2016 澳洲 AMC D-Intermediate 真题 答案 详解

中英双语真题

1-10 Questions 1 to 10, 3 marks each

1. 算式 20 × 16 等于 What is the value of 20 × 16?
   (A) 320 (B) 140 (C) 2016 (D) 32 (E) 800

2. 右图中，阴影部分占整个圆的几分之几？ In the figure, the shaded region is what fraction of the circle?
   (A) ( \frac{1}{20} ) (B) ( \frac{1}{10} ) (C) ( \frac{1}{2} ) (D) ( \frac{1}{60} ) (E) ( \frac{1}{40} )

3. 环城公路赛跑于上午11:15开始，冠军选手在同日下午2:09抵达终点。请问冠军选手耗时多少分钟？ The cycling road race through the Adelaide Hills started at 11:15 am and the winner finished at 2:09 pm the same day. The winner's time in minutes was
   (A) 135 (B) 174 (C) 164 (D) 294 (E) 186

4. 请问分数 ( \frac{720163}{2016} ) 的值符合下列哪一项叙述？ The fraction ( \frac{720163}{2016} ) is
   (A) between 0 and 1 (B) between 1 and 10 (C) between 10 and 100 (D) between 100 and 1000 (E) greater than 1000

英文真题

Intermediate Division
Questions 1 to 10, 3 marks each

1. What is the value of $20 \times 16$?
   (A) 320 (B) 140 (C) 2016 (D) 32 (E) 800

2. In the figure, the shaded region is what fraction of the circle?
   (A) $\frac{1}{20}$ (B) $\frac{1}{10}$ (C) $\frac{1}{2}$ (D) $\frac{1}{60}$ (E) $\frac{1}{40}$

3. The cycling road race through the Adelaide Hills started at 11:15 am and the winner finished at 2:09 pm the same day. The winner's time in minutes was
   (A) 135 (B) 174 (C) 164 (D) 294 (E) 186

4. The fraction $\frac{720163}{2016}$ is
   (A) between 0 and 1 (B) between 1 and 10 (C) between 10 and 100 (D) between 100 and 1000 (E) greater than 1000

5. What is the value of $(1 \div 2) \div (3 \div 4)$?
   (A) $\frac{2}{3}$ (B) $\frac{3}{2}$ (C) $\frac{3}{8}$ (D) $\frac{1}{6}$ (E) $\frac{1}{24}$

6. 0.75% of a number is 6. The number is
   (A) 800 (B) 300 (C) 1200 (D) 400 (E) 100

7. In the expression below, the letters A, B, C, D and E represent the numbers 1, 2, 3, 4 and 5 in some order.
   $A \times B + C \times D + E$
   What is the largest possible value of the expression?
   (A) 24 (B) 27 (C) 26 (D) 51 (E) 25

真题文字详解(英文)

Solutions – Intermediate Division 1. 20 × 16 = 320, hence (A). 2. $$\frac{1}{2} + \frac{1}{4} + \frac{1}{5} = \frac{10+5+4}{20} = \frac{19}{20}$$ so that $$\frac{1}{20}$$ is shaded, hence (A). 3. Between 11:15 am and 2:09 pm, there are 45 + 120 + 9 = 174 minutes, hence (B). 4. (Also J10) Estimating, $$\frac{720163}{2016} \approx \frac{720000}{2000} = \frac{720}{2} = 360$$. This suggests that 100 < $$\frac{720163}{2016}$$ < 1000. Checking, 201600 < 720163 < 2016000 and so 100 < $$\frac{720163}{2016}$$ < 1000, hence (D). 5. $$\frac{1}{2} ÷ \frac{3}{4} = \frac{1}{2} × \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$$, hence (A). 6. Alternative 1 Let the number be x. Then $$\frac{3}{4} × \frac{1}{100} × x = 6$$, so $$\frac{x}{400} = 2$$ and x = 800, hence (A). Alternative 2 0.25% of the number is 2 (one-third of the given amount), so 1% of the number is 8 and 100% of the number is 800, hence (A). 7. (Also J16) If A = 1, then A × B + C × D + E = B + E + C × D. On the other hand, if we swap A and E, we get E × B + C × D + A = E × B + 1 + C × D, which is larger, since both B and E are 2 or more. So the largest possible value can’t have A = 1. Similarly, the largest possible value can’t have any of B, C, or D equal to 1. Thus E = 1. Then we only need to consider the following cases. • 2 × 3 + 4 × 5 + 1 = 27 • 2 × 4 + 3 × 5 + 1 = 24 • 2 × 5 + 3 × 4 + 1 = 23 Therefore, the largest possible value for the expression is 27, hence (B). 2016 AMC – Intermediate Solutions