Mathematics · May / June 2026 · Paper 42 · Question 12
0580
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0580/42/M/J/26 © Cambridge University Press & Assessment 2026 12 A scientist records the mass of a radioactive substance at the same time each day. On 10 January, the scientist records a mass of 150 grams. Each day, the mass of the substance decreases by 5%. Find the date on which the scientist first records a mass of less than 96 grams. [3] ĬÑĊ Ġ
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19 January nfww [3]
For 19 January accept e.g. 19/1, 1/19. For 3 marks if exponential method used and correct answer then do not class inaccurate
B2 for 8.7… or 9 [days] nfww values as wrong working. OR For method do not accept e.g. 150 × (95%)n alone. 8 5
M2 for 150 × 1 100 − correctly evaluated oe Implied by 99[.5…] 5 96 − For M2 accept n log 1 = log or 100 150 better. 9 5 or 150 × − Implied by 94[.5…] 1 100 correctly evaluated oe or 0.958 and 96 150 correctly evaluated Implied by 0.66[3...] and 0.64 or 0.959 and 96 Implied by 0.63[0…] and 0.64 150 correctly evaluated n 5 M1 implied by any value in 2nd column to 3sf or or M1 for 150 × − 1 100 oe accept n or better with 0.64, or any value in 3rd column to 4sf rounded or truncated 150 oe (allow = , >, ⩽, ⩾) where value n > 1 n 5 < 96 − or 1 100 n 0.95n 150 × 0.95n 2 0.9025 135.375 3 0.857375 128.60625 4 0.814506 122.17594 5 0.773781 116.06714 6 0.735092 110.26378 7 0.698337 104.75059 10 0.598736 89.81054
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