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IB Mathematics: Applications and Interpretation SL · 12.7: Mathematical Models · 12.7.4

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) 45.0
    2. (b) 9.00
    3. (c) 13.3
    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)

Section B: long questions

    1. (a) amplitude 7.00, mean 10.0
    2. (b) 15.0
    3. (c) \(C=7.00\sin(15.0(t−8))+10.0\)
    4. (d) 16.8
    5. (e) 5.92 hours
    6. (f) t = 14.0
    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 = 36.0, 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 SL · 12.7.4 Unit review