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Mathematics Past Questions

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26
Evaluate: \(\int^{z}_{0}(sin x - cos x) dx \hspace{1mm}

Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)
  • A. \(\sqrt{2 +1}\)
  • B. \(\sqrt{2 }-1\)
  • C. \(-\sqrt{2 }-1\)
  • D. \(1-\sqrt{2}\)
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27
Find the volume of solid generated when the area enclosed by y = 0, y = 2x, and x = 3 is rotated about the x-axis.
  • A. 81 π cubic units
  • B. 36 π cubic units
  • C. 18 π cubic units
  • D. 9 π cubic units
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28
What is the derivative of t2 sin (3t - 5) with respect to t?
  • A. 6t cos (3t - 5)
  • B. 2t sin (3t - 5) - 3t2 cos (3t - 5)
  • C. 2t sin (3t - 5) + 3t2 cos (3t - 5)
  • D. 2t sin (3t - 5) + t2 cos 3t
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29
Evaluate \(\int^{1}_{-2}(x-1)^{2}dx\)
  • A. \(\frac{-10}{3}\)
  • B. 7
  • C. 9
  • D. 11
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30
Find the value of x for which the function y = x3 - x has a minimum value.
  • A. \(-\sqrt{3}\)
  • B. \(-\sqrt{\frac{3}{3}}\)
  • C. \(\sqrt{\frac{3}{3}}\)
  • D. \(\sqrt{3}\)
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