2003 年

Let $k$ be a constant. If $\alpha$ and $\beta$ are the roots of the equation $x^2-3x+k=0$, then $\alpha^2+3\beta=$

The figure shows the graph of $y=-x^2+ax+b$. Which of the following is true?

Which of the following systems of inequalities has its solution represented by the shaded region in the figure?

In the figure, $ABCD$ and $PQRS$ are two rectangles of equal perimeter. If $AB:BC=3:2$ and $PQ:QR=4:3$, then area of $ABCD$ : area of $PQRS=$

For $0^\circ\le\theta<360^\circ$, how many roots does the equation $2\cos^2\theta-5\sin\theta-4=0$ have?

$\dfrac{\tan(180^\circ-\theta)}{\cos(90^\circ-\theta)}=$

1 degree $=$

The figure shows a cuboid. Which of the following are right angles? I. $\angle CAF$ II. $\angle DHG$ III. $\angle AGC$

In the figure, $PQ=x\text{ cm}$ and $SR=y\text{ cm}$. Find $PS$.

The figure shows a circle with diameter $AD$. If $AB=BC=CD$, find $x+y+z$.