Questions

• Quadratic Equations in One Unknown Understand relations between the roots and coefficients, form equations using these relations Form quadratic equations from given roots

  如果 $\alpha \neq \beta$ 且 $\left\{\begin{array}{l}3 \alpha=\alpha^{2}-5 \\ 3 \beta=\beta^{2}-5\end{array}\right.$，則 $\alpha \beta=$？

  2013

• Quadratic Equations in One Unknown Appreciate the development of the number systems including complex numbers Perform addition, subtraction, multiplication, and division of complex numbers

  實部是$i+2i^{2}+3i^{3}+4i^{4}$的是

  2013

• Functions and Graphs Understand the features of the graphs of quadratic functions

  設 $h$ 和 $k$ 為常數。圖示顯示了 $y=h+k \tan 2 x^{\circ}$ 的圖形，其中 $0 \leq x \leq \alpha$。下列哪些是正確的？ I. $h>0$ II. $k<0$ III. $\tan \alpha^{\circ}=\frac{1}{k}$

  

  2013

• Quadratic Equations in One Unknown Solve problems involving quadratic equations Understand relations between the roots and coefficients, form equations using these relations

  若 $p$ 及 $q$ 均為常數，使得 $p x(x-1)+x^{2} \equiv q x(x-2)+4 x$，則 $p=$

  2014

• Quadratic Equations in One Unknown Understand relations between the discriminant of a quadratic equation and the nature of its roots Solve quadratic equations by the quadratic formula

  設 $a$ 為一常數。若二次方程 $x^{2}+ax+a=1$ 有等根，則 $a=$

  2014

• Functions and Graphs Understand the features of the graphs of quadratic functions

  圖中所示爲 $y=m x^{2}+x+n$ 的圖像, 其中 $m$ 及 $n$ 均爲常數。下列何者正確?

  

  2014

• Quadratic Equations in One Unknown Solve problems involving quadratic equations Understand relations between the roots and coefficients, form equations using these relations

  一盒子中有 $m$ 個黃球及 20 個黑球。若從該盒子中隨機抽出一個球, 則抽出黃球的概率爲 $\frac{1}{m}$ 。求 $m$ 的値。

  2014

• Functions and Graphs Understand the features of the graphs of quadratic functions Find the maximum and minimum values of quadratic functions by the algebraic method

  設 $\mathrm{f}(x)=3x^{2}-6x+k$，其中 $k$ 爲一常數。若 $y=\mathrm{f}(x)$ 的圖像的頂點的 $y$ 坐標為 7，則 $k=$？

  2014

• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  若 $\beta$ 為一實數，則 $\frac{\beta^{2}+4}{\beta+2 i}=$

  2014

• Functions and Graphs Understand the features of the graphs of quadratic functions

  下列何者可表示在同一直角坐標系上 $y=f(x)$ 的圖像及 $y= 1-f(x)$ 的圖像？

  2014