Questions

• Functions and Graphs Find the maximum and minimum values of quadratic functions by the algebraic method

  如果 $-1 < h<0$，以下哪一個可能代表 $y=\left(\frac{x}{h}+h\right)^{2}-\frac{h^3-1}{h}$ 的圖形？

  2024

• Functions and Graphs Understand the features of the graphs of quadratic functions

  圖形顯示了$y=ax^{2}+bx+4$的圖表，其中$a$和$b$是常數。以下哪項是正確的？

  

  2024

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

  給定一個等比數列的無窮和為12，且數列的第二項為3，求公比。

  2024

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

  給定一個等比數列的無窮和為20，公比為0.5，求該數列的第四項。

  2024

• Arithmetic and Geometric Sequences and Their Summations Understand the general term of an arithmetic sequence

  給定等差數列：5, 8, 11, 14, ...，確定序列中的哪一項是50。A. 15。B. 16。C. 17。D. 它不是序列的一部分。正確答案：A解釋：等差數列的通項公式為：\[ a_n = a_1 + (n-1)d \]其中 \( a_1 \) 是第一項，\( d \) 是公差。對於給定的序列：\[ a_1 = 5 \]\[ d = 8 - 5 = 3 \]我們需要確定50是否是序列中的一項。因此，我們設 \( a_n = 50 \) 並求解 \( n \)：\[ 50 = 5 + (n-1)3 \]\[ 50 = 5 + 3n - 3 \]\[ 50 = 3n + 2 \]\[ 48 = 3n \]\[ n = \frac{48}{3} \]\[ n = 16 \]

  2024

• Simple Idea of Areas and Volumes understand and use the formulas for surface areas and volumes of cubes, cuboids, prisms and cylinders

  在圖中，直立柱體的體積是

  

  2024

• More About Trigonometry Understand the angle between a line and a plane, and the angle between 2 planes

  圖中顯示了一個直角三角柱 $A B C D E F$。如果 $B C= 29\mathrm{~cm}, C F=20 \mathrm{~cm}$ 且 $C D=45 \mathrm{~cm}$，求 $B D$ 與平面 $C D E F$ 之間的角度，取至最接近的度數。

  

  2024

• More About Trigonometry Understand the angle between a line and a plane, and the angle between 2 planes

  在圖中，$A B C D E F G H$ 是一個長方體。$D G$ 與平面 $EFGH$ 形成一個角度 $\theta$。求 $\cos \theta$。

  

  2024

• More About Trigonometry Understand the angle between a line and a plane, and the angle between 2 planes

  在圖中，$A B C D E F$ 是一個直角三角柱。如果 $\angle A C B=40^{\circ}$ 和 $\angle A C E=30^{\circ}$，求平面 $A B C D$ 與平面 $C D E F$ 之間的角度，取至最接近的度。

  

  2024

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

  如果 \( p \) 與 \( q^{3} \) 成正比，與 \( r \) 成反比，以下哪一項必定是常數？

  2024