2001 年

Which of the following is an identity / are identities? I. $x^2+2x+1=0$ II. $x^2+2x+1=(x+1)^2$ III. $x^2+1>0$

If $\begin{cases}y=x^2-4x-44\\ y=-2x+4\end{cases}$, then $y=$

A piece of wire of length $36\text{ cm}$ is cut into two parts. One part, $x\text{ cm}$ long, is bent into a square and the other part is bent into a circle. If the length of a side of the square is equal to the radius of the circle, which of the following equations can be used to find $x$?

The sum of the first $n$ terms of an arithmetic sequence is $n^2$. Find the 10th term of the sequence.

The $n$th term of a geometric sequence is $-\dfrac{1}{2^n}$. Find the first term and the common ratio.

A bank offers loans at an interest rate of $18\%$ per annum, compounded monthly. A man took a loan of $\$20\,000$ and repays the bank in monthly instalments of $\$4\,000$. Find the outstanding balance after his first instalment.

If $0^\circ<x<y<90^\circ$, which of the following must be true? I. $\sin x<\sin y$ II. $\cos x<\cos y$ III. $\sin x<\cos y$

In the figure, $AEC$ is a diameter and $DEB$ is a straight line. Find $x$.

Which of the following pairs of triangles is/are similar?

In the figure, $x=$