Questions

• Laws of Integral Indices extend and explore the meaning of the index notation of numbers with negative exponents

  \(\frac{(2^{-3} \times 4^2)}{ 8^{-1}}=\).

  2024

• Laws of Integral Indices explore, understand and use the laws of integral indices to simplify simple algebraic expressions (up to 2 variables only)

  \[ \left( \frac{a^3 b^{-2}}{a^{-1} b^4} \right)^{-2} = \]

  2024

• Laws of Integral Indices explore, understand and use the laws of integral indices to simplify simple algebraic expressions (up to 2 variables only)

  \((a^3 \times b^{-2})^2 \times (a^{-1} \times b^4)^{-1} = \)

  2024

• Rational and Irrational Numbers be aware of the existence of irrational numbers and surds

  以下哪個數字是無理數？

  2024

• Variations Understand joint and partial variations, and their applications to solving real-life problems

  \( y \)分別與\( x^2 \)成正變，與\( x \)成反變。當\( x = 2 \)時，\( y = 10 \)。當\( x = 4 \)時，\( y = 5 \)。求當\( x = 8 \)時，\( y \)的值。

  2024

• Variations Understand joint and partial variations, and their applications to solving real-life problems

  設\( y \)部分直接與\( x^2 \)成正比，部分直接與\( x^3 \)成正比。當\( x = 2 \)時，\( y = 20 \)，當\( x = 3 \)時，\( y = 81 \)。如果\( x \)增加50%，\( y \)的百分比變化是多少？

  2024

• Exponential and Logarithmic Functions Understand the properties of exponential functions and logarithmic functions and recognize the features of their graphs

  設\(\log_b(x) = p\)和\(\log_b(y) = q\)，用\(p\)和\(q\)表示\(\log_b\left(\frac{x^3 \cdot y^2}{\sqrt{x \cdot y^4}}\right)\)。

  2024

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

  設 \(\log_2(x^3) + \log_2(8) - \log_2(4x) = 4\)，求 \(x\) 的值。

  2024

• Introduction to Coordinates describe intuitively the effects of transformation such as translation, reflection with respect to lines parallel to x-axis, y-axis and rotation about the origin through

  在直角坐標系統中給定一點 \( P (3, 4) \) ，將點 \( P \) 沿著 y 軸反射。由原點 \( O \) 、原始點和反射點形成的三角形的周界是多少？

  2024

• Introduction to Coordinates calculate areas of figures that can be cut into or formed by common 2-D rectilinear figures

  在直角坐標系統中給定四點：\( A(2, -3) \)、\( B(7, -3) \)、\( C(5, 2) \) 和 \( D(1, 2) \)。這四點形成的四邊形的面積是多少？

  2024