TPS 4NA Prelim P1 2023 MS

Mark scheme 2023 4N Prelim Paper 1 Qn Answer Marks 1a) 11.2 × 3 8.2 − 4.7 = 9.6 (Accept 48 5 ) B1 1b) √5.1 + 3.752 = 4.4 B1 2a) 0.312̇ B1 2b) 21 B1 2c) 5 7, 21, √64, 0.312̇ B1 (all correct) 3) −4𝑥 ≥ 73 𝑥 ≥ −73 4 𝑥 ≤ −18.25 The largest integer is −19. M1 A1 4a) 𝑥2 + 10𝑥 + 21 = 𝑥2 + 10𝑥 + ( 10 2 ) 2 − ( 10 2 ) 2 + 21 = (𝑥 + 5)2 − 4 𝑎 = 5 𝑏 = −4 M1 A1 A1 4b) 𝑥2 + 10𝑥 + 21 = 0 (𝑥 + 5)2 − 4 = 0 (𝑥 + 5)2 = 4 (𝑥 + 5) = 2 𝑜𝑟 (𝑥 + 5) = −2 𝑥 = −3 𝑜𝑟 𝑥 = −7 M1 A1, A1 5a) 9 students B1 5b) Number of students with at least $5 of average daily pocket money = 18 Required probability= 18 50. = 9 25. B1

6a) 250 4 = 62.5 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑢𝑝𝑐𝑎𝑘𝑒𝑠 = 62 × 24 = 1488 Amount= 1488 × 1.80 = 2678.40 M1 M1 A1 6b) Amount of eggs used= 62 × 4 = 248 Percentage of eggs not used= 2 250 × 100 = 0.8% M1 A1 6c) Butter: Flour and Milk = 115: 180 + 120 = 115: 300 = 23: 60 M1 A1 7a) Speed at AB = 15 10 = 1.5𝑚/𝑠 Speed at CD = 10 10 = 1𝑚/𝑠 Hence, the statement is incorrect. It is travelling faster at AB. M1 A1 7b) During BC. Duration =10s. B1 7c) The electric toy car is making a u-turn to return back to the original position. B1 7d) Average speed = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 = 50 50 𝑚/𝑠 = 1𝑚/𝑠 M1 A1 8a) 1050 = 2 × 3 × 5 × 5 × 7 𝑥 = 1 𝑦 = 2 B1 B1

8b) 1050𝑘 = 2 × 3 × 5 × 5 × 7 × 𝑘 𝑘 = 2 × 3 × 7 = 42 B1 8c) 𝐻. 𝐶. 𝐹 = 2 × 5 × 5 × 7 = 350 M1 A1 9) B2 (shape, size) 10a) 𝑝 = 102 2 = 51 𝑐𝑚 B1 10b) 𝑞 = 75° B1 10c) 𝑟 = 180 − 60 − 75 = 45° (sum of angles in a triangle) M1 A1 11a) B1-Shape B1-Points 11b) Line of symmetry is 𝑥 = 1. B1 11c) Coordinates = (1, −9) B1 12a) Deposit = 10 100 × 6200 = $620 M1 A1 12b) Let the monthly payment be 𝑥. 620 + 12𝑥 = 7400 𝑥 = 565 Each monthly payment is $565. M1 A1

13a) 𝑦 + 2𝑥 = 18 𝑦 = −2𝑥 + 18 Let 𝑥 = 0 Coodinates of 𝐴 = (0, 18) Let 𝑦 = 0 Coodinates of 𝐵 = (9, 0) B1 B1 13b) Distance = √(8 − 0)2 + (20 − 0)2 = 21.5𝑢𝑛𝑖𝑡𝑠 M1 A1 14) Gradient of 𝐴𝐵 = 1 2 7−0 𝑝+2 = 1 2 14 = 𝑝 + 2 𝑝 = 12 M1 A1 15) Area = 1 2 (38 + 48)(25) = 1075𝑚2 M1 A1 16a) 𝑥2 + 𝑥 − 6 = (𝑥 − 2)(𝑥 + 3) B1 16b) 50𝑦2 − 18 = 2(25𝑦2 − 9) = 2(5𝑦 − 3)(5𝑦 + 3) M1 A1 17a) 3𝑝 𝑞 = 5𝑟 + 1 3𝑝 = 5𝑟𝑞 + 𝑞 𝑝 = 5𝑟𝑞+𝑞 3 B1 17b) 1 𝑥2−9 + 2 𝑥+3 = 1 𝑥2−9 + 2𝑥−6 𝑥2−9 = 2𝑥−5 𝑥2−9 M1 A1 18a) Brand Colour X R X B X G Y R Y B Y G A1 A1

18b) 𝑃(Ali chooses a blue pen) = 2 6 = 1 3 B1 19a) - Inconsistent scale on vertical axis. - Missing years represented. - Inaccurate title description. B1 (any of these) 19b) - The inconsistency may have caused viewers to have the perception that the number of visitors have doubled. - The difference between the years. Not all the years are shown. Attendance in the missing years could have been higher. - The title is biased and does not allow reader to make their own judgement. B1 (any of these)

20a) B1 [𝑃𝑅], B1 [𝑄𝑅] 20b) Angle 𝑄𝑃𝑅 = 48° B1 20c) As above diagram B1