 10(a) 10(b) x = – 1 11 28 23 (3 )(3 )x x x+=+ − + 2(3 ) 8 2( 3)(3 ) x xx −+ =+− 26 2 8 2(3 9 3 )x x x x− + = − + − 214 2 2 18xx− =− + 22 2 4 0xx− − = 2 20xx− − = ( 1)( 2) 0xx+ − = 1x=− or 2x= 12 Volume of remaining cube = 21110 10 10 32 xx  −    31987.652 1000 6 x=− 31 1000 987.6526 x =− 3 6(12.348)x = 3 74.088x= 4.2x= 13(a) 225( 2 )( 2 )y x y x= + − 13(b) 3 ( 2 ) ( 2 )a x y b x y= − − − ( 2 )(3 )x y a b= − − 14 A : B : C 1.5 : 1 1 : 0.9 15 : 10 : 9 Box A : Box C 15 : 9 O y x 1 (-1, 2)

15 50YXZ =  (vert. opp.  s) 90XZY =  (adj.  s on a st. line) 180 90 50XYZ = − − (  sum of  ) = 40º 180 40XYC = − (adj.  s on a st. line) = 140º EDC = (5 2) 180 5 − = 108º 180 108 2ECD CED − = = (base  s of isos.  ) 36= º 180 36 140CEY = − − (  sum of  ) = 4º 16(a) 6 4 0 4 8 6 y x −− =−− (Grad. of AB and DC) 1 32yx=− + --- (1) 4 0 6 8 6 4 y x −− =−− (Grad. of AD and BC) 6 2 8yx− = − 22yx=− --- (2) Sub (2) into (1), 12 2 3 2xx− =− + 4 4 6xx− =− + 5 10x= 2x= When x = 2, from (2), y = 2 Coordinates of D = (2, 2) (Also accept use of vectors or mid-points) 16(b) Length of AB = 22(6 4) (4 8)− + − = 20 cm OR Length of CD = 22(2 0) (2 6)− + − = 20 cm Length of BC = 22(4 0) (8 6)− + − = 20 cm OR Length of DA = 22(6 2) (4 2)− + − = 20 cm Since ABCD is a parallelogram a