Questions

• 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

• Inequalities and Linear Programming Represent the graphs of linear inequalities in two unknowns in the rectangular coordinate plane Solve systems of linear inequalities in two unknowns

  考慮以下不等式系統： $$ \left\{\begin{array}{l} x \geq 2 \\ y \geq 0 \\ x+4 y \leq 22 \\ 4 x-y \leq 20 \end{array}\right. $$ 設 $D$ 為上述不等式系統的解集區域。如果 $(x, y)$ 是位於 $D$ 中的一點，那麼 $3 y-4 x+15$ 的最大值是

  2013

• Arithmetic and Geometric Sequences and Their Summations Understand the general term of an arithmetic sequence

  一個數列的第$n$項是$2n-19$。以下哪些是正確的？ I. 25是數列的一項。 II. 數列有10個負數項。 III. 數列的前$n$項和是$n^{2}-18n$。

  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

• More about Areas and Volumes

  若一個正四面體的高為 $2 \mathrm{~cm}$，則該四面體的體積為

  2013

• Basic Properties of Circles Understand the angle properties of a circle Understand the properties of tangents to a circle and angles in the alternate segments

  在圖中，$O$ 是圓 $A B C$ 的中心。$D E$ 是在 $A$ 處的圓的切線。如果 $A B$ 是 $\angle C A E$ 的角平分線，那麼 $\angle A C O=$ 是多少？

  

  2013

• Equations of Circles Find the coordinates of the intersections of a straight line and a circle and understand the possible intersection of a straight line and a circle

  找出$k$的值域，使得圓$x^{2}+y^{2}+2x-2y-7=0$與直線$3x-4y+k=0$相交。

  2013

• Equations of Circles Understand the equation of a circle Find the coordinates of the intersections of a straight line and a circle and understand the possible intersection of a straight line and a circle

  設$O$為原點。如果點$A$和$B$的坐標分別為$(0,12)$和$(30,12)$，那麼$\triangle O A B$的外心的$y$坐標是

  2013

• Permutations and Combinations Understand the concept and notation of permutation Solve problems on the permutation of distinct objects without repetition

  如果一個八位數的電話號碼的前三位和最後五位分別由$5,6,9$的排列和$2,3,4,7,8$的排列組成，那麼可以形成多少個不同的八位數電話號碼？

  2013

• Measures of Dispersion Understand the effect of adding/multiplying a constant on the dispersion of data

  若五個數字 $x_{1}, x_{2}, x_{3}, x_{4}$ 和 $x_{5}$ 的方差為 $13$，則五個數字 $3 x_{1}+4,3 x_{2}+4,3 x_{3}+4,3 x_{4}+4$ 和 $3 x_{5}+4$ 的方差為

  2013