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

Exponents and logarithms: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) 3.56
    2. (b) \(x=\frac{99}{4}\) (24.8)
    3. (c) \(x=e^{\frac{9}{4}}\) (9.49)
    1. (a) \(a = \frac{2}{3}\), p = 19
    2. (b) \(\frac{125}{8}\)
    1. (a) \(\frac{1}{16}\)
    2. (b) a = 9, k = −7
    3. (c) \(x^2 + 4x^{-\frac12}\)
    1. (a) x = 25
    2. (b) \(x=\frac{12}{5}\)
    1. (a) \(3 + \frac{1}{2}p − 2q\)
    2. (b) \(\ln 20\)
    1. (a) \(\frac{125}{27}\)
    2. (b) \(a = \frac{1}{2}\), p = 11
    1. (a) x = 6.48
    2. (b) x = 4
    1. (a) \(2.4\times10^{4}\)
    2. (b) \(8.16\times10^{9}\)
    3. (c) \(7.2\times10^{12}\)
    1. (a) \(3.16\times10^{-4}\)
    2. (b) 1000

Section B: long questions

    1. (a) x = 23
    2. (b) 5.51
    3. (c) 4.36
    4. (d) x = 25
    1. (a) 30; 60.3
    2. (b) 11.5
    3. (c) 12.1
    4. (d) 16.5
    1. (a) −1.40, 1.18, 3.90
    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) \(y=5.11x^{0.298}\)
    5. (e) 26.5
    6. (f) a = 5.01, b = 2.51
    1. (a) 60; 17.3
    2. (b) 22%
    3. (c) t = 3.52 hours
    4. (d) 14 hours
    1. (a) k = 0.236
    2. (b) t = 12.4 hours
    3. (c) 1.65 hours
    1. (a) b = 2.42, a = 1.44
    2. (b) 10.7 species per plot
    3. (c) 78 km²

jmaths.xyz · AI HL · 12.6.5 Unit review