數學 2011 年 DSE、CE 選擇題

1.

$5^{334}\left(\dfrac{-1}{5}\right)^{333}=$

2.

If $\dfrac{2+a}{a}=\dfrac{2-x}{x}$ , then $x=$

3.

$(x-2y)(x+2y-2)=$

4.

If $x$ and $y$ are non-zero numbers with $x<y$ , which of the following must be true? I. $-x>-y$ II. $\dfrac{1}{x^2}>\dfrac{1}{y^2}$ III. $x^3<y^3$

5.

The solution of $2(1-x)+5\geq 17$ is

6.

The price of $5$ pens and $4$ pencils is $\$46$ while the price of $2$ pens and $3$ pencils is $\$24$ . Find the price of $3$ pens and $2$ pencils.

7.

Which of the following statements about the graph of $y=25-(x-3)^2$ is true?

8.

Let $\mathrm{f}(x)=x^2+2x+k$ , where $k$ is a constant. Find $\mathrm{f}(5)-\mathrm{f}(3)$ .

9.

In the figure, the 1st pattern consists of $4$ dots. For any positive integer $n$ , the $(n+1)$ th pattern is formed by adding $3$ dots to the $n$ th pattern. Find the number of dots in the 8th pattern.

10.

A sum of $\$15\,000$ is deposited at an interest rate of $6\%$ per annum for $10$ years, compounded monthly. Find the interest correct to the nearest dollar.