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Further Mathematics Past Questions

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1

If \(log_{y}\frac{1}{8}\) = 3, find the value of y.

  • A. -2
  • B. -\(\frac{1}{2}\)
  • C. \(\frac{1}{2}\)
  • D. 2
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2

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).

  • A. \(-4\sqrt{3}\)
  • B. \(\frac{-4\sqrt{3}}{3}\)
  • C. \(\frac{-3\sqrt{3}}{4}\)
  • D. \(\frac{-3\sqrt{3}}{4}\)
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3

Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)

  • A. \(1- \frac{1}{2}\sqrt{3}\)
  • B. \(1+ \frac{1}{2}\sqrt{3}\)
  • C. \(\sqrt{3}\)
  • D. \(1+\sqrt{3}\)
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4

If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.

  • A. 3, 4
  • B. \(\pm3\)
  • C. \(\pm5\)
  • D. \(\pm6\)
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5

Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)

  • A. (-2,4)
  • B. (\(\frac{-2}{3}, \frac{4}{3}\))
  • C. (\(\frac{2}{3}, \frac{-4}{3}\))
  • D. (2, -4)
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