[Tampines] [2023] 4E EM 4052 Prelims P2_MS

1   A B  Tampines Secondary School 2023 Sec 4E/5N Mathematics 4052/02 Preliminary Examination Mark Scheme [√ means follow through] Total Marks : 90 Qn Solutions Marks Allocation 1a(i) 5 B1 1a(ii) 2 2 2 2 64 64 64 ( ) 64 64 qrp q qrp q p q qr q p r q pr −= −= =− += = + M1: Sq both sides M1: Remove fraction A1 1(b) 54 266 54 266 1 26 1 12 2 5.5 xx xx x x x +=−− −=−− =− =− = M1: Combine fraction M1: Remove fraction A1 1(c) 503 7 6 3 41 133 39 41 xx x x −  + − − M1 A1 1c(i) • | x 39 41− B1 1c(ii) 0 B1 11 2a(i) 1 2 6 3 5 4 8 7 9 10 B1

2 2a(ii) 1, 6, 8, 9, 10 B1 2a(iii) n(A) = 4. If C is a proper subset of A, the number of elements in C must be less than 4. Hence Anthony’s claim in not valid. B1: soi n(A) = 4 B1: soi n(C) <4 2b(i) a = 20, b = 26 B2 2b(ii) 6n + 2 B1 2b(iii) 6n + 2 = 2258 n = 376 No. of squares = 1128 M1 A1 9 3a(i) 5.985  106 B1 3a(ii) 5985000 8150.6734.3 = = 8.2  103 M1 A1 3(b) Value in 2022 = 84 20000 $16800100= Value in 2021 16800 100%120= = $14 000 M1 M1 A1 3(c) If exchange in Singapore Amount of RM= 3350 If exchange in Malaysia Amount of RM = 1000 10033.5 = 2985.07 Since RM 3350 in Singapore > RM2985 in Malaysia, I do not agree with Mrs Raj. A1 M1 A1 9 4a(i) 8 6PR = PR = 10 units M1 A1 4a(ii) 11 2 23 9 1 PQ PO OQ PO OP =+    =+       −= M1 A1 4b(i) 3 : 2 B1 4b(ii) 2a + 4b A1 4b(iii) AE AB BE=+ 8a + 4b = 6a + BE

3 BE = 2a + 4b = AD Hence ABED forms a parallelogram. A1 4biv(a) 1 : 2 B1 4biv(b) 3 : 2 B1 9 5a(i) 60 minutes B1 5a(ii) 72 minutes B1 5a(iii) 76 – 66 = 10 minutes M1 A1 5(b) 12.5%  200 = 25 boys n = 80 M1 B1 5(c) The cumulative frequency would be shifted to the left by 5 minutes. B1 5(d) Secondary 1 Girls Median = 62 minutes Interquartile range = 7 minutes 1. The girls took a shorter time to complete the task as compared to the boys because the girls’ median at 62 minutes is shorter than then boys’ median at 72 minutes. 2. The time taken by the girls to complete the task is more consistent because the interquartile ranges for the girls at 7 minutes is shorter than the boys’ at 10 minutes. B1 B1 9 6a(i) Angle STU = 80 (Angles in the same segment) Angle TUS = 180 − 60 − 80 (Sum of angles in triangle) = 40 B1 B1 6a(ii) 3