2018 澳洲 AMC E-Senior 真题 答案 详解

中英双语真题

1-10 题，每题 3 分
Questions 1 to 10, 3 marks each

1. 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°

2. 有一场竞走比赛全长 250 km。如果有位选手打算用 8 天走完全程，请问他每天必须大约走多远？
   The Great North Walk is a 250 km long trail from Sydney to Newcastle. If you want to complete it in 8 days, approximately how far do you need to walk each day?
   (A) 15 km (B) 20 km (C) 30 km (D) 40 km (E) 80 km

3. 一个数的一半是 32。请问这个数的两倍是多少？
   Half of a number is 32. What is twice the number?
   (A) 16 (B) 32 (C) 64 (D) 128 (E) 256

4. 请问这个正六边形的几分之几被涂上阴影？
   What fraction of this regular hexagon is shaded?
   (A) ( \frac{1}{2} ) (B) ( \frac{2}{3} ) (C) ( \frac{3}{4} ) (D) ( \frac{3}{5} ) (E) ( \frac{4}{5} )

5. 算式 9 × 1.2345 - 9 × 0.1234 之值等于
   The value of 9 × 1.2345 - 9 × 0.1234 is
   (A) 9.9999 (B) 9 (C) 9.0909 (D) 10.909 (E) 11.111

6. 请问算式 ( 2^0 - 1^8 ) 之值是什么？
   What is ( 2^0 - 1^8 )?
   (A) 0 (B) 1 (C) 2 (D) 3 (E) 10

7. 一个数的 1000% 等于 100，请问这个数是什么？
   1000% of a number is 100. What is the number?
   (A) 0.1 (B) 1 (C) 10 (D) 100 (E) 1000

英文真题

Senior Division Questions 1 to 10, 3 marks each 1. In the diagram, PQRS is a square. What is the size of ∠XPY? (A) 25° (B) 30° (C) 35° (D) 40° (E) 45° 2. The Great North Walk is a 250 km long trail from Sydney to Newcastle. If you want to complete it in 8 days, approximately how far do you need to walk each day? (A) 15km (B) 20km (C) 30km (D) 40km (E) 80km 3. Half of a number is 32. What is twice the number? (A) 16 (B) 32 (C) 64 (D) 128 (E) 256 4. What fraction of this regular hexagon is shaded? (A) ( \frac{1}{2} ) (B) ( \frac{2}{3} ) (C) ( \frac{3}{4} ) (D) ( \frac{3}{5} ) (E) ( \frac{4}{5} ) 5. The value of (9 \times 1.2345 - 9 \times 0.1234) is (A) 9.9999 (B) 9 (C) 9.0909 (D) 10.909 (E) 11.1111 6. What is (2^0 - 1^8)? (A) 0 (B) 1 (C) 2 (D) 3 (E) 10

真题文字详解(英文)

Solutions – Senior Division
1. (Also I4) The three angles at P add to 90°, so ∠XPY = 90° - 50° = 40°, hence (D).
2. Since 8 × 30 = 240, slightly more than 30 km per day is required, hence (C).
3. The number is 64, so twice the number is 128, hence (D).
4. (Also UP18, J14, I10) There are many subdivisions of the hexagon into equal areas that show that the shaded area is (\frac{2}{3}) of the total:
[ \begin{array}{c|c} \text{Subdivision} & \text{Shaded Area Fraction}\ \hline \text{First} & \frac{2}{3}\ \text{Second} & \frac{4}{6}\ \text{Third} & \frac{4}{6}\ \text{Fourth} & \frac{8}{12}\ \end{array} ]
hence (B).
5. (Also I9) Using the distributive law,
(9 \times 1.2345 - 9 \times 0.1234 = 9 \times (1.2345 - 0.1234) = 9 \times 1.1111 = 9.9999)
hence (A).
6. (2^0 = 1) and (1^8 = 1) so that (2^0 - 1^8 = 0), hence (A).
7. (Also J11) 1000% means '10 times', since 1000% = 10 × 100%. So 10 times the number is 100, and the number is 10, hence (C).
8. (Also J13, I11) To feed 4 dogs for 1 day costs $60 ÷ 3 = $20, and then to feed 1 dog for 1 day costs $20 ÷ 4 = $5. To feed 7 dogs for 7 days will cost $5 × 7 × 7 = $245, hence (C).

2018 AMC
Senior Solutions
69