2011 年

$1000010000101_2=$

In the figure, the equations of $PQ$, $QR$ and $RS$ are $x-y=7$, $x+y=5$ and $y=3$ respectively. If $(x,y)$ is a point lying in the shaded region $PQRS$ (including the boundary), at which point does $2x-3y+35$ attain its greatest value?

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

If the 3rd term and the 12th term of an arithmetic sequence are $42$ and $6$ respectively, then the sum of the first $n$ terms of the sequence is

The product of the 1st term and the 2nd term of a geometric sequence is $18$ while the product of the 3rd term and the 4th term of the sequence is $288$. The product of the 4th term and the 5th term of the sequence is

Let $a$ be a constant and $-90^\circ<\theta<90^\circ$. If the figure shows the graph of $y=a\cos(x^\circ+\theta)$, then

In the figure, the area of $\triangle ABC=$

In the figure, $ABCDE$ is a circle. $AC$ and $BD$ intersect at $F$. If $AE\parallel BD$, $\angle DAE=20^\circ$ and $\angle CFD=70^\circ$, then $\angle CBD=$

In the figure, $BC$ is a diameter of the circle $ABC$. $BCD$ is a straight line and $DA$ is the tangent to the circle at $A$. If $\angle ABC=28^\circ$, then $\angle ADB=$

In the figure, $ABCDEFGH$ is a cuboid. If $\angle FHG=x$, $\angle BFG=y$ and $\angle HBG=z$, then $\tan z=$