Manjusri 4045 02 Prelim 2024 MS

2024 4NA Prelim Paper 2 Answer Key 1 (a) −1.5 (b) 2.42 (3 s.f.) 2 3.29 × 109 3 (a) x = 6, y =3 (b) p = 2×3×7 = 42 4 x = 7, y = 4 5 The price in UK is cheaper. 6 (a) (i) 76 cm (ii) 61 cm (b) (i) 64.6 cm (ii) 12.7 cm 7 Rose should choose Plan A 8 QR 2 + PR 2 =162 + 282 = 1 040 PQ2,= 342, = 1156 Since 162 + 282 ≠ 342, ∠PRQ is not a right angle. Hence, PQ is not a diameter. 9 (a) 46 639 or 0.0720 (b) 145 852 or 0.170 (c) 1961 2556 or 0.767 10 (a) 23.4° (1 d.p.) (b) 35.0 km 2 (c) 3.18 km 11 (a) 5 cm (b) 31.4 cm (c) 2. 42 radians 12 (a) $568 (b) $340.80 (c) $72.58 13 (a) (i) 1.77 million (ii) 5.64 million (iii) 12.7% (c) 219.5° 14 (a) −15.5 (b) (c) When x = 0, 2 x is undefined, so y is undefined. (d) x = −2, −0.4 or 2.45. (±0.1) (e) Correct tangent drawn Gradient = 3.57 ± 0.2 15 (a) 4 3m/s2 (b) 45 (c) 14.5 m/s (d) 86.4 km/h

16 (a) (i) 20 (ii) 73 (iii) 66 (b) (i) Max mark = 5+93 = 98 B1 (ii) Interquartile range = 82 − 21 = 61 (c) 4H because 4H’s interquartile range is smaller than 4I.

2024 4NA Prelim Paper 2 Marking Scheme 1 (a) −1.5 B1 (b) 2.42 (3 s.f.) B1 2 3 292 498 114 = 3.29 × 109 B1 3 (a) 8640 = 26×33×5 x = 6, y =3 B1 B1 (b) p = 2×3×7 = 42 B1 4 5 3 23xy−= −−−−−−−(1) 2 18xy+= −−−−−−−(2) (2) × 3: 6x + 3y = 54 −−−−−−(3) (1) + (3): 11x = 77 x = 7 Sub x = 7 into (2): 2×7 + y = 18 y = 4 M1 M1 A1 5 Price of Perfume in UK: £62.00 = S$ (62 ÷ 0.58) = S$ 106.90 (2 dp) Price of perfume in Singapore: S$102 × 1.09 = S$ 111.18 The price in UK is cheaper. M1 M1 A1 Accept S$102 × 1.09 = S$ 111.18 111.18 × £0.58 =£64.48 >£62 6 (a)(i) Mode = 76 cm B1 (ii) Median = 61 cm B1 (b)(i) Mean = (43+51+57+60+61+73+76+76+84) ÷ 9 = 64.6 cm (3 s.f.) M1 A1 (ii) Standard deviation = 12.7 cm (3 s.f.) B1 7 Plan A’s total interest after 5 years = $5000 × 3% × 5 M1

= $750 Plan B’s interest after 5 years = $5000 (1+2.8%)5 − $5000 = $740.31 (2 d.p.) Or Plan A’s total amount = $5000 × 3% × 5 + $5000 = $5750 = Plan B’s total amount after 5 years = $5000 (1+2.8%) 5 = $5740.31 < $5750 Rose should choose Plan A for higher interest (or higher total amount) after 5 years M1 M1 (M1) (M1) (M1) A1 For total amt of plan B For interest For simple interest For total amount Must provide reason 8 The sum of the square of the two shorted sides =QR 2 + PR 2 = 162 + 282 = 1 040 The square of the longest side PQ 2,= 342, = 1156 Since 16 2 + 282 ≠ 342, ∠PRQ is not a right angle. Angle in semicircle is not a right angle, so PQ is not a diameter. M1 M1