Questions

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

  下列何者為等差數列？ I. $\pi^{30}, \pi^{45}, \pi^{60}$ II. $30 \pi, 45 \pi, 60 \pi$ III. $\pi-30, \pi-45, \pi-60$

  2017

• 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

  考慮以下的不等式組： $$ \left\{\begin{array}{l} y \leq 9 \\ x-y-9 \leq 0 \\ x+y-9 \geq 0 \end{array}\right. $$ 設 $R$ 為表示以上的不等式組的解之區域。若 $(x, y)$ 為 $R$ 中的一點, 則 $x-2 y+43$ 的最大值為

  2017

• Pythagoras’ Theorem

  圖中, $A B C D$ 為一長方形。若 $E$ 為 $A C$ 上的一點使得 $A E=30 \mathrm{~cm}$, 則 $D E=$

  

  2017

• More About Trigonometry Understand the angle between a line and a plane, and the angle between 2 planes Solve related 2-dimensional and 3-dimensional problems

  圖中, $A D$ 為立於水平地面 $B C D$ 上的鉛垂柱。若 $A B=25 \mathrm{~m} 、 A D=15 \mathrm{~m} 、 B C=29 \mathrm{~m}$及 $C D=21 \mathrm{~m}$, 求 $A B$ 與平面 $A C D$ 間的交角準確至最接近的度。

  

  2017

• Basic Properties of Circles Understand the angle properties of a circle Use the basic properties of circles to perform simple geometric proofs

  圖中，$O$ 為圓 $ABC$ 的圓心。$DE$ 為圓在 $A$ 的切線。若 $\angle BAD=68^\circ$ 及 $\angle BCO=26^\circ$，則 $\angle ABC=$？

  

  2017

• Coordinate Geometry of Straight Lines Understand the equation of a straight line Understand the possible intersection of two straight lines

  設 $O$ 為原點。點 $P$ 及點 $Q$ 的坐標分別為 $(p, 0)$ 及 $(0, q)$ ，其中 $p$ 及 $q$ 均為正數。若 $\triangle O P Q$ 的內心在直線 $3 x+4 y=3 p$ 上, 則 $p: q=$

  2017

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

  某委員會有 13 名學生及 6 名教師。若從該委員會中選出 5 名學生及 4 名教師組成一隊，則可組成多少不同的隊？

  2017

• More About Probability Recognize the notation of set language including union, intersection, and complement Understand the addition law of probability and concepts of mutually exclusive events and complementary events

  當佩怡擲一飛鏢時，她擲中目標的概率為 0.7。若佩怡擲該飛鏢 4 次，求她擲中目標至多 3 次的概率。

  2017

• Measures of Dispersion Understand the concept of standard deviation for both grouped and ungrouped data sets Compare dispersions of different data sets using appropriate measures

  志誠在某數學考試的標準分為 -2 。若志誠在該數學考試的得分為 33 分且該數學考試的得分的平均值為 45 分, 則該數學考試的得分的標準差為

  2017

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

  設 $m_{1}$ 、 $r_{1}$ 及 $v_{1}$ 分別為某組數 $\left\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}\right\}$ 的眾數、四分位數間距及方差,而 $m_{2}$ 、 $r_{2}$ 及 $v_{2}$ 分別為 $\left\{8 x_{1}, 8 x_{2}, 8 x_{3}, 8 x_{4}, 8 x_{5}, 8 x_{6}, 8 x_{7}\right\}$ 這組數的眾數、四分位數間距及方差。下列何者必為正確? I. $m_{2}=8 m_{1}$ II. $r_{2}=8 r_{1}$ III. $v_{2}=8 v_{1}$

  2017