Questions

• Quadratic Equations in One Unknown Understand relations between the discriminant of a quadratic equation and the nature of its roots Solve quadratic inequalities in one unknown by the algebraic method

  設 $k$ 為一常數。求 $k$ 值的範圍使得對任意實數 $x, x^{2}+k x+k+8 \geq 0$ 。

  2021

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

  若 $m$ 及 $n$ 均為常數使得 $(x+3)^{2}+mx \equiv(x-n)(x+1)+2n$, 則 $m=$

  2022

• Quadratic Equations in One Unknown Solve quadratic equations by the factor method

  設 $c$ 為一常數。解方程 $(x-c)(x-4c)=(3c-x)(x-4c)$ 。

  2022

• 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 $\mathrm{f}(x)=x^{2}-x+1$ 。若 $k$ 為一常數, 則下列何者必為正確?

  2022

• 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 $h$ 及 $k$ 均為實常數使得 $hk<0$ 。下列有關 $y=(h-x)(k-x)$ 的圖像之敍述, 何者正確? I. 該圖像開口向上。 II. 該圖像有兩個 $x$ 截距。 III. 該圖像的 $y$ 截距為正值。

  2022

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

  設 $z=4+5 i^{10}-k i^{15}+6 i^{21}+2 k i^{28}$，其中 $k$ 為一實數。若 $z$ 的實部與虛部相等，則 $z$ 的實部為

  2022

• Functions and Graphs Recognize the notation of functions and use tabular, algebraic, and graphical methods to represent functions Understand the features of the graphs of quadratic functions

  若$f(x)=\frac{x+1}{x-1}$，則$f\left(\frac{1}{x}\right)=$是什麼？

  2024

• Functions and Graphs Recognize the notation of functions and use tabular, algebraic, and graphical methods to represent functions Understand the features of the graphs of quadratic functions

  設$f(x)=ax+b$為$x$的線性函數，其中$a$和$b$為實數常數。已知$f(2013) \leq f(2014), f(2015) \geq f(2016)$且$f(2017)=2018$。以下哪項必定為真？

  2024

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

  設$f(x)$為一函數，使得$f(x-1)=2x^{2}-x+7$，則$f(x+2)=$

  Premium 2024

• Quadratic Equations in One Unknown Solve quadratic equations by the factor method Solve problems involving quadratic equations

  如果一個正$n$邊形的內角和是一個外角的12倍，以下哪項是正確的？

  2024