[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) 35 (Angle at centre = 2 angle at circumference) B1 6a(iii) 55 (OS = OR, sum of angles in isos triangle) B1 6a(iv) Angle SRQ = 180 − 80 (angles in opp segment) = 100 Angle ORQ = 100 − 55 = 45 M1 A1 6a(v) Angle OSR = 55 Angle SRQ = 100 Since Angle OSR + Angle SRQ  180, Angle OSR + Angle SRQ are not interior angles of parallel lines lines OS and QR are not parallel. M1 A1

4 6b(i) 2 3 4 1 19 2 3 4 1 18 2 22 6 2 19 20 4 22 132 44 380 76 56 366 6( ) nn n n n n n nn n n shown + + − =+ + − + − + =+ + = + = = M1 A1 6b(ii) 15 14 105 44 43 946= M1, A1 12 7(a) 24 cm B1 7(b) 18 10 24 r = r = 17 2 (shown) M1 A1 7(c) Surface area = SA of hemisphere + SA of cone = 2(10)2 + 26(10) – (7.5) 2218 7.5+ = 986 cm2 M1: 2(10)2 M1: 2218 7.5+ A1 7(d) Volume = Vol of hemisphere + Volume of frustrum = 322 37 1(10) (10) 243 64 3 +   = 3550 cm3 M1: 32 (10)3 M1: 21 (10) 243  A1 9 8(a) −2.5 B1 8(b) Smooth curve passing through all points 5 or less points marked correctly; All points marked correctly G1 P1/2 8(c) x > 2.8 [0.2] B1 8(d) Gradient = 3.2 ( 1) 3 1.7 −− − = 3.23 B1: Tangent on graph A1 8e(i) y = x – 1 drawn on grid B1 8e(ii) 3 3 3 3 2 12 4 3 02 8 6 0 ( ) x xx x x x x shown − + = − − + = − + = M1 A1 8e(iii) 0.8; 2.25 [0.1] B2 12

5 Question 8 Mark Scheme 2 - 3 - 4 - 5 - 6 - −3 −2 −1 1 2 3 0 1 - −1 - −2 - x y        3 322 xyx= − + y = 5 (3, 3,2) (1.7, −1) y = x – 1

6 Question 9 Mark Scheme Qn Solutions Marks Allocation 9a(i) Correct construction B1 Scale: 2 km | | X • Y •

7 9a(ii) 21 B1 9a(iii) Correct construction B1 9a(iv) 24 & 26 B1 9(b) Renting from GetCar Car rental & mileage charges = ($74) + ($0.3967) = $54.13 Renting from FindCar Car rental & mileage charges = ($31 + $53) + ($0.3967) = $44.13 Amount of petrol needed = 67 12.5 = 5.36 litres Fuel Charges = $2.20  5.36 = $11.792 Total charges = 44.13 + 11.792 = $55.92 > $54.13 Since it costs less to rent from GetCar, Sally should rent from Company GetCar. M1: 74 M1: 0.3967 M1: $31 + $53 M1 M1 A1