2005 澳洲 AMC E-Senior 真题 答案 详解

2005 年 E-Senior 真题,中英双语,答案,详解

英文真题

Senior Division
Questions 1 to 10, 3 marks each

1. The value of $(4 \times 5) \div (2 \times 10)$ is
   (A) $4$ (B) $\frac{1}{4}$ (C) $2$ (D) $\frac{1}{2}$ (E) $1$

2. In the diagram, the value of $x$ is
   (A) $20$ (B) $90$ (C) $30$ (D) $80$ (E) $60$

3. $1 + \frac{1}{3 + \frac{1}{2}}$ equals
   (A) $\frac{6}{5}$ (B) $\frac{7}{6}$ (C) $\frac{9}{2}$ (D) $\frac{3}{2}$ (E) $\frac{9}{7}$

4. The straight line $y = x + g$ passes through the point $(2,3)$. The value of $g$ is
   (A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $-1$

5. A two-digit number has tens digit $t$ and its units digit $u$. If the digit $8$ is placed between these digits, the value of the three-digit number is
   (A) $t + u + 8$ (B) $10t + 80 + u$ (C) $10t + u + 8$ (D) $100t + 10u + 8$ (E) $100t + 80 + u$

6. $\triangle PXQ$ is a right angled triangle with sides of length $3$ and $7$ as shown. At $P$, $PR$ is drawn so that $\angle RPQ = 90^\circ$ and $PR = PQ$. The area of $\triangle PRQ$ is
   (A) $\frac{21}{2}$ (B) $29$ (C) $\sqrt{58}$ (D) $58$ (E) $100$