Questions

• 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

  圖中所示為一陰影區域（包括邊界在内）。若 $(a, b)$ 為陰影區域中的一點, 則下列何者正確? I. $a \leq 4$ II. $a \geq b-5$ III. $a \geq 10-2b$

  

  2015

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

  設 $x_{n}$ 為一等比數列的第 $n$ 項。若 $x_{6}=216$ 及 $x_{8}=96$, 則下列何者必為正確? I. $x_{3}=729$ II. $\frac{x_{5}}{x_{7}}>1$ III. $x_{2}+x_{4}+x_{6}+\cdots+x_{2n}<2015$

  2015

• More About Trigonometry Solve the trigonometric equations a sin θ = b, a cos θ = b, a tan θ = b (0° to 360°) and other equations Understand the functions sine, cosine, and tangent, their graphs and properties

  當 $0^{\circ} \leq x<360^{\circ}$ 時，方程式 $\cos^{2}x-\sin x=1$ 有幾個根？

  2015

• More About Trigonometry Understand the functions sine, cosine, and tangent, their graphs and properties Solve the trigonometric equations a sin θ = b, a cos θ = b, a tan θ = b (0° to 360°) and other equations

  設 $k$ 為一正常數且 $-180^{\circ}<\theta<180^{\circ}$ 。若圖中所示為 $y=\sin \left(k x^{\circ}+\theta\right)$ 的圖像, 則

  

  2015

• Pythagoras’ Theorem

  圖中, $A B$ 及 $A C$ 分別為圓在 $B$ 及 $C$ 的切線。 $B D$ 為該圓的一直徑。 $A C$ 的延線與 $B D$ 的延線相交於 $E$ 。若 $A B=6 \mathrm{~cm}$ 及 $A E=10 \mathrm{~cm}$, 則 $B D=$

  

  2015

• 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

  求常數 $k$ 使得圓 $x^{2}+y^{2}+2 x-6 y+k=0$ 與直線 $x+y+4=0$ 只相交於一點。

  2015

• Equations 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 $(0,60)$ 及 $(96,48)$。$\triangle OPQ$ 的垂心的 $x$ 坐標為

  2015

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

  6名男生與2名女生排成一隊。若沒有女生相鄰而排，則可排成多少不同的隊形？

  2015

• 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

  $P$ 袋內有 2 個紅球及 4 個綠球，而 $Q$ 袋內有 1 個紅球及 3 個綠球。若隨機選取一袋且隨後從該袋中隨機抽出一個球，求抽出綠球的概率。

  2015

• 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

  設 $x_{1} 、 y_{1}$ 及 $z_{1}$ 分別為某組數 $\left\{a_{1}, a_{2}, a_{3}, \ldots, a_{50}\right\}$ 的平均值、中位數及方差, 而 $x_{2} 、 y_{2}$及 $z_{2}$ 分別為 $\left\{a_{1}, a_{2}, a_{3}, \ldots, a_{49}\right\}$ 這組數的平均值、中位數及方差。若 $x_{1}=a_{50}$, 則下列何者必為正確? I. $x_{1}=x_{2}$ II. $y_{1} \geq y_{2}$ III. $z_{1}<z_{2}$

  2015