2008 年

If the sum and the product of two numbers are $34$ and $120$ respectively, then the difference between the two numbers is

In the figure, the equations of $PQ$ and $QR$ are $3x+y=36$ and $x+y=20$ respectively. If $(x,y)$ is a point lying in the shaded region $OPQR$ (including the boundary), then the least value of $2x-3y+180$ is

Let $a$, $b$ and $c$ be positive integers. Which of the following must be arithmetic sequences? I. $a+10,\ 2a+7,\ 3a+4,\ 4a+1$ II. $8^b-1,\ 8^{2b}-2,\ 8^{3b}-3,\ 8^{4b}-4$ III. $\log c^3,\ \log c^8,\ \log c^{13},\ \log c^{18}$

If $a-6,\ a,\ a+5$ is a geometric sequence, then the common ratio of the sequence is

For $0^\circ\le\theta<360^\circ$, how many roots does the equation $3\sin^2\theta+2\sin\theta-1=0$ have?

Let $a$ and $b$ be constants. If the figure shows the graph of $y=a\cos(2x^\circ+120^\circ)+b$, then

For $0^\circ\le\theta\le360^\circ$, the least value of $\dfrac{2+\sin\theta}{2-\sin\theta}$ is

In the figure, $AB\parallel CD$, $AB=150\text{ cm}$ and $CD=80\text{ cm}$. Find $BD$ correct to the nearest cm.

The figure shows a right prism $ABCDEF$ with a right-angled triangle as the cross-section. $A$, $B$, $E$ and $F$ lie on the horizontal ground. $G$ and $H$ are two points on the horizontal ground so that $G$, $A$, $B$ and $H$ are collinear. It is given that $AB=6\text{ m}$, $AG=3\text{ m}$ and $BH=2\text{ m}$. If $\angle DAE=a$, $\angle CBF=b$, $\angle CHF=c$ and $\angle DGE=d$, which of the following must be true?

In the figure, $O$ is the centre of the circle $ABCD$. If $\angle ADC=84^\circ$ and $\angle CBO=38^\circ$, then $\angle AOB=$