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IB Mathematics: Applications and Interpretation HL · 12.7: Mathematical Models · 12.7.7

Mathematical models: exam review Exam review: second paper Answers

Section A: short questions

1. (a) 0.0866
2. (b) 99.0 g
3. (c) 34.5 days
4. (d) The isotope decays at a rate proportional to the mass present, and none is added.
1. (a) a = 2.45, b = 5.05
2. (b) 19.6
3. (c) 32.3
1. (a) B = 24, A = 176
2. (b) 0.0606
3. (c) 31.6 minutes
4. (d) 11.4 minutes
1. (a) 45.0
2. (b) 9.00
3. (c) 13.3
1. (a) a = −5
2. (b) a = 1.33
3. (c) a = 0.828
1. (a) a = 60, time = 7.5 days
2. (b) t becomes very large (it tends to infinity). With fewer than one worker the model makes no sense: n must be a whole number of at least 1.
3. (c) T = 20, k = 160
4. (d) 15.9 minutes
1. (a) -0.0943
2. (b) 3950 years
1. (a) 0 < x < 12
2. (b) 2100 cm³ (x = 4.85)

1. (a) amplitude 7.00, mean 10.0
2. (b) 0.262
3. (c) \(C=7.00\sin(0.262(t−8))+10.0\)
4. (d) 16.8
5. (e) 5.92 hours
6. (f) t = 14.0
1. (a) 11.5
2. (b) 0.588
3. (c) 3110
4. (d) 4.15 months
5. (e) 5000
6. (f) The logistic model levels off at the carrying capacity; an exponential model grows without limit
1. (a) 650×0.95^n
2. (b) 41 days
3. (c) 0.0770
4. (d) 43.3 days
1. (a) n = -15p + 405
2. (b) Each £1 increase in price reduces the number of tickets sold by 15.
3. (c) p = 13.5, R = 2730
4. (d) 9.55 < p < 17.4
5. (e) 0 ≤ p ≤ 27.0; a price of £40 would give a negative number of tickets
1. (a) a = -3, b = 0.628, d = 3.5
2. (b) 5.93 m
3. (c) 3.33 seconds
4. (d) The radius of the wheel, 3 m
5. (e) The wheel is assumed to turn at a constant speed; in reality the speed of the stream changes, so the wheel does not turn at a constant speed.

jmaths.xyz · AI HL · 12.7.7 Unit review