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IB Mathematics: Applications and Interpretation SL · 13.5: Integration · 13.5.9

Integration: exam review Exam review Answers

Section A: short questions

    1. (a) 48 m
    2. (b) 228 m
    1. (a) \(3x^{3} + 4x + \frac{4}{x^{2}} + c\)
    2. (b) \(\frac{2}{3}x^{3} + \frac{1}{2}x^{2} - 15x + c\)
    3. (c) \(2x^{3} - 9x - \frac{2}{x} + c\)
    1. (a) \(-\dfrac{5}{2x^{2}}+c\)
    2. (b) \(x^{4}-6+\dfrac{9}{x^{4}}\); \(\dfrac{x^{5}}{5}-6x-\dfrac{3}{x^{3}}+c\)
    3. (c) \(f(x)=6x^{2}-\dfrac{10}{x^{3}}\)
    1. (a) \(y=2x^{3} + 2x + \frac{4}{x^{2}} - 4\)
    2. (b) 4
    1. (a) \(f(x)=x^{3}-x^{2}+5\)
    2. (b) 11.3
    1. (a) \(\displaystyle\int_{1}^{4}\left(x^{2} - 6x + 10\right)dx\)
    2. (b) 6
    3. (c) 19.5
    1. (a) \(r=6t\)
    2. (b) 4800 g
    1. (a) 4.946, 8.155, 13.45
    2. (b) 19.6
    3. (c) Greater than the exact value: the curve bends upwards, so the tops of the trapeziums lie above the curve.
    1. (a) 4620 m²
    2. (b) 675 m²
    3. (c) 3950 m²

Section B: long questions

    1. (a) \(k=0.5\)
    2. (b) 53 litres
    3. (c) \(t=7.49\) minutes
    4. (d) The amount that flows in between \(t=4\) and \(t=8\): 15.2 litres
    5. (e) The rate keeps increasing for ever, which is not realistic: a pump cannot run faster and faster without limit.
    1. (a) The distance travelled
    2. (b) 206 m
    3. (c) Less than the true distance: the curve bends downwards, so the tops of the trapeziums lie below it.
    4. (d) 213 m
    5. (e) 3.51%
    6. (f) 9.65 s
    1. (a) \(x=8\)
    2. (b) \(x=6\)
    3. (c) \(\displaystyle\int_0^{6}\left(6x-x^{2}\right)dx\)
    4. (d) 36 m²
    5. (e) 85.3 m²
    6. (f) 42.2%
    7. (g) 54 m³
    1. (a) \(x=2.30\) and \(x=8.70\)
    2. (b) \(\displaystyle\int_{2.30}^{8.70}\left((11-x)-\frac{20}{x}\right)dx\); 8.59 m²
    3. (c) 33.7 m²
    4. (d) 32.2
    5. (e) 4.59%
    6. (f) 3.44 m³

jmaths.xyz · AI SL · 13.5.9 Unit review