2018 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 (\frac{2018 - 18}{1000}) 之值等于 The value of (\frac{2018 - 18}{1000}) is
(A) 0.02 (B) 0.1 (C) 1 (D) 2 (E) 2000

1. 请问这个普遍使用的仪表所指示的值是什么？ What value is indicated on this charisma-meter?
   (A) 36.65 (B) 37.65 (C) 38.65 (D) 37.15 (E) 37.3

2. 请问4与5的积及和之差是什么？ What is the difference between the sum and the product of 4 and 5?
   (A) 1 (B) 8 (C) 9 (D) 11 (E) 20

3. 在右图中，PQRS 是一个正方形。请问 ∠XPY 的大小是什么？ In the diagram, PQRS is a square. What is the size of ∠XPY?
   (A) 25° (B) 30° (C) 35° (D) 40° (E) 45°

4. 请问下列哪一项内的算式之值不是一个整数？ Which of the following is not a whole number?
   (A) (350 \div 2) (B) (350 \div 7) (C) (350 \div 5) (D) (350 \div 25) (E) (350 \div 20)

5. NORA、ANNE、WARREN 与 ANDREW 四人购买塑料字母以便在生日蛋糕上拼出他们的名字。他们的生日都在不同的日期，所以他们打算重复使用一些字母在不同的蛋糕上。请问他们至少共需要多少个塑料字母牌？ Nora, Anne, Warren and Andrew bought plastic capital letters to spell each of their names on their birthday cakes. Their birthdays are on different dates, so they planned to reuse letters on different cakes. What is the smallest number of letters they needed?
   (A) 8 (B) 9 (C) 10 (D) 11 (E) 12

英文真题

Intermediate Division
Questions 1 to 10, 3 marks each

1. The value of (\frac{2018 - 18}{1000}) is
   (A) 0.02 (B) 0.1 (C) 1 (D) 2 (E) 2000

2. What value is indicated on this charisma-meter?
   (A) 36.65 (B) 37.65 (C) 38.65 (D) 37.15 (E) 37.3

3. What is the difference between the sum and the product of 4 and 5?
   (A) 1 (B) 8 (C) 9 (D) 11 (E) 20

4. In the diagram, PQRS is a square. What is the size of ∠XPY?
   (A) 25° (B) 30° (C) 35° (D) 40° (E) 45°

5. Which of the following is not a whole number?
   (A) (350 \div 2) (B) (350 \div 7) (C) (350 \div 5) (D) (350 \div 25) (E) (350 \div 20)

真题文字详解(英文)

Solutions – Intermediate Division
1. (\frac{2018 - 18}{1000} = \frac{2000}{1000} = 2), hence (D).
2. (Also J6) The major markings are 36, 37 and 38, so the minor markings are 0.2 units apart. Then the arrow is 0.3 to the right of 37, so it is on 37.3, hence (E).
3. The sum is (4 + 5 = 9) and the product is (4 \times 5 = 20). Their difference is (20 - 9 = 11), hence (D).
4. (Also S1) The three angles at P add to 90°, so ∠XPY = 90° − 50° = 40°, hence (D).
5. (350 = 7 \times 50) and 50 is a multiple of 2, 5 and 25, so 350 ÷ 2, 350 ÷ 7, 350 ÷ 5 and 350 ÷ 25 are all whole numbers. However, (\frac{350}{20} = \frac{35}{2} = 17\frac{1}{2}) is not a whole number, hence (E).
6. (Also J12) Alternative 1
Tabulate the letters needed.
| Letter | A | D | E | N | O | R | W | |--------|---|---|---|---|---|---|---| | Nora | 1 | - | - | 1 | 1 | 1 | - | | Anne | 1 | - | 1 | 2 | - | - | - | | Warren | 1 | - | 1 | 1 | - | 2 | 1 | | Andrew | 1 | 1 | 1 | 1 | - | 1 | 1 | | Needed | 1 | 1 | 1 | 2 | 1 | 2 | 1 |

Then we need 9 letters to cover every name, hence (B).

Alternative 2
ANDREW requires letters ADENRW (in alphabetical order). For WARREN, an additional R is needed: ADENRRW. For ANNE, an additional N is needed: ADENNRRW. For NORAA, an O is needed: ADENNORRW. In all, 9 letters are needed, hence (B).