2003 年

If $\mathrm{f}(x)=2x^2+kx-1$ and $\mathrm{f}(-2)=\mathrm{f}\left(\dfrac{1}{2}\right)$, then $k=$

Let $\mathrm{f}(x)=x^3+2x^2+k$, where $k$ is a constant. If $\mathrm{f}(-1)=0$, find the remainder when $\mathrm{f}(x)$ is divided by $x-1$.

If $a=\dfrac{b-1}{b-2}$, then $b=$

$3^x\cdot 9^y=$

If the equation $x^2-4x+k=1$ has no real roots, then the range of values of $k$ is

If $(2x+3)(x-a)\equiv 2x^2+b(x+1)$, then

If $\begin{cases}y=x^2+4\\ y=-3x+4\end{cases}$, then $y=$

The solution of $x>1$ and $13<3x-2<25$ is

If $0.8448<a<0.8452$, which of the following must be true?

The sum of the 4th term and the 5th term of a geometric sequence is $-4$. If the sum of the first two terms is $32$, find the first term of the sequence.