KSS_2023_Prelims_4NA Maths P2 (Solutions)

1 | P a g e KRANJI SEC SCHOOL 4NA PRELIMS 2023 PAPER 2 (SOLUTIONS) 1 (a) √3147 3 = 14.7 (b) 8 × 600 0.08 = 60000 2 (a) 0.000 987 = 9.87 × 10−4 (b) 5.642×106 7.18×102 = 7.86 × 103 people / km2 3 (a) Total interior angle of Pentagon = 180(5) − 360 = 540° 1 interior angle = 540 5 = 108° ∠𝐵𝐶𝐷 = 360° − 90° − 108° = 162° (b) 1 exterior angle = 180° − 162° = 18° → 𝑛 = 360° 18° = 20 4 (a) 13 students (b) SD = √1638.95 20 = 9.05 𝑘𝑔 5 (a) 𝑇3 = − 3 3 + 7 = 6 (b) − 𝑛 3 + 7 + (− 𝑛 + 1 3 + 7) = 9 − 𝑛 3 − 𝑛 + 1 3 + 14 = 9 −2𝑛−1 3 = −5 → 𝑛 = 7 6 𝐾𝐵𝑆: $400000 + 400000×2.2×15 100 = $532000 ; 𝐾𝐶𝐵𝐶: 400000 (1 + 2.5 100) 5 = 452563.2852 452563.2852 (1 + 1.5 100) 10 = $525218.17 → KBS Bank is better. 7 (a) 94900 × 90 100 = $85410 $85410 + $30000 = $115410 (b) (i) $115410 × 20 100 = $23082 (ii) 23082 + 60 × 1700 = $125082 8 9a(i) (𝑚 − 2𝑦)(𝑚 + 2𝑦) 9a(ii) (𝑥 − 5)(2𝑥 − 1) 9(a) (iii) 12𝑎𝑥 − 8𝑏𝑥 + 9𝑎𝑦 − 6𝑏𝑦 = 4𝑥(3𝑎 − 2𝑏) + 3𝑦(3𝑎 − 2𝑏) = (3𝑎 − 2𝑏)(4𝑥 + 3𝑦) 9(b) 5ℎ𝑘 = 𝑘 + 2 5ℎ𝑘 − 𝑘 = 2 𝑘(5ℎ − 1) = 2 𝑘 = 2 5ℎ − 1

2 | P a g e 10 (a) 350 x (b) 210 x + 10 (c) 350 𝑥 + 210 x + 10 = 6 350(𝑥 + 10) + 210𝑥 𝑥(𝑥 + 10) = 6 350(𝑥 + 10) + 210𝑥 = 6𝑥(𝑥 + 10) 350𝑥 + 3500 + 210𝑥 = 6𝑥2 + 60𝑥 6𝑥2 − 500𝑥 − 3500 = 0 3𝑥2 − 250𝑥 − 1750 = 0 (d) 𝑥 = −(−250) ± √(−250)2 − 4(3)(−1750) 2(3) 𝑥 = 250 + √83500 6 𝑜𝑟 250 − √83500 6 𝑥 = 89.83 𝑘𝑚/ℎ or −6.494 𝑘𝑚/ℎ Speed of the car from Singapore to Kuala Lumpur = 89.8 km/h 11 (a) x 0.5 1 1.5 2 2.5 3 3.5 4 y 4.05 1.20 0.45 0.30 0.45 0.80 1.31 1.95 (b) (c) Gradient = −2.67 (d) x = 1.35 or 2.75 12 (a) 1 3 × 𝜋 × (3.6)2 × 11.1 − 1 3 × 𝜋 × (2.4)2 × 7.4 = 106.0099 𝑐𝑚3 = 106 𝑐𝑚3 (3 s.f.) (b) Volume of the cylinder = 𝜋 × 72 × 30 = 4618.1412 𝑐𝑚3 Total number of cups possible = 4618.1412 ÷ 106.0099 = 43.56 𝑐𝑢𝑝𝑠 ≈ 43 𝑐𝑢𝑝𝑠 (c) Assuming Mr Aziz orders 2 batches of tea for 11 am to 5 pm (6 hours), Total number of filled cups = 43.56 × 2 = 87cups, meaning most guest may drink about 3 cups each. Cost of 2 batches: The Tea Bros: ($57 + $57 + $2 × 6 + $12) × 0.9 = $124.20 Tarik King: $46 + $46 + $3 × 6 + $10 = $120 Miss Teh Tarik: $52 + $52 + $2 × 6 = $116

3 | P a g e A sensible budget is $130 as this will cover the cost of tea from all companies. Assumptions: • Mr Aziz orders 2 batches of Teh Tarik • Each guest will come in and drink three cups (i.e. Take a refill). • No spillage of tea • Tea is filled to the brim of the dispenser. • Each guest dispense tea into their cups to the brim. 13 (a)(i) Median (50th Percentile) = 8.7 mins (a)(ii) Lower quartile = 7.6 mins Upper quartile = 9.6 mins Interquartile range = 9.6 – 7.6 = 2 mins (a)(iii) 60th Percentile = 9.0 mins (b)(i) P(first person chosen is a boy who passed and the second person is a girl who passed) = 30 80 × 24 79 = 9 79 (b)(ii) P(both people chosen are girls) = 34 80 × 33 79 = 561 3160 (b) (iii) P(at least one of the person chosen is