Questions

• 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，$PQ$ 是圓 $ABC$ 在 $O$ 處的切線，其中 $O$ 是半圓 $PBQ$ 的中心。已知 $BCP$ 是一條直線。如果 $\angle BPQ=12^{\circ}$，那麼 $\angle BAC=$多少？

  

  2012

• 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

  求$k$的值範圍，使得圓$x^{2}+y^{2}+2x-4y-13=0$與直線$x-y+k=0$在兩個不同點相交。

  2012

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

  一個戲劇俱樂部由12個男孩和8個女孩組成。如果從俱樂部中選出5名學生組成一個參加比賽的隊伍，並且隊伍中至少要有一名女孩，可以組成多少個不同的隊伍？

  2012

• 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

  一個盒子裡有六個編號分別為$7,8,8,9,9$和$9$的球。約翰重複隨機地從盒子裡抽出一個球，直到抽到的數字為$9$為止，不放回。求他恰好需要抽三次的概率。

  2012

• Measures of Dispersion Understand the concept of dispersion Understand the concept of standard deviation for both grouped and ungrouped data sets

  設 $m_{1}, r_{1}$ 和 $v_{1}$ 分別是一組數字 $\left\{x_{1}, x_{2}, x_{3}, \ldots, x_{100}\right\}$ 的平均值、範圍和方差。如果 $m_{2}, r_{2}$ 和 $v_{2}$ 分別是數字組 $\left\{x_{1}, x_{2}, x_{3}, \ldots, x_{100}, m_{1}\right\}$ 的平均值、範圍和方差，以下哪些必定為真？ I. $m_{1}=m_{2}$ II. $r_{1}=r_{2}$ III. $v_{1}=v_{2}$

  2012

• Exponential and Logarithmic Functions Understand the laws of rational indices

  $\left(27 \cdot 9^{n+1}\right)^{3}=$

  2013

• More About Equations Solve problems involving equations which can be transformed into quadratic equations

  如果 $\frac{y-1}{c}=\frac{y+1}{d}$，則 $y=$

  2013

• More About Polynomials Perform division of polynomials

  $h \ell-k \ell+h m-k m-h n+k n=$

  2013

• Approximation and Errors acquire further concepts and skills of rounding off numbers to a required number of significant figures understand and calculate different types of errors such as absolute errors, relative errors and percentage errors.

  $0.0504545=$

  2013

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

  $x-\frac{x-1}{2}>5$ 或 $1<x-11$ 的解為

  2013