Questions

• Laws of Integral Indices inter-convert between simple binary/hexadecimal numbers to decimal numbers

  \[ 17 \times 16^{6} + 22 \times 16^{4} + 16^{2} + 22 \]

  2024

• Equations of Straight Lines Understand the equation of a straight line

  給定直線\(L_{1}\)的方程式為\(3x - 4y + 8 = 0\)。另一條直線\(L_{2}\)，與\(L_{1}\)平行，並通過點\((-2, -3)\)。求\(L_{2}\)、\(x\)軸和\(y\)軸形成的三角形的面積。

  2024

• Exponential and Logarithmic Functions Understand the laws of rational indices

  \[\frac{16x^{-3} y^{4} \cdot 25z^{2}}{5x^2 y^{-2} \cdot z^{-4}} = \]

  2024

• Loci Describe the locus of points with algebraic equations

  考慮兩個不同的點 \( A(3, 4) \) 和 \( B(7, 8) \)。下列哪一個方程式代表了與點 \( A \) 和 \( B \) 等距離的點的軌跡？

  2024

• 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

  設圓方程式：\[ C: x^2 + y^2 + 2x - 4y - 4 = 0 \]和線性方程式：\[ L: x - y - 2 = 0 \]找出\(L\)和\(C\)交點的坐標是什麼？

  2024

• 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

  設圓的方程式 \( C: x^2 + y^2 + 6x + 8y + k = 0 \) 和線性方程式 \( L: 2x - 3y + 4 = 0 \)，找出 \( k \) 的範圍，使得直線與圓相交於兩點。

  2024

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

  \(\log_3 \left(\frac{27^2 \cdot x}{9 \cdot y^3}\right) =\)

  2024

• Rate and Ratio apply the ability in using rate, ratio to solve real-life problems including mensuration problems

  假設蘋果與橙子的數量比是3:5。如果香蕉的數量是蘋果的兩倍，找出蘋果、橙子和香蕉的比例。

  2024

• Rate and Ratio apply the ability in using rate, ratio to solve real-life problems including mensuration problems

  假設遊戲機的數量是智能手機數量的60%。如果平板電腦與遊戲機的數量比是3:2，求平板電腦、遊戲機和智能手機的數量比。

  2024

• Rate and Ratio apply the ability in using rate, ratio to solve real-life problems including mensuration problems

  假設遊戲機的數量是智能手機數量的40%。如果筆記型電腦與遊戲機的數量比是3:2，求筆記型電腦與智能手機的數量百分比。

  2024