Further Mathematics Past Questions

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
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. $$\frac{-3\sqrt{3}}{4}$$
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. $$1+\sqrt{3}$$
4

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

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