Serangoon Garden 4E5NA E Maths Prelim P2 2021 MS

SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 Serangoon Garden Secondary School 2021 Sec 4E/5NA Prelims P2 Suggested Mark Scheme Qn Solution Mark Scheme 1(a) M1 (for “×”) B1 1(b) M1 (base 3) A1 1(c) or M1 (remove denominator) A1 1(d) M1 for M1 for A1 1(e) M1 Correctly eliminate 1 variable. A1, A1 Total for Q1 12 m

2 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 2(a) B1 2(b) B1 2(c)(i) M1 Accept mix number or improper fraction M1 remove denominator A1 2(c)(ii) B1 B1,B1 2(c)(iii) M1 Sub 26.563858 into correct expression A1 Total for Q2 10 m

3 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 3(a)(i) B2 Minus 1 mark for each error. 3(a)(ii) P(sum more than 5) = M1 For A1 3(b) Let x be the initial no. of green balls Possible no. of initial green balls is 5. M1 M1 remove denominator correctly M1 A1 Total for Q3 8 m

4 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 4(a) See Graph Paper B1 All points plotted correctly B1 All points joined B1 Smooth Curve 4(b) By drawing the line , the equation only has 1 solution because the line cuts the curve only at 1 point. M1 Draw A1 “Line cuts curve at only 1 point” 4(c) Mathematically calculated gradient = 1.25. Based on points selected, sub points into gradient formula and calculate. M1 Draws acceptable tangent at A1 (mark base on points chosen) Cannot give marks if negative gradient. 4(d)(i) See Graph Paper B1 Cuts y-axis at 1 Or correct table of values B1 4(d)(ii) x = −2.3, −0.6 and 2.9 But mark based on the graph drawn. B1 4(d)(iii ) M1 Line = curve A1 4(e) Mathematically calculated answer = But mark based on drawing a parallel tangent o the curve. B1 Total for Q4 13 m

5 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 5(a) B1 5(b) M1 for A1 5(c) T represents the total cost to make caramel and strawberry cakes for the whole week respectively. B1 5(d)(i) Cakes sold = = M1 for A1 5(d)(ii) Selling price = Sales = = Profit = Total Profit = 273 + 231 = $504 M1 A1 Total for Q5 8 m

6 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 6(a)(i) 49 B1 6(a)(ii) B1 6(a)(iii) Let Since n is not an integer, 256 is not part of the sequence. M1 A1 “Not an integer” 6(b) 4th term = 25 8th term = 49 Volume of Cone B = M1 for square root M1 for cube A1 Total for Q6 7 m 7(a) Area M1 Sector M1 Triangle M1 attempts to do (sector – triangle) A1 7(b) M1 M1 M1 (OM ÷ AM) A1 Total for Q7 8 m 8(a)(i) Angle ABD = 90o (angle in semi circle) Angle ADB (angle sum of triangle) M1 A1 8(a)(ii) Angle EOF M1 A1

7 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 (Base angles of isosceles triangle) 8(a)(iii) Angle ECF (angle at centre = 2 angle at circumference) B1 8(b) M1 A1 Total for Q8 7 m 9(a) M1 (uses Pythagoras) M1 A1 9(b) Let L be the slant height of pyramid M1 M1 (attempts to add square + 4 triangles) A1 9(c) Volume of Pyramid Volume of lower part Volume of upper part Height of upper part Total height = 4 + 1.04124 = 5.04 cm M1 M1 M1 M1 A1 Total for Q9 11 m

8 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 10(a) M1 A1 10(b)(i) Let x be be the shortest distance from C to AB Error carry forward for entire 10(b) M1 (sine rule usage) M1 (for AC) A1 10b(ii) Let G be the position of the guest when he is nearest to C. The spotlight needs to bend the most (41.4749o) when the guest is nearest to C and needs to be 48.5251o Since can be as small as 45 o, the spot light can reach the guest at all times. M1 (find depression) M1 (find ) A1 (compares 45o to the required 48.5o.) Total for Q10 8 m

9 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 11(a) Angle AOC (reflex) = 241.2 (angle at center = twice angle at circumference) Angle AOC = M1 M1 (trigo ratio) A1 11(b) M1 A1 11(c) Speed (km/h) 🡪 Speed (M/min) 4.5 km / h 5.0 km / h 4.0 km / h 3.5 km / h Since distance of walkway is 59.8 m, the speed of the shoppers must be able to cover at least 59.8 m per min. John should avoid 5 pm to 7 pm on both weekdays and weekends. Or Min Speed required is 59.8 m / min. = M2 Converts km/h to m / min correctly A1 or M1 (59.8m/min) M1 converts correctly

10 SGS/Mathematics/4E5N/2021/Prelims/4048/MS/P2 Should avoid speed slower than 3.588 km / h. John should avoid 5 pm to 7 pm on both weekdays and weekends. A1 Total for Q11 8 m