1996 年

The curve in the figure is the graph of $y=-x^2+bx+c$. Find the area of the rectangle $OPQR$.

If the common difference of the A.P. $a_1, a_2, a_3,\ldots$ is $d$, then the common difference of the A.P. $2a_1+3, 2a_2+3, 2a_3+3,\ldots$ is

The length of a rectangle is decreased by $20\%$. If the area remains unchanged, find the percentage increase of its width.

The following table shows the compositions of Tea A and Tea B which are mixtures of Chinese tea and Indian tea:

$\begin{array}{|c|c|}\hline & \text{Ratio of Chinese tea and Indian tea by weight}\\\hline\text{Tea A} & 3:1\\\hline \text{Tea B} & 2:3\\\hline\end{array}$

If $4\text{ kg}$ of tea A and $10\text{ kg}$ of tea B are mixed, find the ratio of Chinese tea and Indian tea in the mixture.

The figure shows a frustum of a right circular cone. The radii of the upper face and the base are $1\text{ cm}$ and $2\text{ cm}$ respectively. If the height is $3\text{ cm}$, find the volume.

In the figure, if $\dfrac{\text{Area of triangle }CDE}{\text{Area of triangle }BCE}=\dfrac{1}{2}$, find $\dfrac{\text{Area of triangle }CDE}{\text{Area of trapezium }ABCD}$.

In the figure, find $\theta$ correct to the nearest degree.

In the figure, the bearings of two ships $A$ and $B$ from a lighthouse $L$ are $020^\circ$ and $080^\circ$ respectively. $B$ is $400\text{ m}$ and at a bearing of $130^\circ$ from $A$. Find the distance of $B$ from $L$.

The figure shows a right prism with a right-angled triangle as the cross-section. Find the angle between the line $BF$ and the plane $ABCD$ correct to the nearest degree.

In the figure, $O$ is the centre of the circle. $AP$, $AB$ and $BR$ are tangents to the circle at $P$, $Q$ and $R$ respectively. Which of the following must be true?

I. $AP+BR=AB$ II. $OQ$ bisects $\angle AOB$ III. $\angle AOB=\dfrac{1}{2}\angle POR$