1996 年

If $\alpha$ and $\beta$ are the roots of the equation $2x^2+4x-3=0$, find $\dfrac{\alpha}{\beta}+\dfrac{\beta}{\alpha}$.

Find the $n$-th term of the A.P. $4, 2, 0, -2, \ldots$.

The sum to infinity of a G.P. is $2$. If the first term is $\dfrac{3}{2}$, find the common ratio.

Shop A offers a $10\%$ discount on a book marked at $\$P$. Shop B offers a $15\%$ discount on the same book marked at $\$Q$. If the selling price of the book is the same in both shops, express $Q$ in terms of $P$.

In the figure, area of $\triangle ACD$ : area of $\triangle BCD=$

In the figure, $O$ is the centre of the circle. $AB$ and $AC$ are tangents to the circle at $B$ and $C$ respectively. Area of the shaded region $=$

In the figure, the area of $ABCD$ is

In the figure, A and B are two right solid cylinders with the same base radius $1$. If the heights of A and B are $1$ and $2$ respectively, find $\dfrac{\text{the total surface area of A}}{\text{the total surface area of B}}$.

If $0^\circ\le\theta\le360^\circ$, solve $2\sin\theta=-\sqrt3$.

$\dfrac{\dfrac{1}{\cos\theta}-\cos\theta}{\tan^2\theta}=$