YCKSS EM P2 PRELIM MS 2025

1 Yio Chu Kang Secondary School 4E/5N Prelim Mathematics P2 2025 Mark Scheme Qn Solutions Marks Marker’s Comments 1(a) 5 2 3 7 5 2 3 2 3 7 1 5 15 Prime numbers are 2, 3, 5. x xx xx x −  −  −  − −  −   −   M1 M1 A1 Many students did not combine final inequality to 15 x−   . Avoid doing by guess-and-check. Form simultaneous inequalities to solve. Those who simply wrote 2, 3, 5 get a maximum of 2 marks. Some still think that negative numbers and ‘1’ are prime. 1(b) 3 3 5 2 3 33 3 5 2 22 18 3 5 10 18 10 53 12 c d c d ff c d f f c d d cf  = = B2 (deduct 1 m for 1 error) No mark awarded for ‘keep, change, flip’. 1(c) 3 8 4 12 3 4 12 4 48 9 6 16 81 3 2 27 8 y x x y x y −   = = M1 A1 Cannot have a fraction within another fraction. That is not simplified.

2 1(d) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 32 2121 3 2 2 1 21 3 4 2 21 2 21 x xx xx x xx x x x − −− −−= − −+= − −+= − M1 A1 2(2 1) (2 1)(2 1)x x x−  − + Many still get this Sec 2 identity mixed up. 2 (a)(i) 120 32 15 1 5 5 67 68 335 3 15 3 4 5 1 1 0 8      =    = =  T T T M1 A1 1 mark awarded for matrix multiplication without 1 1 1    matrix. (a)(ii) The elements represent the total number of mangoes, apples and oranges sold by seller A and B respectively in 5 days. B1 “Weekdays” not allowed. It is ‘5 days’, “weekday” or “weekend” not mentioned. Total number, not average number. (b)(i) 80 70 0.80 0.70 50 40 or 0.50 0.40 60 50 0.60 0.50        ==          CC B1 (b)(ii) 80 7020 32 15 50 4015 35 18 60 50 4100 3430 41.00 34.30 or 4030 3350 40.30 33.50  =      =       P P A1 for 2 correct elements A2 for 4 correct elements

3 (b)(iii ) Seller A receives a total of $41 while seller B receives $33.50. Seller A made a higher profit. B1 “Total sales/total revenue” not “total selling price” (c) 0.8 0 0 80 70 0 0.9 0 50 40 0 0 1 60 50 64 56 45 36 60 50      =        = N N M1 A1 Many still do not know that the orders of matrices are important for matrix multiplication. 3(a) 17 ( 1)Gradient of 7 ( 2) = 2 1Gradient of 2 1Equation of : 2 Sub (20,3) 13 (20)2 13 1Equation of : 13 2 PR SQ SQ y x c S c c SQ y x −−= −− =− =− + =− + = =− + M1 M1 M1 A1 Error carried forward (ecf) maximum of 2 marks.

4 (b) 22 22 2 [5 ( 4)] (3 ) 15 9 (3 ) 225 (3 ) 144 3 12 or 3 12 9 or 15 Since 0, 15 h h h hh hh hh − − + − = + − = −= − = − =− =− = = M1 M1 A1 281 ( 3) 9 ( 3)!!!hh+ −  + − For example, 81 25 10.3+= correct 81 25 9 5+ = + 14= 3.74= incorrect!!! (c) 2 6 0 26