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

Mathematical models: exam review Exam review Answers

Section A: short questions

    1. (a) 0.116
    2. (b) 152 mg
    3. (c) 23.6 hours
    4. (d) The amount is lost at a rate proportional to the amount present, and no more medicine is taken.
    1. (a) a = 23.4, b = 16.8
    2. (b) 73.6
    3. (c) 29.2
    1. (a) B = 21, A = 71
    2. (b) 0.0742
    3. (c) 17.8 minutes
    4. (d) 9.35 minutes
    1. (a) 40.0
    2. (b) 6.67
    3. (c) 12.2
    1. (a) a = −3
    2. (b) a = 1.50
    3. (c) a = 1.15
    1. (a) a = 36, time = 6 hours
    2. (b) t becomes very large (it tends to infinity). With fewer than one pump the model makes no sense: n must be a whole number of at least 1.
    3. (c) T = 4, k = 21
    4. (d) 19.9 minutes
    1. (a) -0.128
    2. (b) 8680 years
    1. (a) 0 < x < 15
    2. (b) 4100 cm³ (x = 6.07)

Section B: long questions

    1. (a) amplitude 2.30, mean 3.50
    2. (b) 0.507
    3. (c) \(h=2.30\sin(0.507(t−2.1))+3.50\)
    4. (d) 5.79
    5. (e) 5.34 hours
    6. (f) t = 5.20
    1. (a) 7.00
    2. (b) 0.442
    3. (c) 804
    4. (d) 4.40 years
    5. (e) 1200
    6. (f) The logistic model levels off at the carrying capacity; an exponential model grows without limit
    1. (a) 900×0.93^n
    2. (b) 31 days
    3. (c) 0.0578
    4. (d) 53.9 days
    1. (a) n = -12p + 320
    2. (b) Each £1 increase in price reduces the number of tickets sold by 12.
    3. (c) p = 13.3, R = 2130
    4. (d) 10.0 < p < 16.7
    5. (e) 0 ≤ p ≤ 26.7; a price of £30 would give a negative number of tickets
    1. (a) a = -15, b = 0.785, d = 17
    2. (b) 27.6 m
    3. (c) 2.57 minutes
    4. (d) The radius of the wheel, 15 m
    5. (e) The wheel is assumed to turn at a constant speed with no stops; in reality it stops to load riders.

jmaths.xyz · AI HL · 12.7.7 Unit review