Serangoon Garden 4E5NA E Maths Prelim P1 2021 MS

SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 Serangoon Garden Secondary School 2021 Sec 4E/5NA Prelims P1 Suggested Mark Scheme Qn Solution Mark Scheme 1(a) B1 (b) 10.199 = 10.2 (3 s.f) B1 Total for Q1 2 m 2 US$5.40 = S$ US$5.40 = S$7.182 Cost of 1 litre of petrol in Los Angeles in terms of S$ = S$ = S$ = S$ 1.894 = S$1.89 ˂S$1.98 M1 Hence, petrol in Los Angeles is cheaper than Singapore. A1 Total for Q2 2 m 3(a) B1 B1 (b) Total for Q3 2 m 4 Amount of energy produced in 2020 = watts M1 watts = watts = watts (exact answer and should not be rounded off) A1 Total for Q4 2 m 5 ( is an isosceles triangle as OA = OP) M1 ( is bisected) Hence, . Since , OP is parallel to AB. A1 Total for Q5 2 m 6 Let the largest angle be .

2 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 M2 110.48º 110.5º A1 Total for Q6 3 m 7(a) 1: 50 000. 1 cm: 50 000 cm 1 cm: 0.5 km 12 cm: 6 km The actual distance between the two towns is 6 km. B1 (b) 1 cm: 0.5 km 1 cm2 : 0.25 km2 M1 72 cm2: 18 km2 The area of the theme park on the map is 72 cm2. A1 Total for Q7 3 m 8(a) m B1 (b) Distance the diver is below the sea level = Distance the diver is from the sea bed = B1 Total for Q8 2 m 9(a) B1 (b)(i) LCM = B1 (ii) is a perfect square as the power of each of its factor is even for all B1 values of . Total for Q9 3 m 10(a) M1 A1 (b) The minimum point is B1

3 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 (c) The graph will not cut the -axis as the minimum point is above the -axis. B1 Total for Q10 4 m 11(a) Initial amount of water = 9 litres B1 (b) Gradient = or M1 Equation is A1 Total for Q11 3 m 12(a) Let the original price of the washing machine be $ M1 The original price of the washing machine is $2600. A1 (b) Discount (%) = M1 = = 51% Hence, Jamie is incorrect as he is given only 51% discount and not 60% discount. A1 Total for Q12 4 m 13(a)(i ) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} = {integers : ˃ 5} = { ˃ 1}= {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} B1 – Set B proper subset of set A B1 – Correct placement of 4 4, 6, 8, 9, 10 B 2, 3, 5, 7, 11 A

4 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 the members of each set (a)(ii) n ( ) = 5 B1 (b) B1 Total for Q13 4 m 14(a) M1 = or A1 (b) M1 A1 OR [M1] [A1] Total for Q14 4 m 15(a) M1 0, 1

5 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 or A1 OR [M1] or [A1] (b) OR M1 A1 Total for Q15 4 m 16(a) B1 (b)(i) B1 (ii)

6 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 M1 When , The new pressure is 24 N/cm2. A1 Total for Q16 4 m 17(a) B1 B1 (b) Interquartile range = 80.5 - 68.5 = 12 B1 Total for Q17 3 m 18(a) Median speed = 62 km/h B1 (b) B1 (c)(i) = 8 B1 (ii) Standard deviation = 15.216 = 15.2 km/h B1 Total for Q18 4 m 19(a) Total amount to be received by Keith = $ M1 Interest earned by Keith = $ - $8000 = $1009.299

7 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 = $1009.30 (correct to 2 d.p) A1 19(b)(i) Method 1 15% of annual pay = $936 + 12% of annual pay 3% of annual pay = $936 M1 100% of annual pay = $31200 Linda’s monthly pay = = $2600 A1 Method 2 Let x be Linda’s current annual pay. [M1] Linda’s monthly pay = = $2600 [A1] (b)(ii) Pamela’s pay is > $2600 whereas Hafiz’s pay is < $2600. B1 (OR Pamela’s pay is greater than Linda’s pay and Hafiz’s pay is lesser than Linda’s pay. / The $936 for Hafiz is more than 3% of his salary, whereas for Pamela, the $936 is less than 3% of her salary.) [B1] Total for Q19 5 m 20(a) or 0.4 radian B1 (b) Method 1 Area of = M1 Area of circle = = M1 Area of shaded region = M1 = 27.502 cm2 = 27.5 cm2 A1 Method 2

8 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 Area of sector = [M1] Area of = [M1] Area of shaded region = [M1] = 27.5 cm2 [A1] Total for Q20 5 m 21(a)(i) 8 units3 – 240 seconds 1 units3 – 30 seconds B1 (a)(ii) B1 for the correct shape of graph and passing through(0, 0), (30, 0.5h) and (240, h) (b) Let the slant height be cm , M1 Surface area in contact with water = = M1 = 330.67 cm2 = 331 cm2 A1 Total for Q21 5 m 22(a) (corresponding angles) B2 (any of the three reasons) (corresponding angles) (common angle) Hence, and are similar. (AA Similarity Test)

9 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P1 (b) B1 (c)(i) area of : area of = = = : 25 B1 (ii) area of : area of quad = 4: 21 area of quadrilateral = =42 cm2 B1 Total for Q22 5 m