1989 年

$\dfrac{(1-x^2)^n+(1-x)^n}{(1-x)^{2n}}=$

$\log_4 2\sqrt{2}=$

If $x=\sqrt{a+1}-\sqrt{a}$, where $a>0$, then $x+\dfrac{1}{x}=$

If $p$ is a root of $ax^2+bx+c=0$, which of the following is a root of $a\left(\dfrac{x-3}{2}\right)^2+b\left(\dfrac{x-3}{2}\right)+c=0$?

The figure shows the graph of a quadratic function $y=\mathrm{f}(x)$. Given that the graph has vertex $(2,18)$ and it cuts the $x$-axis at $(5,0)$, find the quadratic function.

If $2\sin^2\theta-\sin\theta\cos\theta-\cos^2\theta=0$, then $\tan\theta=$

In the figure, $VABCD$ is a right pyramid of height 3 cm. The base $ABCD$ is a square of side 2 cm. Let $\theta$ be the angle between the face $VBC$ and the base. Find $\tan\theta$.

In the figure, if $\cos\theta=\dfrac{3}{4}$, find the value of $x$.

A vertical rectangular wall on the horizontal ground, 1 m high and 10 m long, runs east and west as shown in the figure. If the sun bears $\text{S}60^\circ\text{E}$ at an elevation of $45^\circ$, find the area of the shadow of the wall on the ground.

In the figure, $ABCD$ is a trapezium with $AB /\!/ DC$. If $BC=1$, then $AD=$