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IB Mathematics: Applications and Interpretation HL · 12.6: Exponents & Logarithms · 12.6.5

Exponents and logarithms: exam review Exam review Answers

Section A: short questions

    1. (a) 2.40
    2. (b) \(x=\frac{103}{2}\) (51.5)
    3. (c) \(x=e^{\frac{5}{3}}\) (5.29)
    1. (a) \(a = \frac{3}{2}\), p = 11
    2. (b) \(\frac{16}{9}\)
    1. (a) \(\frac{1}{8}\)
    2. (b) a = 36, k = −5
    3. (c) \(x + 5x^{-\frac12}\)
    1. (a) x = 343
    2. (b) \(x=\frac{24}{7}\)
    1. (a) \(1 + 3p − \frac{1}{2}q\)
    2. (b) \(\ln 30\)
    1. (a) \(\frac{81}{16}\)
    2. (b) \(a = 8\), p = 8
    1. (a) x = 4.39
    2. (b) x = 5
    1. (a) \(1.28\times10^{6}\)
    2. (b) \(4.05\times10^{12}\)
    3. (c) 3200 gigabytes
    1. (a) \(1.58\times10^{14}\)
    2. (b) 3.16e+04

Section B: long questions

    1. (a) x = 196
    2. (b) 8.96
    3. (c) 9.43
    4. (d) x = 27
    1. (a) 45; 88.8
    2. (b) 13.2
    3. (c) 13.2
    4. (d) 20.3
    1. (a) −1.52, 1.08, 3.70
    2. (b) The values cover several powers of 10, so the logs are small numbers that fit on one graph
    3. (c) A power model: log y against log x has r closer to 1, so it is nearer a straight line
    4. (d) \(y=3.57x^{0.748}\)
    5. (e) 56.4
    6. (f) a = 7.94, b = 2.00
    1. (a) 250; 109
    2. (b) 8%
    3. (c) t = 11.0 days
    4. (d) 31 days
    1. (a) k = 0.237
    2. (b) t = 11.9 hours
    3. (c) 1.98 hours
    1. (a) b = 3.39, a = 0.849
    2. (b) 12.4 cm
    3. (c) 64.9 days

jmaths.xyz · AI HL · 12.6.5 Unit review