Questions

• Measures of Dispersion Understand the concept of dispersion Construct and interpret the box-and-whisker diagram to compare data distributions

  下面的盒鬚圖顯示了6A班學生在某天復習所花時間（以分鐘計）的分佈。以下哪一項必定是真的？ I. 該分佈的範圍與四分位距之差為0.2小時。 II. 至少一半的6A班學生那天在復習上花費超過55分鐘。 III. 如果隨機選擇一名6A班的學生，他/她那天在復習上花費68分鐘或以上的概率為0.25。

  

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• Introduction to Various Stages of Statistics

  累積頻率多邊形顯示了一個班級學生身高的分佈。以下哪一個是這組數據的頻率多邊形？

  

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• Linear Equations in Two Unknowns plot and explore the graphs of linear equations in 2 unknowns formulate and solve simultaneous equations by algebraic and graphical methods

  

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• Trigonometric Ratios and Using Trigonometry explore the properties and relations of trigonometric ratios apply trigonometric ratios to find measures of 2-D figures

  對於 $0^{\circ} \leq \theta \leq 360^{\circ}$，方程式 $3(1-\sin \theta)=\frac{2 \sin \left(270^{\circ}+\theta\right)}{1+\sin \theta}$ 有幾個根？

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• Identities explore the meaning of identities and distinguish between equations and identities discover and use the identities : difference of two squares; the perfect square expression; difference and sum of two cubes

  如果$\frac{i}{p-i^{2022}}+\frac{q}{i+q}$是一個實數，其中$p$和$q$是非零常數，那麼$q(p-1)$的最小值是

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• Angles related with Lines and Rectilinear Figures explore and use the properties of lines and angles of triangles explore and use the angle properties associated with intersecting lines and parallel lines

  在圖中，$A B C$ 是一個等腰三角形，滿足 $A B=A C$，位於以 $O$ 為中心的半圓內。$A C$ 延長至點 $D$。假設 $\angle C B D=30^{\circ}$，則 $\angle O C A=$多少度？

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• Exponential and Logarithmic Functions Understand the definition and properties of logarithms (including the change of base) Solve exponential equations and logarithmic equations

  如果 $m \neq n$ 且 $\left\{\begin{array}{l}\left(\log _{k} m\right)^{2}=\log _{k} m^{12}-18 \\ \left(\log _{k} n\right)^{2}=\log _{k} n^{12}-18\end{array}\right.$，其中 $k>1$，則 $m$ 與 $n$ 的乘積是

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• Coordinate Geometry of Straight Lines

  在圖中，$ABCD$是一個正方形，$\triangle CDE$是一個等邊三角形。$F$和$G$分別是$AD$和$BC$上的點。已知$AF=2\mathrm{~cm}，GC=3\mathrm{~cm}$且$AB=10\mathrm{~cm}。$FG$分別在$DE$和$CE$上交於$H$和$K$。求$HK$的長度。

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• Inequalities and Linear Programming Solve systems of linear inequalities in two unknowns Solve linear programming problems

  考慮以下線性不等式系統： $$ \left\{\begin{array}{c} x-2 y \leq 15 \\ 3 x-y \geq-5 \\ x+3 y \leq 15 \\ y \geq-2 x \end{array}\right. $$ 設 $R$ 為上述不等式系統解的區域，且 $(x, y)$ 為位於 $R$ 內的一點。若 $T=x^{2}+y^{2}-10 x-2 y+2020$，求 $T$ 的值域。

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• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of geometric sequences Explore the general formulae of the sum to infinity for certain geometric sequences and use the formulae to solve related problems

  設$a_{n}$為公比為$r$的等比數列的第$n$項。已知$a_{2}>0$且該數列的無窮級數和為-3。下列哪些是正確的？ I. $-1<r<0$ II. $-6<a_{1}<-3$ III. 如果$k$是一個正整數，則$a_{1}+a_{2}+\ldots+a_{2k-1}+a_{2k}>3$。

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