Questions

• More About Polynomials Understand the concepts of the greatest common divisor and the least common multiple of polynomials

  $3x^{4}y^{2}z、4xy^{5}z$ 及 $6x^{2}y^{3}$ 的最大公因數為

  2014

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

  圖中所示爲在同一直角坐標系上 $y=b^{x}$ 的圖像及 $y=c^{x}$ 的圖像, 其中 $b$ 及 $c$ 均爲正常數。若一水平線 $L$ 分別與 $y$ 軸 $\quad y=b^{x}$ 的圖像及 $y=c^{x}$ 的圖像相交於 $A 、 B$ 及 $C$,則下列何者正確? I. $b<c$ II. $b c>1$ III. $\frac{A B}{A C}=\log _{b} c$

  

  2014

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

  下列何者最大？

  2014

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

  $7 \times 2^{10} + 2^{8} +5 \times 2^{3} - 2^{3}$

  2014

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

  設 $\mathrm{f}(x)=3x^{2}-6x+k$，其中 $k$ 爲一常數。若 $y=\mathrm{f}(x)$ 的圖像的頂點的 $y$ 坐標為 7，則 $k=$？

  2014

• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  若 $\beta$ 為一實數，則 $\frac{\beta^{2}+4}{\beta+2 i}=$

  2014

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

  若 $m>1$，則下列何者為等比數列？ I. $2^{m}, 2^{2m}, 2^{3m}, 2^{4m}$ II. $m, 2m^{2}, 3m^{4}, 4m^{8}$ III. $\log m, \log m^{2}, \log m^{4}, \log m^{8}$

  2014

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

  下列何者可表示在同一直角坐標系上 $y=f(x)$ 的圖像及 $y= 1-f(x)$ 的圖像？

  2014

• 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 $0^{\circ} \leq x \leq 360^{\circ}$ 時，方程式 $7 \sin ^{2} x=\sin x$ 有多少個根？

  2014

• Pythagoras’ Theorem

  圖中, $A B$ 爲立於水平地面 $B C D$ 上的鉛垂柱, 其中 $\angle C B D=90^{\circ}$ 。若平面 $A C D$ 與水平地面間之交角爲 $\theta$, 則 $\tan \theta=$

  

  2014